Research ArticleSemisupervised SVM Based on CuckooSearch Algorithm and Its Application

Ziping He Kewen Xia Wenjia Niu Nelofar Aslam and Jingzhong Hou

School of Electronics and Information Engineering Hebei University of Technology Tianjin 300401 China

Correspondence should be addressed to Kewen Xia kwxiahebuteducn

Received 12 June 2018 Revised 15 July 2018 Accepted 14 August 2018 Published 13 September 2018

Academic Editor Francesco Riganti-Fulginei

Copyright copy 2018 Ziping He et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Semisupervised support vectormachine (S3VM) algorithmmainly depends on the predicted accuracy of unlabeled samples if lotsof misclassified unlabeled samples are added to the training will make the training model performance degrade Thus the cuckoosearch algorithm (CS) is used to optimize the S3VM which also enhances the model performance of S3VM Considering that thecuckoo search algorithm is limited to the local optimum problem a new cuckoo search algorithm based on chaotic catfish effectoptimization is proposed First use the chaoticmechanismwith high randomness to initialize the nest for range expansion Secondchaotic catfish nest is introduced into the effective competition coordination mechanism after falling into the local optimum sothat the candidatersquos nest can jump out of the local optimal solution and accelerate the convergence ability In the experiment resultsshow that the improved cuckoo search algorithm is effective and better than the particle swarm optimization (PSO) algorithm andthe cuckoo search algorithm on the benchmark functions In the end the improved cuckoo search algorithm is used to optimizesemisupervised SVM which is applied into oil layer recognition Results show that this optimization model is superior to thesemisupervised SVM in terms of recognition rate and time

1 Introduction

Semisupervised learning [1] studies how to improve learningperformance by using labeled and unlabeled samples simulta-neously It has become a research focus and hotspot in patternrecognition and machine learning In such a mixed datalearning process the sample distribution information of theunlabeled dataset is transferred to the final learning modelso that the trained learning model has better performanceLiterature [2] proposes a novel graph for semisuperviseddiscriminant analysis which is called combined low-rank andk-nearest neighbor (LRKNN) graph and map the data to theLR feature space and then the KNN is adopted to satisfy thealgorithmic requirements of Semisupervised DiscriminantAnalysis (SDA) Semisupervised support vector machine isfirst proposed by Professor V Vapnik [3] when the labeledsamples are not enough and it is difficult to achieve satisfac-tory performance support vectormachine (SVM) can use thetransductive learning to improve the performance It can beregarded as the generalization of the SVM in the unlabeledsamples S3VM has received extensive attention in recent

years Qing Wu et al [4] described a smooth piecewise func-tion and research smooth piecewise semisupervised SVMand used a converging linear PSO to train semisupervisedSVM to get better classification accuracy Luo et al [5]introduced semisupervised learning for the least squaressupport vector machine (LSSVM) algorithm to improve theaccuracy of model predictions and is used to predict thedistribution of porosity and sandstone in the Jingzhou studyarea Literature [6] puts forward a method with the name ofEnsemble S3VM which deals with the unknown distributionby ensemble learning and applies the algorithm to groundcover classification for polarimetric synthetic aperture radarimages

Cuckoo search [7] algorithm is a new nature-inspiredmetaheuristic based on the obligate brood parasitic behaviorof cuckoo species [8] and the Levy flight search mechanismto effectively solve the optimization problem [9] In orderto further optimize the CS algorithm many experts andscholars have studied itWhen Srivastava et al [10] investigatelocal search in Levy flights they enter tabu search idea toavoid falling into local optimumwhich is successfully applied

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 8243764 13 pageshttpsdoiorg10115520188243764

2 Mathematical Problems in Engineering

to solve the problem of automatic generation of softwaretest data Yang and Deb [11] proposed a multitarget cuckoosearch which was applied to engineering optimization andachieved good results Zhang et al [12] prescribed a modifiedadaptive cuckoo search (MACS) to improve the performanceof CS Wang et al [13] used an evaluation strategy basedon a dimension-by-dimension update for the progress ofthe iteration of the improved algorithm and proposed anenhanced CS algorithm In literature [14] a new local-enhanced cuckoo search algorithm is designed aiming to dealwith some multimodal numerical problems Literature [15]considers utilizing multiple chaotic maps simultaneously toperform the local search within the neighborhood of theglobal best solution found by the chaotic cuckoo searchalgorithm

The above-improved versions of CS algorithm jumpedout of the local optimal or improve the convergence speed ofthe algorithm In view of the fact that CS algorithm is comingto the end of the iteration population groups tend to convergetoo early and lead to local optimum First we use chaosmapping instead of general randomization to initialize nestposition it makes the initial nest location not only has thedistribution randomness but also strengthens the diversity ofthe birdrsquos nest distribution Second according to the literature[16] they used catfish effect to optimize artificial bee colony(ABC) algorithm in order to obtain a good ability to jumpout of local optimum we applied the catfish effect to CSalgorithm added it to the nest and then get the chaotic catfishnest Consequently it improves the convergence rate of thewhole population and the shortage of the algorithm into alocal optimum Finally the CS algorithm based on the above-improved strategy is used to optimize the S3VM algorithmand apply it to the oil layer recognition and establish anew semisupervised oil layer recognition model expecting abetter recognition of oil layers

2 Cuckoo Search Algorithm andIts Improvement

21 Cuckoo Search Algorithm Principle

211 Cuckoo Breeding Behavior According to the long-termobservations of an entomologist cuckoo has adopted aspecial breeding strategy parasitic brood [8] It lays eggs inthe nests of other birds and allows other birds to hatch Inorder to reduce the possibility of being discovered by hostbirds the cuckoo will choose the host birds that are basicallyalike in eating habits and easy to imitate ovately and colorWhen it flies to a nest it only produces one and removes thehostrsquos egg before spawning or all out of the nest forcing thehost to lay eggs again Once the cuckoorsquos hatchlings hatchit has the habit of bringing the host chicks out of the nestthus enjoying the host birdrsquos tending But when the host birdsfind their nests have foreign eggs they also throw the parasiticeggs or abandon their nests and build a nest in other places

212 Levy Flights Various studies have shown that the flightbehavior of many animals and insects has demonstrated

the typical characteristics of Levy flights [17ndash19] A studyby Reynolds and Frye shows that fruit flies or Drosophilamelanogaster explore their landscape using a series of straightflight paths punctuated by a sudden 90∘ turn leading toa Levy-flight-style intermittent scale-free search patternStudies on human behavior such as the Jursquohoansi hunter-gatherer foraging patterns also show the typical feature ofLevy flights Even light can be related to Levy flights [20] Andwhen the target location is random and sparsely distributedLevy flight is the best search strategy for M independentsearch seekers

Levy flight belongs to one type of random walk andthe walking step satisfies a stable distribution of heavy-tailed In this form of walking short distance explorationand occasional long distance walk alternate Levy flight inintelligent optimization algorithm can expand search scopeincrease population diversity and make it easier to jump outof local optimum

Subsequently such behavior has been applied to opti-mization and optimal search and preliminary results showits promising capability [18]

213 Cuckoo Search The cuckoo search algorithm is basedon the parasitic propagation mechanism of cuckoo birdand Levy flights search principle It is mainly based on thefollowing three ideal rules

(1) Each cuckoo lays one egg at one time and selects a nestrandomly to hatch it

(2) The best nests will be preserved to the next generationin a randomly selected group of nests

(3) The number of nests available is fixed and theprobability that the host bird of a nest will find theexotic birdrsquos egg is 119901119886 119901119886 isin [0 1]

On the basis of the above three ideal rules the routing andlocation updating formula of cuckoorsquos nest is as follows

119909119905+1119894 = 119909119905119894 + 120572 oplus levy (120582) (1)

In the case 120572 is the size of step 120572=1 in general oplus is pointmultiplication and levy(120582) is the search path

The Levy flight essentially provides a random walk whilethe random step length is drawn from a levy distribution asshown in the following formula

Levy sim 120583 = 119905minus120582 1 lt 120582 le 3 (2)

which has an infinite variance with an infinite mean Here thesteps essentially form a random walk process with a power-law step-length distribution with a heavy tail Some of thenew solutions should be generated by Levy walk around thebest solution obtained so far this will speed up the localsearch However a substantial fraction of the new solutionsshould be generated by far-field randomization and whoselocation should be far enough from the current best solutionthis will make sure the system will not be trapped in a localoptimum

To sum up the main steps of the CS algorithm can bedescribed as follows

Mathematical Problems in Engineering 3

Step 1 The objective function is 119891(119883) 119883 = (1199091 119909119889)119879initialization group and generates the initial position of Nbirdrsquos nest 119883119894 (119894 = 1 2 119899) randomly

Step 2 Calculate the objective function value of each nest andrecord the current best solution

Step 3 Keep the location of the best nest in the previousgeneration and update the position of other birdrsquos nestaccording to formula (1)

Step 4 Comparing the existing birdrsquos nest with the previousgeneration if it is better it takes it as the best position atpresent

Step 5 Using a randomnumberR comparewith119901119886 if119877 gt 119901119886then change the nest position randomly and get a new set ofnest position

Step 6 If the end condition is not met return Step 2

Step 7 Output global optimal position

22 The Cuckoo Search Algorithm Based on Chaotic CatfishEffect

221 Initial Chaotic Nest The initial nest location of thebirdrsquos nest is an important link in the CS algorithm It notonly affects the convergence speed of the algorithm but alsorestricts the quality of the final solution of the problemAccording to the randomness regularity and mutual corre-lation of chaotic systems we use chaos mapping to extractand capture information in the solution space to enhancethe diversity of the initial bird nest location In this paperthe logistic chaotic mapping is adopted and its mathematicaliterative equation is as follows

120582119905+1 = 120583 times 120582119905 (1 minus 120582119905) 119905 = 0 1 2 119879 (3)

Among them T is a presupposed maximum number ofchaotic iterations and 120582119905 is a random number distributeduniformly on the interval (0 1) because the initial valuecannot take any of the fixed points otherwise it is a stableorbit and cannot generate chaos so 1205820 notin 0 025 05 075 1120583 is chaos control parameters the system will be in a state ofcomplete chaos when 120583=4

Firstly a set of chaotic variables is produced by using for-mula (3) secondly wemap the location of n d dimensionnest119883119894 to the chaotic interval [119865119898119894119899 119865119898119886119909] by the chaotic sequenceonce according to formula (4) 119865119898119894119899 and 119865119898119886119909 represent thelargest and the smallest boundary of 119865119894 respectively Theaverage accuracy 120572119896minus119888V is the fitness function which is basedon the k-fold cross-validation approach The distribution ofnest is shown in Figure 1

Finally the fitness of each nest was calculated

119891119894119895 = 119891119898119894119899119895 + 120582119894119905 (119891119898119886119909119895 minus 119891119898119894119899119895) (4)

222 Updating the Catfish New Nest The catfish effect isderived from a few catfish placed in the sardine sink by Nor-way merchants to drive and stir the sardine group makingthe sardines more likely to survive In other words the catfishnests can guide nests trapped in a local optimum onto anew region of the search space and thus to potentially betternest solutions In literature [21] the catfish effect is appliedto the particle swarm optimization which improves thealgorithmrsquos ability to solve In literature [16] the catfish effectis fused into the artificial bee colony algorithm to enhancethe probability of obtaining the global optimal solutionLiterature [22] combined with catfish effect and cloudmodelin particle swarm optimization increased particle diversityand improved accuracy and finally is applied to the circuitbreaker effectively improving the design efficiency Literature[23] uses the catfish effect to improve the bat algorithm toattract the population to jump out of the current local optimalsolution so as to maintain population diversity and get betterglobal search ability and high convergence speed

In the CS algorithm if the ldquolimitrdquo times do not updatethe nest position then we can see that the algorithm hasbeen trapped in the local optimal solution which leads tothe algorithm failure which cannot get the globally optimalsolution and only at this local solution stagnation Accordingto literature [16]rsquos idea of chaotic catfish bee this paperproposes a chaotic catfish nest in order to jump out of thelocal optimal solution which is trapped in the local optimalsolution and finally converge to the global optimal solutionThe concrete steps are as follows

Step 1 (sort and mark) The corresponding fitness values ofthe current n birdrsquos nest were arranged in ascending ordermarking the last 10 bird nest as the worst bird nest position

Step 2 (the nest of a chaotic catfish is produced) Set the initialposition vector of the nest of the chaotic catfish 119881119889119898(0) =(V1119898(0) V2119898(0) V119889119898(0))119898 = 1 2 119872 in accordance withthe following formula

V119895119898 (0) = V119898119886119909119898119895 119903 gt 05V119898119894119899119898119895 119903 le 05 (5)

Among them V119898119886119909119898119895 and V119898119894119899119898119895 are the maximum andminimum

value of the j dimension of the m catfish wasp respectivelyr is a random number in the [0 1] interval and 05 is theboundary point to make the distribution of V119895119898 approximateat the two polar values

Step 3 (update the nest of the chaotic catfish) The position ofthe chaotic catfish nest is updated with formula (6) in whichT is a chaotic iterative threshold

119881119889119898 (119905) = 119881 + (119881119898119886119909 minus 119881119898119894119899) times 119881119889119898 (119905) 119881119889119898 isin [119881119898119886119909 119881119898119894119899]

119881119889119898 (119905 + 1) = 120583 times 119881119889119898 (119905) times (1 minus 119881119889119898 (119905)) 119905 = 0 1 119879

(6)

4 Mathematical Problems in Engineering

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(a)minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(b)

Figure 1 Distribution of nest (a) distribution of random nest (b) distribution of chaotic nest

Step 4 (the nest of a chaotic catfish is introduced) The nestwhich ismarked as the worst bird nest position is abandonedand the nest of the same amount of chaotic catfish birdrsquos nestis placed in the original nest of the worst bird nest

Step 5 (update the location of the birdrsquos nest) The fitnessvalue of the chaotic catfish nests was calculated by usingformula (4) and the new nest location and correspondingfitness value were updated to enter the next iteration

Finally the steps of cuckoo search algorithm based onchaotic catfish effect (CCCS) can be shown in Algorithm 1

Among them Count is a column vector of 119873 times 1 If theoptimal solution is updated at 119894119905ℎ iteration then119862119900119906119899119905(119894) = 1otherwise 119862119900119906119899119905(119894) = 0 c is the number of successive 0 inthe vector 119862119900119906119899119905 if 119888 ge 119897119894119898119894119905 the algorithm can be found tobe in the local optimal and the new nest of catfish is addedto replace some inferior nests in order to help the algorithmjump out of the local optimal

23 Simulation Test and Analysis

231 Benchmark Functions In order to verify the effec-tiveness and generalization of the improved algorithm wecompare the improved algorithm with CS algorithm [7] par-ticle swarm optimization Algorithm(PSO) [24] and chaoticgravitation search algorithm (CGSA) that the first method toincorporate chaos into gravitation search algorithm (GSA) inliterature [25] on 8 benchmark functions The 8 benchmarkfunctions and their parameter settings are shown in Table 1

232 Parameter Settings In our experiment the dimensionrsquos(Dim) size for each function was 2 and the correspondingmaximum number of iteration was 1000 We carried out 30independent runs for CS CCCS PSO and CGSA

The parameter settings of CS CCCS PSO and CGSAwere assigned as follows size of populationnest 119904119894119911119890 =20 maximum iteration 119868119905119890119903119886119905119894119900119899119898119886119909 = 1000 119875120572=025 the

largest renewal number of birdrsquos nest limit=5 and the largestiteration number of chaos T=300

233 Experimental Results and Discussion The evolutioncurves of the best fitness value of the standard CS CCCSPSO andCGSAwhen themaximum iteration number is 1000is shown in Figure 2 for each kind of algorithm the programruns 30 times independently

The experiment selected Schaffer Schwefel Sphere andSum of different power four unimodal functions and AckleyRastrigrin Branin andGriewank fourmultimodal functionsFirstly we can see that when testing on unimodal functionsfrom Figure 2 the CCCS algorithm can find the optimalsolution for most benchmark functions in the number ofiterations that are far less than 1000 times For examplewhen using the Sphere function the optimal solution isobtained only in the 750th iteration Secondly the CCCSalgorithm can get the best solution for 1198912 1198913 1198914 1198915 1198916 11989171198918 For example the optimal solution is obtained in the 957stiteration when using the Griewank function however CSPSO and CGSA cannot find the optimal solution within 1000iterations Thirdly when multimodal functions are selectedbecause of the complexity of multimodal functions and theexistence of multiple local minima the CCCS algorithm stillhas a strong ability to find the global optimal solution andthe convergence speed of the CCCS algorithm is better thanthe other three algorithms For instance the CCCS algorithmcan find the optimal solution for all multimodal functionssuch that the optional solution is obtained in 824th iterationwhen using the Ackley function Finally comparing CCCSalgorithm with CS algorithm the CCCS algorithm alwaysconverges quickly and finds the global optimal solution in thesame iteration

Evaluating algorithm performance by statistics of themaximum value minimum value average value and vari-ance the numerical test results are shown in Table 2

It can be seen from the numerical result of Table 2 thatthe CCCS algorithm has a superior search performance to the

Mathematical Problems in Engineering 5

(01) Input Dimension of the nest d Total number of the nest n Maximum number ofiterations timeThe probability of being discovered by the host 119901119886 The maximum numberof updates of the birdrsquos nest limit Maximum chaotic iterations T

(02)Output The best nest119883119894(03) Begin(04) Initial chaotic nest 119899 ℎ119900119904119905 119899119890119904119905119904 119883119894 119894 = 1 2 119899(05) Calculated fitness 119865119894(119894 = 1 2 119899)(06) While (present iterations le time)(07) Generate a new solution 119883119894 by Levy flight(08) If (cgelimit)(09) 119865119894 from small to large in accordance with 119883119894(10) Delete the solution 119883119894 of the end 10(11) Generate m catfish new nest Placed in the tail of119883119894 119898 = 119899 times 10(12) Output the catfish new solution 119883119894(13) End(14) Select candidate solution 119883119895(15) If (119865119894 gt 119865119895)(16) The new solution is used instead of the candidate solution(17) Count(present iterations)=1(18) Else(19) Count(present iterations)=0(20) End(21) Discarding the worst solution according to the probability 119875119886(22) A new solution is used to replace the discarded solution with a preference random walk(23) Keep the best solution(24) End(25) End

Algorithm 1 CCCS

other three algorithms under all the performance index anddifferent functions

3 Improved CS Algorithm OptimizedSemisupervised SVMModel

31 Semisupervised SVM Basic Model Semisupervised SVMcan improve the prediction accuracy of an algorithm basedon SVM with both labeled and unlabeled samples It canbe considered as a perfect realization based on low-densityhypothesis and clustering hypothesis [26] Recently it hasbecome a hotspot in the field of machine learning The mainprinciples are as follows

Given a labeled dataset L

(1199091 1199101) sdot sdot sdot (119909119897 119910119897) 119909119894 isin 119877119898 119910119894 isin minus1 +1 (7)

and unlabeled dataset U

119909lowast1 sdot sdot sdot 119909lowast119896 (8)

find an effective method to predict the label of unlabeledsamples and get its semilabeled samples 119884lowast

119910lowast1 119910lowast119896 (9)

Getting a hybrid set containing labeled and semilabeledsamples

(1199091 1199101) (119909119897 119910119897) (119909lowast1 119910lowast1 ) (119909lowast119896 119910lowast119896 ) (10)

can be separated at the maximum interval and the largerclassification interval means that the classifier has bettergeneralization ability

When the optimal hyperplane

120596 sdot 119909 + 119887 = 0 (11)

separates the mixed data set the classification results canmaximize the interval where 120596 is a vector normal to thehyperplane and 119887 is a constant such that 119887120596 is the distanceof the hyperplane from the origin The above problem can beformalized as the following optimization problem

min

12 1205962 + 119862 119897sum119894=1

120585119894 + 119862lowast 119896sum119895=1

120585lowast119895forall119897119894=1 119910lowast119894 (120596 sdot 119909119894 + 119887) ge 1 minus 120585119894120585119894 ge 0 119894 = 1 2 sdot sdot sdot 119897forall119896119895=1 119910lowast119895 (120596 sdot 119909lowast119895 + 119887) ge 1 minus 120585lowast119895

120585lowast119895 ge 0 119895 = 1 2 sdot sdot sdot 119896

(12)

119862 and 119862lowast are the regularization parameters associated withthe labeled and semilabeled samples respectively 120585119894 and 120585lowast119895are the corresponding slack variables The kernel function isradial basis kernel function (RBF) 119870(119909 119909119894) = exp(minus120574119909 minus1199091198942) and 120574 is kernel parameters

6 Mathematical Problems in Engineering

Table 1 Formula and parameter settings of the eight benchmark functions

Function Name Formula Searching Space Opt Trait

1198911 Schaffer 1198911 (119909 119910) = 05 + sin2(1199092 minus 1199102) minus 05(1 + 0001(1199092 minus 1199102))2 [minus10 10] 0 Unimodal

1198912 Schwefel 222 1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 [minus10 10] 0 Unimodal

1198913 Sphere 1198913 (119909) = 119899sum119894=1

1199092119894 [minus100 100] 0 Unimodal

1198914 Sum of different power 1198914 (119909) = 119873sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816119894+1 [minus3 3] 0 Unimodal

1198915 Ackley 1198915 (119909) = minus20119890minus02radic(1119899)sum119899119894=1 1199092119894 minus 119890(1119899)sum119899119894=1 cos 2120587119909119894 [minus32 32] 0 Multimodal

1198916 Rastrigrin 1198916 (119909) = 119863sum119894=1

(1199092119894 minus 10 cos (2120587119909119894) + 10) [minus512 512] 0 Multimodal

1198917 Branin 1198917 (119909) = (1 minus 2119910 + 120 sin 4120587119910 minus 119909)2 + (119910 minus 12 sin 2120587119909)2 [minus10 10] 0 Multimodal

1198918 Griewank 1198918 (119909) = 119873sum119894=1

11990921198944000 minus 119873prod119894=1

cos( 119909119894radic119894) + 1 [minus600 600] 0 Multimodal

Table 2 Comparison of numerical testing results

Function Algorithm Maximum Minimum Average Variance

1198911CS 00296 36427e-21 84440e-04 13215e-05

CCCS 00218 78064e-33 81488e-04 12582e-05PSO 04786 00100 00158 00017CGSA 05362 00098 00108 30341e-04

1198912CS 06626 0 00029 00010

CCCS 05690 0 00027 73280e-04PSO 266960 106037 106359 05174CGSA 22731 94231e-10 00431 00358

1198913CS 07740 18489e-32 00031 00013

CCCS 06371 0 00031 00011PSO 53003e+03 00101 174638 58025e+04CGSA 13660e+04 30835e-18 306816 28436e+05

1198914CS 06047 0 00034 00012

CCCS 05616 0 00022 62698e-04PSO 33220e+05 00100 9510100 27004e+08CGSA 148439 9 90251 01110

1198915CS 11919 20256e-31 00044 00028

CCCS 09859 0 00036 00019PSO 202544 37769 49084 64985CGSA 207509 34519e-09 02963 16965

1198916CS 11351 0 00048 00031

CCCS 10239 0 00038 00022PSO 54272e+03 15607 248489 75573e+04CGSA 440831 36602 42440 72125

1198917CS 05721 11381e-30 00032 00011

CCCS 05493 0 00027 79073e-04PSO 49874e+04 00298 1430958 55309e+06CGSA 2683960 606185 609033 452938

1198918CS 01298 44998e-30 00021 15972e-04

CCCS 00984 0 00014 71452e-05PSO 22087 00050 00174 00128CGSA 1298682 64933 79713 909936

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

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Mathematical Problems in Engineering 3

Step 1 The objective function is 119891(119883) 119883 = (1199091 119909119889)119879initialization group and generates the initial position of Nbirdrsquos nest 119883119894 (119894 = 1 2 119899) randomly

Step 2 Calculate the objective function value of each nest andrecord the current best solution

Step 3 Keep the location of the best nest in the previousgeneration and update the position of other birdrsquos nestaccording to formula (1)

Step 4 Comparing the existing birdrsquos nest with the previousgeneration if it is better it takes it as the best position atpresent

Step 5 Using a randomnumberR comparewith119901119886 if119877 gt 119901119886then change the nest position randomly and get a new set ofnest position

Step 6 If the end condition is not met return Step 2

Step 7 Output global optimal position

22 The Cuckoo Search Algorithm Based on Chaotic CatfishEffect

221 Initial Chaotic Nest The initial nest location of thebirdrsquos nest is an important link in the CS algorithm It notonly affects the convergence speed of the algorithm but alsorestricts the quality of the final solution of the problemAccording to the randomness regularity and mutual corre-lation of chaotic systems we use chaos mapping to extractand capture information in the solution space to enhancethe diversity of the initial bird nest location In this paperthe logistic chaotic mapping is adopted and its mathematicaliterative equation is as follows

120582119905+1 = 120583 times 120582119905 (1 minus 120582119905) 119905 = 0 1 2 119879 (3)

Among them T is a presupposed maximum number ofchaotic iterations and 120582119905 is a random number distributeduniformly on the interval (0 1) because the initial valuecannot take any of the fixed points otherwise it is a stableorbit and cannot generate chaos so 1205820 notin 0 025 05 075 1120583 is chaos control parameters the system will be in a state ofcomplete chaos when 120583=4

Firstly a set of chaotic variables is produced by using for-mula (3) secondly wemap the location of n d dimensionnest119883119894 to the chaotic interval [119865119898119894119899 119865119898119886119909] by the chaotic sequenceonce according to formula (4) 119865119898119894119899 and 119865119898119886119909 represent thelargest and the smallest boundary of 119865119894 respectively Theaverage accuracy 120572119896minus119888V is the fitness function which is basedon the k-fold cross-validation approach The distribution ofnest is shown in Figure 1

Finally the fitness of each nest was calculated

119891119894119895 = 119891119898119894119899119895 + 120582119894119905 (119891119898119886119909119895 minus 119891119898119894119899119895) (4)

222 Updating the Catfish New Nest The catfish effect isderived from a few catfish placed in the sardine sink by Nor-way merchants to drive and stir the sardine group makingthe sardines more likely to survive In other words the catfishnests can guide nests trapped in a local optimum onto anew region of the search space and thus to potentially betternest solutions In literature [21] the catfish effect is appliedto the particle swarm optimization which improves thealgorithmrsquos ability to solve In literature [16] the catfish effectis fused into the artificial bee colony algorithm to enhancethe probability of obtaining the global optimal solutionLiterature [22] combined with catfish effect and cloudmodelin particle swarm optimization increased particle diversityand improved accuracy and finally is applied to the circuitbreaker effectively improving the design efficiency Literature[23] uses the catfish effect to improve the bat algorithm toattract the population to jump out of the current local optimalsolution so as to maintain population diversity and get betterglobal search ability and high convergence speed

In the CS algorithm if the ldquolimitrdquo times do not updatethe nest position then we can see that the algorithm hasbeen trapped in the local optimal solution which leads tothe algorithm failure which cannot get the globally optimalsolution and only at this local solution stagnation Accordingto literature [16]rsquos idea of chaotic catfish bee this paperproposes a chaotic catfish nest in order to jump out of thelocal optimal solution which is trapped in the local optimalsolution and finally converge to the global optimal solutionThe concrete steps are as follows

Step 1 (sort and mark) The corresponding fitness values ofthe current n birdrsquos nest were arranged in ascending ordermarking the last 10 bird nest as the worst bird nest position

Step 2 (the nest of a chaotic catfish is produced) Set the initialposition vector of the nest of the chaotic catfish 119881119889119898(0) =(V1119898(0) V2119898(0) V119889119898(0))119898 = 1 2 119872 in accordance withthe following formula

V119895119898 (0) = V119898119886119909119898119895 119903 gt 05V119898119894119899119898119895 119903 le 05 (5)

Among them V119898119886119909119898119895 and V119898119894119899119898119895 are the maximum andminimum

value of the j dimension of the m catfish wasp respectivelyr is a random number in the [0 1] interval and 05 is theboundary point to make the distribution of V119895119898 approximateat the two polar values

Step 3 (update the nest of the chaotic catfish) The position ofthe chaotic catfish nest is updated with formula (6) in whichT is a chaotic iterative threshold

119881119889119898 (119905) = 119881 + (119881119898119886119909 minus 119881119898119894119899) times 119881119889119898 (119905) 119881119889119898 isin [119881119898119886119909 119881119898119894119899]

119881119889119898 (119905 + 1) = 120583 times 119881119889119898 (119905) times (1 minus 119881119889119898 (119905)) 119905 = 0 1 119879

(6)

4 Mathematical Problems in Engineering

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(a)minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(b)

Figure 1 Distribution of nest (a) distribution of random nest (b) distribution of chaotic nest

Step 4 (the nest of a chaotic catfish is introduced) The nestwhich ismarked as the worst bird nest position is abandonedand the nest of the same amount of chaotic catfish birdrsquos nestis placed in the original nest of the worst bird nest

Step 5 (update the location of the birdrsquos nest) The fitnessvalue of the chaotic catfish nests was calculated by usingformula (4) and the new nest location and correspondingfitness value were updated to enter the next iteration

Finally the steps of cuckoo search algorithm based onchaotic catfish effect (CCCS) can be shown in Algorithm 1

Among them Count is a column vector of 119873 times 1 If theoptimal solution is updated at 119894119905ℎ iteration then119862119900119906119899119905(119894) = 1otherwise 119862119900119906119899119905(119894) = 0 c is the number of successive 0 inthe vector 119862119900119906119899119905 if 119888 ge 119897119894119898119894119905 the algorithm can be found tobe in the local optimal and the new nest of catfish is addedto replace some inferior nests in order to help the algorithmjump out of the local optimal

23 Simulation Test and Analysis

231 Benchmark Functions In order to verify the effec-tiveness and generalization of the improved algorithm wecompare the improved algorithm with CS algorithm [7] par-ticle swarm optimization Algorithm(PSO) [24] and chaoticgravitation search algorithm (CGSA) that the first method toincorporate chaos into gravitation search algorithm (GSA) inliterature [25] on 8 benchmark functions The 8 benchmarkfunctions and their parameter settings are shown in Table 1

232 Parameter Settings In our experiment the dimensionrsquos(Dim) size for each function was 2 and the correspondingmaximum number of iteration was 1000 We carried out 30independent runs for CS CCCS PSO and CGSA

The parameter settings of CS CCCS PSO and CGSAwere assigned as follows size of populationnest 119904119894119911119890 =20 maximum iteration 119868119905119890119903119886119905119894119900119899119898119886119909 = 1000 119875120572=025 the

largest renewal number of birdrsquos nest limit=5 and the largestiteration number of chaos T=300

233 Experimental Results and Discussion The evolutioncurves of the best fitness value of the standard CS CCCSPSO andCGSAwhen themaximum iteration number is 1000is shown in Figure 2 for each kind of algorithm the programruns 30 times independently

The experiment selected Schaffer Schwefel Sphere andSum of different power four unimodal functions and AckleyRastrigrin Branin andGriewank fourmultimodal functionsFirstly we can see that when testing on unimodal functionsfrom Figure 2 the CCCS algorithm can find the optimalsolution for most benchmark functions in the number ofiterations that are far less than 1000 times For examplewhen using the Sphere function the optimal solution isobtained only in the 750th iteration Secondly the CCCSalgorithm can get the best solution for 1198912 1198913 1198914 1198915 1198916 11989171198918 For example the optimal solution is obtained in the 957stiteration when using the Griewank function however CSPSO and CGSA cannot find the optimal solution within 1000iterations Thirdly when multimodal functions are selectedbecause of the complexity of multimodal functions and theexistence of multiple local minima the CCCS algorithm stillhas a strong ability to find the global optimal solution andthe convergence speed of the CCCS algorithm is better thanthe other three algorithms For instance the CCCS algorithmcan find the optimal solution for all multimodal functionssuch that the optional solution is obtained in 824th iterationwhen using the Ackley function Finally comparing CCCSalgorithm with CS algorithm the CCCS algorithm alwaysconverges quickly and finds the global optimal solution in thesame iteration

Evaluating algorithm performance by statistics of themaximum value minimum value average value and vari-ance the numerical test results are shown in Table 2

It can be seen from the numerical result of Table 2 thatthe CCCS algorithm has a superior search performance to the

Mathematical Problems in Engineering 5

(01) Input Dimension of the nest d Total number of the nest n Maximum number ofiterations timeThe probability of being discovered by the host 119901119886 The maximum numberof updates of the birdrsquos nest limit Maximum chaotic iterations T

(02)Output The best nest119883119894(03) Begin(04) Initial chaotic nest 119899 ℎ119900119904119905 119899119890119904119905119904 119883119894 119894 = 1 2 119899(05) Calculated fitness 119865119894(119894 = 1 2 119899)(06) While (present iterations le time)(07) Generate a new solution 119883119894 by Levy flight(08) If (cgelimit)(09) 119865119894 from small to large in accordance with 119883119894(10) Delete the solution 119883119894 of the end 10(11) Generate m catfish new nest Placed in the tail of119883119894 119898 = 119899 times 10(12) Output the catfish new solution 119883119894(13) End(14) Select candidate solution 119883119895(15) If (119865119894 gt 119865119895)(16) The new solution is used instead of the candidate solution(17) Count(present iterations)=1(18) Else(19) Count(present iterations)=0(20) End(21) Discarding the worst solution according to the probability 119875119886(22) A new solution is used to replace the discarded solution with a preference random walk(23) Keep the best solution(24) End(25) End

Algorithm 1 CCCS

other three algorithms under all the performance index anddifferent functions

3 Improved CS Algorithm OptimizedSemisupervised SVMModel

31 Semisupervised SVM Basic Model Semisupervised SVMcan improve the prediction accuracy of an algorithm basedon SVM with both labeled and unlabeled samples It canbe considered as a perfect realization based on low-densityhypothesis and clustering hypothesis [26] Recently it hasbecome a hotspot in the field of machine learning The mainprinciples are as follows

Given a labeled dataset L

(1199091 1199101) sdot sdot sdot (119909119897 119910119897) 119909119894 isin 119877119898 119910119894 isin minus1 +1 (7)

and unlabeled dataset U

119909lowast1 sdot sdot sdot 119909lowast119896 (8)

find an effective method to predict the label of unlabeledsamples and get its semilabeled samples 119884lowast

119910lowast1 119910lowast119896 (9)

Getting a hybrid set containing labeled and semilabeledsamples

(1199091 1199101) (119909119897 119910119897) (119909lowast1 119910lowast1 ) (119909lowast119896 119910lowast119896 ) (10)

can be separated at the maximum interval and the largerclassification interval means that the classifier has bettergeneralization ability

When the optimal hyperplane

120596 sdot 119909 + 119887 = 0 (11)

separates the mixed data set the classification results canmaximize the interval where 120596 is a vector normal to thehyperplane and 119887 is a constant such that 119887120596 is the distanceof the hyperplane from the origin The above problem can beformalized as the following optimization problem

min

12 1205962 + 119862 119897sum119894=1

120585119894 + 119862lowast 119896sum119895=1

120585lowast119895forall119897119894=1 119910lowast119894 (120596 sdot 119909119894 + 119887) ge 1 minus 120585119894120585119894 ge 0 119894 = 1 2 sdot sdot sdot 119897forall119896119895=1 119910lowast119895 (120596 sdot 119909lowast119895 + 119887) ge 1 minus 120585lowast119895

120585lowast119895 ge 0 119895 = 1 2 sdot sdot sdot 119896

(12)

119862 and 119862lowast are the regularization parameters associated withthe labeled and semilabeled samples respectively 120585119894 and 120585lowast119895are the corresponding slack variables The kernel function isradial basis kernel function (RBF) 119870(119909 119909119894) = exp(minus120574119909 minus1199091198942) and 120574 is kernel parameters

6 Mathematical Problems in Engineering

Table 1 Formula and parameter settings of the eight benchmark functions

Function Name Formula Searching Space Opt Trait

1198911 Schaffer 1198911 (119909 119910) = 05 + sin2(1199092 minus 1199102) minus 05(1 + 0001(1199092 minus 1199102))2 [minus10 10] 0 Unimodal

1198912 Schwefel 222 1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 [minus10 10] 0 Unimodal

1198913 Sphere 1198913 (119909) = 119899sum119894=1

1199092119894 [minus100 100] 0 Unimodal

1198914 Sum of different power 1198914 (119909) = 119873sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816119894+1 [minus3 3] 0 Unimodal

1198915 Ackley 1198915 (119909) = minus20119890minus02radic(1119899)sum119899119894=1 1199092119894 minus 119890(1119899)sum119899119894=1 cos 2120587119909119894 [minus32 32] 0 Multimodal

1198916 Rastrigrin 1198916 (119909) = 119863sum119894=1

(1199092119894 minus 10 cos (2120587119909119894) + 10) [minus512 512] 0 Multimodal

1198917 Branin 1198917 (119909) = (1 minus 2119910 + 120 sin 4120587119910 minus 119909)2 + (119910 minus 12 sin 2120587119909)2 [minus10 10] 0 Multimodal

1198918 Griewank 1198918 (119909) = 119873sum119894=1

11990921198944000 minus 119873prod119894=1

cos( 119909119894radic119894) + 1 [minus600 600] 0 Multimodal

Table 2 Comparison of numerical testing results

Function Algorithm Maximum Minimum Average Variance

1198911CS 00296 36427e-21 84440e-04 13215e-05

CCCS 00218 78064e-33 81488e-04 12582e-05PSO 04786 00100 00158 00017CGSA 05362 00098 00108 30341e-04

1198912CS 06626 0 00029 00010

CCCS 05690 0 00027 73280e-04PSO 266960 106037 106359 05174CGSA 22731 94231e-10 00431 00358

1198913CS 07740 18489e-32 00031 00013

CCCS 06371 0 00031 00011PSO 53003e+03 00101 174638 58025e+04CGSA 13660e+04 30835e-18 306816 28436e+05

1198914CS 06047 0 00034 00012

CCCS 05616 0 00022 62698e-04PSO 33220e+05 00100 9510100 27004e+08CGSA 148439 9 90251 01110

1198915CS 11919 20256e-31 00044 00028

CCCS 09859 0 00036 00019PSO 202544 37769 49084 64985CGSA 207509 34519e-09 02963 16965

1198916CS 11351 0 00048 00031

CCCS 10239 0 00038 00022PSO 54272e+03 15607 248489 75573e+04CGSA 440831 36602 42440 72125

1198917CS 05721 11381e-30 00032 00011

CCCS 05493 0 00027 79073e-04PSO 49874e+04 00298 1430958 55309e+06CGSA 2683960 606185 609033 452938

1198918CS 01298 44998e-30 00021 15972e-04

CCCS 00984 0 00014 71452e-05PSO 22087 00050 00174 00128CGSA 1298682 64933 79713 909936

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

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4 Mathematical Problems in Engineering

minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(a)minus5 minus4 minus3 minus2 minus1 0 1 2 3 4 5

minus5

minus4

minus3

minus2

minus1

0

1

2

3

4

5

(b)

Figure 1 Distribution of nest (a) distribution of random nest (b) distribution of chaotic nest

Step 4 (the nest of a chaotic catfish is introduced) The nestwhich ismarked as the worst bird nest position is abandonedand the nest of the same amount of chaotic catfish birdrsquos nestis placed in the original nest of the worst bird nest

Step 5 (update the location of the birdrsquos nest) The fitnessvalue of the chaotic catfish nests was calculated by usingformula (4) and the new nest location and correspondingfitness value were updated to enter the next iteration

Finally the steps of cuckoo search algorithm based onchaotic catfish effect (CCCS) can be shown in Algorithm 1

Among them Count is a column vector of 119873 times 1 If theoptimal solution is updated at 119894119905ℎ iteration then119862119900119906119899119905(119894) = 1otherwise 119862119900119906119899119905(119894) = 0 c is the number of successive 0 inthe vector 119862119900119906119899119905 if 119888 ge 119897119894119898119894119905 the algorithm can be found tobe in the local optimal and the new nest of catfish is addedto replace some inferior nests in order to help the algorithmjump out of the local optimal

23 Simulation Test and Analysis

231 Benchmark Functions In order to verify the effec-tiveness and generalization of the improved algorithm wecompare the improved algorithm with CS algorithm [7] par-ticle swarm optimization Algorithm(PSO) [24] and chaoticgravitation search algorithm (CGSA) that the first method toincorporate chaos into gravitation search algorithm (GSA) inliterature [25] on 8 benchmark functions The 8 benchmarkfunctions and their parameter settings are shown in Table 1

232 Parameter Settings In our experiment the dimensionrsquos(Dim) size for each function was 2 and the correspondingmaximum number of iteration was 1000 We carried out 30independent runs for CS CCCS PSO and CGSA

The parameter settings of CS CCCS PSO and CGSAwere assigned as follows size of populationnest 119904119894119911119890 =20 maximum iteration 119868119905119890119903119886119905119894119900119899119898119886119909 = 1000 119875120572=025 the

largest renewal number of birdrsquos nest limit=5 and the largestiteration number of chaos T=300

233 Experimental Results and Discussion The evolutioncurves of the best fitness value of the standard CS CCCSPSO andCGSAwhen themaximum iteration number is 1000is shown in Figure 2 for each kind of algorithm the programruns 30 times independently

The experiment selected Schaffer Schwefel Sphere andSum of different power four unimodal functions and AckleyRastrigrin Branin andGriewank fourmultimodal functionsFirstly we can see that when testing on unimodal functionsfrom Figure 2 the CCCS algorithm can find the optimalsolution for most benchmark functions in the number ofiterations that are far less than 1000 times For examplewhen using the Sphere function the optimal solution isobtained only in the 750th iteration Secondly the CCCSalgorithm can get the best solution for 1198912 1198913 1198914 1198915 1198916 11989171198918 For example the optimal solution is obtained in the 957stiteration when using the Griewank function however CSPSO and CGSA cannot find the optimal solution within 1000iterations Thirdly when multimodal functions are selectedbecause of the complexity of multimodal functions and theexistence of multiple local minima the CCCS algorithm stillhas a strong ability to find the global optimal solution andthe convergence speed of the CCCS algorithm is better thanthe other three algorithms For instance the CCCS algorithmcan find the optimal solution for all multimodal functionssuch that the optional solution is obtained in 824th iterationwhen using the Ackley function Finally comparing CCCSalgorithm with CS algorithm the CCCS algorithm alwaysconverges quickly and finds the global optimal solution in thesame iteration

Evaluating algorithm performance by statistics of themaximum value minimum value average value and vari-ance the numerical test results are shown in Table 2

It can be seen from the numerical result of Table 2 thatthe CCCS algorithm has a superior search performance to the

Mathematical Problems in Engineering 5

(01) Input Dimension of the nest d Total number of the nest n Maximum number ofiterations timeThe probability of being discovered by the host 119901119886 The maximum numberof updates of the birdrsquos nest limit Maximum chaotic iterations T

(02)Output The best nest119883119894(03) Begin(04) Initial chaotic nest 119899 ℎ119900119904119905 119899119890119904119905119904 119883119894 119894 = 1 2 119899(05) Calculated fitness 119865119894(119894 = 1 2 119899)(06) While (present iterations le time)(07) Generate a new solution 119883119894 by Levy flight(08) If (cgelimit)(09) 119865119894 from small to large in accordance with 119883119894(10) Delete the solution 119883119894 of the end 10(11) Generate m catfish new nest Placed in the tail of119883119894 119898 = 119899 times 10(12) Output the catfish new solution 119883119894(13) End(14) Select candidate solution 119883119895(15) If (119865119894 gt 119865119895)(16) The new solution is used instead of the candidate solution(17) Count(present iterations)=1(18) Else(19) Count(present iterations)=0(20) End(21) Discarding the worst solution according to the probability 119875119886(22) A new solution is used to replace the discarded solution with a preference random walk(23) Keep the best solution(24) End(25) End

Algorithm 1 CCCS

other three algorithms under all the performance index anddifferent functions

3 Improved CS Algorithm OptimizedSemisupervised SVMModel

31 Semisupervised SVM Basic Model Semisupervised SVMcan improve the prediction accuracy of an algorithm basedon SVM with both labeled and unlabeled samples It canbe considered as a perfect realization based on low-densityhypothesis and clustering hypothesis [26] Recently it hasbecome a hotspot in the field of machine learning The mainprinciples are as follows

Given a labeled dataset L

(1199091 1199101) sdot sdot sdot (119909119897 119910119897) 119909119894 isin 119877119898 119910119894 isin minus1 +1 (7)

and unlabeled dataset U

119909lowast1 sdot sdot sdot 119909lowast119896 (8)

find an effective method to predict the label of unlabeledsamples and get its semilabeled samples 119884lowast

119910lowast1 119910lowast119896 (9)

Getting a hybrid set containing labeled and semilabeledsamples

(1199091 1199101) (119909119897 119910119897) (119909lowast1 119910lowast1 ) (119909lowast119896 119910lowast119896 ) (10)

can be separated at the maximum interval and the largerclassification interval means that the classifier has bettergeneralization ability

When the optimal hyperplane

120596 sdot 119909 + 119887 = 0 (11)

separates the mixed data set the classification results canmaximize the interval where 120596 is a vector normal to thehyperplane and 119887 is a constant such that 119887120596 is the distanceof the hyperplane from the origin The above problem can beformalized as the following optimization problem

min

12 1205962 + 119862 119897sum119894=1

120585119894 + 119862lowast 119896sum119895=1

120585lowast119895forall119897119894=1 119910lowast119894 (120596 sdot 119909119894 + 119887) ge 1 minus 120585119894120585119894 ge 0 119894 = 1 2 sdot sdot sdot 119897forall119896119895=1 119910lowast119895 (120596 sdot 119909lowast119895 + 119887) ge 1 minus 120585lowast119895

120585lowast119895 ge 0 119895 = 1 2 sdot sdot sdot 119896

(12)

119862 and 119862lowast are the regularization parameters associated withthe labeled and semilabeled samples respectively 120585119894 and 120585lowast119895are the corresponding slack variables The kernel function isradial basis kernel function (RBF) 119870(119909 119909119894) = exp(minus120574119909 minus1199091198942) and 120574 is kernel parameters

6 Mathematical Problems in Engineering

Table 1 Formula and parameter settings of the eight benchmark functions

Function Name Formula Searching Space Opt Trait

1198911 Schaffer 1198911 (119909 119910) = 05 + sin2(1199092 minus 1199102) minus 05(1 + 0001(1199092 minus 1199102))2 [minus10 10] 0 Unimodal

1198912 Schwefel 222 1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 [minus10 10] 0 Unimodal

1198913 Sphere 1198913 (119909) = 119899sum119894=1

1199092119894 [minus100 100] 0 Unimodal

1198914 Sum of different power 1198914 (119909) = 119873sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816119894+1 [minus3 3] 0 Unimodal

1198915 Ackley 1198915 (119909) = minus20119890minus02radic(1119899)sum119899119894=1 1199092119894 minus 119890(1119899)sum119899119894=1 cos 2120587119909119894 [minus32 32] 0 Multimodal

1198916 Rastrigrin 1198916 (119909) = 119863sum119894=1

(1199092119894 minus 10 cos (2120587119909119894) + 10) [minus512 512] 0 Multimodal

1198917 Branin 1198917 (119909) = (1 minus 2119910 + 120 sin 4120587119910 minus 119909)2 + (119910 minus 12 sin 2120587119909)2 [minus10 10] 0 Multimodal

1198918 Griewank 1198918 (119909) = 119873sum119894=1

11990921198944000 minus 119873prod119894=1

cos( 119909119894radic119894) + 1 [minus600 600] 0 Multimodal

Table 2 Comparison of numerical testing results

Function Algorithm Maximum Minimum Average Variance

1198911CS 00296 36427e-21 84440e-04 13215e-05

CCCS 00218 78064e-33 81488e-04 12582e-05PSO 04786 00100 00158 00017CGSA 05362 00098 00108 30341e-04

1198912CS 06626 0 00029 00010

CCCS 05690 0 00027 73280e-04PSO 266960 106037 106359 05174CGSA 22731 94231e-10 00431 00358

1198913CS 07740 18489e-32 00031 00013

CCCS 06371 0 00031 00011PSO 53003e+03 00101 174638 58025e+04CGSA 13660e+04 30835e-18 306816 28436e+05

1198914CS 06047 0 00034 00012

CCCS 05616 0 00022 62698e-04PSO 33220e+05 00100 9510100 27004e+08CGSA 148439 9 90251 01110

1198915CS 11919 20256e-31 00044 00028

CCCS 09859 0 00036 00019PSO 202544 37769 49084 64985CGSA 207509 34519e-09 02963 16965

1198916CS 11351 0 00048 00031

CCCS 10239 0 00038 00022PSO 54272e+03 15607 248489 75573e+04CGSA 440831 36602 42440 72125

1198917CS 05721 11381e-30 00032 00011

CCCS 05493 0 00027 79073e-04PSO 49874e+04 00298 1430958 55309e+06CGSA 2683960 606185 609033 452938

1198918CS 01298 44998e-30 00021 15972e-04

CCCS 00984 0 00014 71452e-05PSO 22087 00050 00174 00128CGSA 1298682 64933 79713 909936

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

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Mathematical Problems in Engineering 5

(01) Input Dimension of the nest d Total number of the nest n Maximum number ofiterations timeThe probability of being discovered by the host 119901119886 The maximum numberof updates of the birdrsquos nest limit Maximum chaotic iterations T

(02)Output The best nest119883119894(03) Begin(04) Initial chaotic nest 119899 ℎ119900119904119905 119899119890119904119905119904 119883119894 119894 = 1 2 119899(05) Calculated fitness 119865119894(119894 = 1 2 119899)(06) While (present iterations le time)(07) Generate a new solution 119883119894 by Levy flight(08) If (cgelimit)(09) 119865119894 from small to large in accordance with 119883119894(10) Delete the solution 119883119894 of the end 10(11) Generate m catfish new nest Placed in the tail of119883119894 119898 = 119899 times 10(12) Output the catfish new solution 119883119894(13) End(14) Select candidate solution 119883119895(15) If (119865119894 gt 119865119895)(16) The new solution is used instead of the candidate solution(17) Count(present iterations)=1(18) Else(19) Count(present iterations)=0(20) End(21) Discarding the worst solution according to the probability 119875119886(22) A new solution is used to replace the discarded solution with a preference random walk(23) Keep the best solution(24) End(25) End

Algorithm 1 CCCS

other three algorithms under all the performance index anddifferent functions

3 Improved CS Algorithm OptimizedSemisupervised SVMModel

31 Semisupervised SVM Basic Model Semisupervised SVMcan improve the prediction accuracy of an algorithm basedon SVM with both labeled and unlabeled samples It canbe considered as a perfect realization based on low-densityhypothesis and clustering hypothesis [26] Recently it hasbecome a hotspot in the field of machine learning The mainprinciples are as follows

Given a labeled dataset L

(1199091 1199101) sdot sdot sdot (119909119897 119910119897) 119909119894 isin 119877119898 119910119894 isin minus1 +1 (7)

and unlabeled dataset U

119909lowast1 sdot sdot sdot 119909lowast119896 (8)

find an effective method to predict the label of unlabeledsamples and get its semilabeled samples 119884lowast

119910lowast1 119910lowast119896 (9)

Getting a hybrid set containing labeled and semilabeledsamples

(1199091 1199101) (119909119897 119910119897) (119909lowast1 119910lowast1 ) (119909lowast119896 119910lowast119896 ) (10)

can be separated at the maximum interval and the largerclassification interval means that the classifier has bettergeneralization ability

When the optimal hyperplane

120596 sdot 119909 + 119887 = 0 (11)

separates the mixed data set the classification results canmaximize the interval where 120596 is a vector normal to thehyperplane and 119887 is a constant such that 119887120596 is the distanceof the hyperplane from the origin The above problem can beformalized as the following optimization problem

min

12 1205962 + 119862 119897sum119894=1

120585119894 + 119862lowast 119896sum119895=1

120585lowast119895forall119897119894=1 119910lowast119894 (120596 sdot 119909119894 + 119887) ge 1 minus 120585119894120585119894 ge 0 119894 = 1 2 sdot sdot sdot 119897forall119896119895=1 119910lowast119895 (120596 sdot 119909lowast119895 + 119887) ge 1 minus 120585lowast119895

120585lowast119895 ge 0 119895 = 1 2 sdot sdot sdot 119896

(12)

119862 and 119862lowast are the regularization parameters associated withthe labeled and semilabeled samples respectively 120585119894 and 120585lowast119895are the corresponding slack variables The kernel function isradial basis kernel function (RBF) 119870(119909 119909119894) = exp(minus120574119909 minus1199091198942) and 120574 is kernel parameters

6 Mathematical Problems in Engineering

Table 1 Formula and parameter settings of the eight benchmark functions

Function Name Formula Searching Space Opt Trait

1198911 Schaffer 1198911 (119909 119910) = 05 + sin2(1199092 minus 1199102) minus 05(1 + 0001(1199092 minus 1199102))2 [minus10 10] 0 Unimodal

1198912 Schwefel 222 1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 [minus10 10] 0 Unimodal

1198913 Sphere 1198913 (119909) = 119899sum119894=1

1199092119894 [minus100 100] 0 Unimodal

1198914 Sum of different power 1198914 (119909) = 119873sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816119894+1 [minus3 3] 0 Unimodal

1198915 Ackley 1198915 (119909) = minus20119890minus02radic(1119899)sum119899119894=1 1199092119894 minus 119890(1119899)sum119899119894=1 cos 2120587119909119894 [minus32 32] 0 Multimodal

1198916 Rastrigrin 1198916 (119909) = 119863sum119894=1

(1199092119894 minus 10 cos (2120587119909119894) + 10) [minus512 512] 0 Multimodal

1198917 Branin 1198917 (119909) = (1 minus 2119910 + 120 sin 4120587119910 minus 119909)2 + (119910 minus 12 sin 2120587119909)2 [minus10 10] 0 Multimodal

1198918 Griewank 1198918 (119909) = 119873sum119894=1

11990921198944000 minus 119873prod119894=1

cos( 119909119894radic119894) + 1 [minus600 600] 0 Multimodal

Table 2 Comparison of numerical testing results

Function Algorithm Maximum Minimum Average Variance

1198911CS 00296 36427e-21 84440e-04 13215e-05

CCCS 00218 78064e-33 81488e-04 12582e-05PSO 04786 00100 00158 00017CGSA 05362 00098 00108 30341e-04

1198912CS 06626 0 00029 00010

CCCS 05690 0 00027 73280e-04PSO 266960 106037 106359 05174CGSA 22731 94231e-10 00431 00358

1198913CS 07740 18489e-32 00031 00013

CCCS 06371 0 00031 00011PSO 53003e+03 00101 174638 58025e+04CGSA 13660e+04 30835e-18 306816 28436e+05

1198914CS 06047 0 00034 00012

CCCS 05616 0 00022 62698e-04PSO 33220e+05 00100 9510100 27004e+08CGSA 148439 9 90251 01110

1198915CS 11919 20256e-31 00044 00028

CCCS 09859 0 00036 00019PSO 202544 37769 49084 64985CGSA 207509 34519e-09 02963 16965

1198916CS 11351 0 00048 00031

CCCS 10239 0 00038 00022PSO 54272e+03 15607 248489 75573e+04CGSA 440831 36602 42440 72125

1198917CS 05721 11381e-30 00032 00011

CCCS 05493 0 00027 79073e-04PSO 49874e+04 00298 1430958 55309e+06CGSA 2683960 606185 609033 452938

1198918CS 01298 44998e-30 00021 15972e-04

CCCS 00984 0 00014 71452e-05PSO 22087 00050 00174 00128CGSA 1298682 64933 79713 909936

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

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Mathematical Problems in Engineering

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Hindawiwwwhindawicom Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

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Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

6 Mathematical Problems in Engineering

Table 1 Formula and parameter settings of the eight benchmark functions

Function Name Formula Searching Space Opt Trait

1198911 Schaffer 1198911 (119909 119910) = 05 + sin2(1199092 minus 1199102) minus 05(1 + 0001(1199092 minus 1199102))2 [minus10 10] 0 Unimodal

1198912 Schwefel 222 1198912 (119909) = 119899sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816 + 119899prod119894=1

10038161003816100381610038161199091198941003816100381610038161003816 [minus10 10] 0 Unimodal

1198913 Sphere 1198913 (119909) = 119899sum119894=1

1199092119894 [minus100 100] 0 Unimodal

1198914 Sum of different power 1198914 (119909) = 119873sum119894=1

10038161003816100381610038161199091198941003816100381610038161003816119894+1 [minus3 3] 0 Unimodal

1198915 Ackley 1198915 (119909) = minus20119890minus02radic(1119899)sum119899119894=1 1199092119894 minus 119890(1119899)sum119899119894=1 cos 2120587119909119894 [minus32 32] 0 Multimodal

1198916 Rastrigrin 1198916 (119909) = 119863sum119894=1

(1199092119894 minus 10 cos (2120587119909119894) + 10) [minus512 512] 0 Multimodal

1198917 Branin 1198917 (119909) = (1 minus 2119910 + 120 sin 4120587119910 minus 119909)2 + (119910 minus 12 sin 2120587119909)2 [minus10 10] 0 Multimodal

1198918 Griewank 1198918 (119909) = 119873sum119894=1

11990921198944000 minus 119873prod119894=1

cos( 119909119894radic119894) + 1 [minus600 600] 0 Multimodal

Table 2 Comparison of numerical testing results

Function Algorithm Maximum Minimum Average Variance

1198911CS 00296 36427e-21 84440e-04 13215e-05

CCCS 00218 78064e-33 81488e-04 12582e-05PSO 04786 00100 00158 00017CGSA 05362 00098 00108 30341e-04

1198912CS 06626 0 00029 00010

CCCS 05690 0 00027 73280e-04PSO 266960 106037 106359 05174CGSA 22731 94231e-10 00431 00358

1198913CS 07740 18489e-32 00031 00013

CCCS 06371 0 00031 00011PSO 53003e+03 00101 174638 58025e+04CGSA 13660e+04 30835e-18 306816 28436e+05

1198914CS 06047 0 00034 00012

CCCS 05616 0 00022 62698e-04PSO 33220e+05 00100 9510100 27004e+08CGSA 148439 9 90251 01110

1198915CS 11919 20256e-31 00044 00028

CCCS 09859 0 00036 00019PSO 202544 37769 49084 64985CGSA 207509 34519e-09 02963 16965

1198916CS 11351 0 00048 00031

CCCS 10239 0 00038 00022PSO 54272e+03 15607 248489 75573e+04CGSA 440831 36602 42440 72125

1198917CS 05721 11381e-30 00032 00011

CCCS 05493 0 00027 79073e-04PSO 49874e+04 00298 1430958 55309e+06CGSA 2683960 606185 609033 452938

1198918CS 01298 44998e-30 00021 15972e-04

CCCS 00984 0 00014 71452e-05PSO 22087 00050 00174 00128CGSA 1298682 64933 79713 909936

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

100

Fitn

ess V

alue

(a) Function 1198911

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(b) Function 1198912

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(c) Function 1198913

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

1010

105

100

Fitn

ess V

alue

(d) Function 1198914

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(e) Function 1198915

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(f) Function 1198916

Figure 2 Continued

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

8 Mathematical Problems in Engineering

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(g) Function 1198917

CSCCCS

CGSA

PSO

100 200 300 400 500 600 700 800 900 10000Iteration

10minus35

10minus30

10minus25

10minus20

10minus15

10minus10

10minus5

105

100

Fitn

ess V

alue

(h) Function 1198918

Figure 2 Fitness value curves of CS CCCS PSO and CGSA on eight benchmark functions

The S3VM is retrained with the new training set and thisprocedure is continued iteratively until a stopping criterion isreached (eg maximum number of iterations) At each iter-ation new semilabeled samples are added to the training setconstructed in the previous iteration while the semilabeledsamples that change their label are removed from the newsemilabeled set and moved back to the unlabeled set

32 Semisupervised SVM Model Based on an ImprovedCuckoo Search Algorithm Improved cuckoo search algo-rithm optimized semisupervised SVMmodel (CCCS-S3VM)is based on improved cuckoo search algorithm optimizedSVM (CCCS-SVM) by adding the semisupervised learningwhich introduced unlabeled samples into the training processand then being trained with labeled samples together finallygetting the CCCS-S3VM model The main idea is to useSVMrsquos regularization parameter 119862 and RBFrsquos kernel parame-ters 120574 as the optimization target of CCCS algorithm in orderto get a set of combination parameters that make SVM getthe best classification accuracy The specific algorithm stepsare shown as in Algorithm 2

33 Oil Layer Recognition Application

331 Design of Oil Layer Recognition System Block diagramof the oil layer recognition system based on CCCS-S3VM isshown in Figure 3

The oil layer recognition mainly has the following steps

Step 1 (data selection and preprocessing) The selection ofthe data set is complete and comprehensive and should beclosely related to layer evaluation The dataset should bedivided into two parts of training and testing samples whichis conducted normalization processing to avoid calculationsaturation phenomenon

Step 2 (attribute discretization and generalization) In orderto achieve the reduction of the sample information attributefirst extract sample information conduct decision attributegeneralization and use curve inflection point approach toachieve continuous attribute discretization

Step 3 (attribute reduction of data information) Oil loggingdata includes sound electricity nuclear and other logginginformation There are more than 10 kinds of logging prop-erty in Logging series but some properties are not importantattribute reduction must be carried out to eliminate con-centrated redundant attributes in data We use the attributereduction based on consistent covering rough set [27]

Step 4 (CCCS-S3VM modeling) In CCCS-S3VM modelinput the sample information after attribute reduction use anS3VM algorithm to train and label the unlabeled samplesUse the CCCS algorithm to speed up the solution speedand accuracy and finally get the CCCS-S3VM classificationmodel

Step 5 (recognition output) The layer of the entire wellsection is recognized by the trained CCCS-S3VMmodel andoutput the results

In order to verify the application effect of the S3VM layerrecognition model based on CCCS we select three loggingdata for training and testing

332 Practical Application Hardware environment MacOS10133Matlab 2016a28GHzIntel Core i716GB

In Section 23 the effectiveness of the improved CCCSalgorithm is simulated and analyzed on benchmark func-tions In order to verify the application effect of the semisu-pervised model optimized by the improved algorithm weselect three logging data for training and testing record as

Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

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Mathematical Problems in Engineering 9

(01) Input(02) Labeled dataset L(03) Unlabeled dataset U(04) Regularization parameter of unlabeled dataset 119862lowast(05)Output(06) The label of unlabeled samples 119884lowast(07) Final model CCCS-S3VM(08) Begin(09) The regularization parameter 119862 and the kernel parameter 120574 of the labeled samples

that obtain by CCCS-SVM algorithm(10) Training the initial model 1198781198811198720 with labeled dataset L(11) Predict the label 119884lowast of unlabeled dataset U using 1198781198811198720119910lowast1 119910lowast119896(12) Initialization 119862lowast ≪ 119862(13) While 119862lowast lt 119862 do(14) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(15) There is a pair of unlabeled samples 119909119894 and 119909119895 Its label 119910119894 and 119910119895 is reverse

and the corresponding relaxation variables are satisfied 120585119894 + 120585lowast119895 gt 2 it means that 119910119894 and119910119895 likely to be a wrong labelThe labels of the two are exchanged and the SVMproblem is solved again The approximate solution of the minimization of theobjective function can be obtained after each round of iteration

(16) While exist119894 119895 | (119910119894119910119895 lt 0) and (120576119894 gt 0) and (120576119895 gt 0) and (120576119894 + 120576119895 gt 2) do(17) 119910119894 = minus119910119894 119910119895 = minus119910119895 label exchange(18) Solve formula (12) based on L U 119884lowast 119862lowast 119862 obtain (120596 119887) and 120585(19) End while(20) 119862lowast = min(2119862lowast 119862)(21) End while(22) End

Algorithm 2 CCCS-S3VM

Sample selectionand preprocessing

Attributediscretization and

generalization

Attributereduction

Build modelbased on

CCCS-S3VM

To be identifiedinformation

Remove redundantattributes andpretreatment

SVMrecognition

Output

Figure 3 Block diagram of the oil layer recognition system based on CCCS-S3VM

1199081 1199082 1199083 respectively In addition its reductions results anddistribution of those logging data are as in Tables 3 and 4respectively

TheCCCS-S3VMmodel trained on the training data set isused to identify the oil layer of the test sample Table 5 showsthe normalized range of four sample attributes in the wholewell after the reduction These attributes are normalized asshown in Figure 4 where the horizontal axis represents thedepth and the vertical axis represents a normalized value

In CCCS-S3VM model the sample information is inputby attribute reduction we use CCCS algorithm to find theoptimal 119862 and 120574 and obtain trained S3VM forecasting modelThere are three test datasets from three wells in different goodsection which are used in oil layer recognition by trainedprediction model we establish SVM model S3VM modeland QPSO-S3VM model respectively their recognition

results are compared with CCCS-S3VM model In additionsupervised SVMmodel trainedwith the full available trainingset but the training set of semisupervised models consists ofthe labeled set and the unlabeled set The labeled set consistsof 10 of the training set and the unlabeled set consists of theremaining data of the training set

In order to measure the performance of the recognitionmodel we define the following performance index

RMSE = radic 1119898119898sum119894=1

(ℎ (119909(119894)) minus 119910(119894))2 (13)

MAE = 1119898119898sum119894=1

10038161003816100381610038161003816ℎ (119909(119894)) minus 119910(119894)10038161003816100381610038161003816 (14)

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

10 Mathematical Problems in Engineering

Table 3 Reduction results of logging data

Well Attributes

Actual Results (1199081) AC CNL DEN GR RT RI RXO SP R2M R025 BZSP RA2 C1 C2 CALI RINC PORT VCLVMA1 VMA6 RHOG SWVO WO PORE VXO VW AC1

Reduction Results (1199081) AC GR RI RXO SP Actual Results (1199082) GR DT SP WQ LLD LLS DEN NPHI PE U TH K CALI Reduction Results (1199082) GR DT SP LLD LLS DEN K Actual Results (1199083) AC CALI GR NG RA2 RA4 RI RM RT RXO SPReduction Results (1199083) AC NG RI SP

Table 4 Distribution of logging data

Well Training set Test setDepth(m) Oil layers Dry layers Depth(m) Oil layers Dry layers1199081 1200sim1280 48 112 1230sim1310 96 5451199082 3300sim3450 63 137 3100sim3200 172 8281199083 1220sim1290 53 228 1180sim1320 105 895

Decisionattribute

119863 = 119889 119889 = 119889119894 = 119894 119894 = 0 1 where 0 1 representsthe dry layer and oil layer respectively

Table 5 The normalized range of attributes in the well

Attribute Minimum value Maximum value1199081 1199082 1199083 1199081 1199082 1199083AC 50 - 0 150 - 600GR 5 4 - 200 20 -RI 0 - -5 100 - 100RXO 0 - - 350 - -SP -35 -50 -50 -5 30 30DT - 150 - - 500 -LLD - 0 - - 25000 -LLS - 0 - - 3310 -DEN - 0 - - 5 -K - 0 - - 5 -NG - - 0 - - 50

Here ℎ(119909(119894)) and 119910(119894) are the recognition output value and thedesired output value respectively

RMSE measured the deviations between the recognitionoutput value and the desired output value which can wellreflect the precision of the measurement MAE is the meanof the absolute value of the deviation of all individual andarithmetic mean values The smaller the RMSE and MAEthe better the performance of the algorithmmodelThereforeRMSE is used as the standard to evaluate the accuracy of eachalgorithm model MAE is used as the actual situation of theprediction and prediction error The performance index dataof each algorithm model are shown in Table 6

Table 6 clearly shows that the recognition efficiency ofsemisupervised algorithms (S3VM PSO-S3VMCCCS-S3VM)is significantly close to the supervised algorithm(SVM)and the proposed model (CCCS-S3VM) in this paper hashigher accuracy than SVM algorithm in wells 1199082 and 1199083Secondly both the PSO and the improved CS algorithm can

improve the performance of semisupervised SVM but theimprovement of its accuracy means longer running time andlarge computational complexity However the CS algorithmbased on chaotic catfish effect can make the semisupervisedSVM algorithm improve the classification accuracy andkeep running speed fast at the same time In summaryCCCS-S3VM constituted catfish effect and chaotic theoryis better than the traditional SVM and S3VM model in oillayer recognition The classification is shown in Figure 5among them (a) (c) and (e) represent the actual oil layerdistribution (b) (d) and (f) represent CCCS-S3VM oil layerdistribution

According to a comparison of recognition results inFigure 5 firstly we know both recognition accuracies in threewells go up to 90 It can effectively recognize the oil layerdistribution accurately Secondly the CCCS-S3VM modelcan predict the distribution of a large number of reservoirsamples only using a small number of labeled samples it

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 11

Table 6 Comparison on performance index

Well Model RMSE MAE Accuracy() Running time(s)

1199081SVM 01894 00359 9641 001S3VM 03824 01463 8537 017

PSO-S3VM 03673 01349 8651 532CCCS-S3VM 02371 00562 9438 178

1199082SVM 03317 01100 8900 002S3VM 03536 01250 8750 042

PSO-S3VM 03151 00993 9007 1021CCCS-S3VM 03043 00926 9074 299

1199083SVM 03240 01050 8950 002S3VM 03521 01240 8760 057

PSO-S3VM 03351 01123 8877 1172CCCS-S3VM 02581 00666 9334 389

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0010203040506070809

1

Nor

mal

ized

Val

ue

AC

GR

(a)

1200 1210 1220 1230 1240 1250 1260 1270 1280

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

RT

SP

RXO

(b)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

DTGR

(c)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

LLD

(d)

3300 3315 3330 3345 3360 3375 3390 3405 3420 3435 3450

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

KDEN

LLS

(e)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

NGAC

(f)

1220 1230 1240 1250 1260 1270 1280 1290

Depth (m)

0

02

04

06

08

1

Nor

mal

ized

Val

ue

SP

RI

(g)

Figure 4 The normalized curves of attributes (a) and (b) attribute normalization of 1199081 (c) (d) and (e) attribute normalization of 1199082 (f)and (g) attribute normalization of 1199083

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

12 Mathematical Problems in Engineering

The Actual Reservoir Distribution

1230 1240 1250 1260 1270 1280 1290 1300 1310Depth (m)

0

1

(a)

CCCS-S3VM Oil layer identification

1230 1240 1250 1260 1270 1280 1290 1300 1310 Depth (m)

0

1

(b)The Actual Reservoir Distribution

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(c)

CCCS-S3VM Oil layer identification

3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200Depth (m)

0

1

(d)The Actual Reservoir Distribution

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(e)

CCCS-S3VM Oil layer identification

1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320Depth (m)

0

1

(f)

Figure 5 Classification of CCCS-S3VM (a) the actual oil layer distribution of1199081 (b) CCCS-S3VMoil layer distribution of1199081 (c) the actualoil layer distribution of 1199082 (d) CCCS-S3VM oil layer distribution of 1199082 (e) the actual oil layer distribution of 1199083 (f) CCCS-S3VM oil layerdistribution of 1199083greatly reduces the need of labeled samples and has a goodapplication prospect

4 Conclusion

In view of the possibility that the cuckoo algorithm islocally optimal the chaotic catfish effect is introduced intothe cuckoo algorithm which enhances the ability of thealgorithm to search for the global optimal solution andvalidates its effectiveness on the benchmark functions Thenthe improved algorithm is used to optimize the semisu-pervised SVM algorithm Finally it is applied to the oillayer recognition to solve the problem that the labeled dataare difficult to get when logging This method has goodclassification effect It improves the recognition rate andreduces data extraction cost when using a small number oflabeled data and runs faster which is obviously better thanother classical algorithms It has good prospects

Data Availability

All data included in this study are available upon request bycontact with the corresponding author

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by Tianjin Natural Science Foun-dation (no 18JCYBJC16500) and Hebei Province NaturalScience Foundation (no E2016202341)

References

[1] D Yarowsky ldquoUnsupervised word sense disambiguation rival-ing supervised methodsrdquo in Proceedings of the 33rd Annualmeeting of the Association for Computational Linguistics pp189ndash196 Morristown NJ USA 1995

[2] B Zu K Xia Y Pan and W Niu ldquoA novel graph constructorfor semisupervised discriminant analysis Combined low-rankand 120581-nearest neighbor graphrdquo Computational Intelligence andNeuroscience vol 2017 Article ID 9290230 11 pages 2017

[3] V Vapnik Statistical Learning Theory Wiley New York NYUSA 1998

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 13

[4] Q Wu S Y Liu and L Y Zhang ldquoParticle swarm optimizationfor semi-supervised support vector machinerdquo Journal of Infor-mation Scienceamp Engineering vol 26 no 5 pp 1695ndash1706 2010

[5] W-P Luo H-Q Li and N Shi ldquoSemi-supervised least squaressupport vector machine algorithm application to offshore oilreservoirrdquo Applied Geophysics vol 13 no 2 pp 406ndash415 2016

[6] D Zhang L Jiao X Bai S Wang and B Hou ldquoA robustsemi-supervised SVM via ensemble learningrdquo Applied SoftComputing vol 65 pp 632ndash643 2018

[7] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature amp BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 IEEE PublicationCoimbatore India 2009

[8] R B Payne M D Sorenson and K KlitzThe Cuckoos OxfordUniversity Press 2005

[9] X S Yang and S Deb ldquoEngineering optimization by cuckoosearchrdquo International Journal of Mathematical Modelling ampNumerical Optimization vol 1 no 4 pp 330ndash343 2012

[10] P R Srivastava R Khandelwal S Khandelwal S Kumar andS S Ranganatha ldquoAutomated test data generation using cuckoosearch and tabu search (CSTS) algorithmrdquo Journal of IntelligentSystems vol 21 no 2 pp 195ndash224 2012

[11] X-S Yang and S Deb ldquoMultiobjective cuckoo search for designoptimizationrdquo Computers amp Operations Research vol 40 no 6pp 1616ndash1624 2013

[12] Y Zhang L Wang and Q Wu ldquoModified Adaptive CuckooSearch (MACS) algorithm and formal description for globaloptimisationrdquo International Journal of Computer Applications inTechnology vol 44 no 2 pp 73ndash79 2012

[13] L J Wang Y L Yin and Y W Zhong ldquoCuckoo searchalgorithmwith dimension by dimension improvementrdquo Journalof Software vol 24 no 11 pp 2687ndash2698 2013

[14] W-H Yang J-R Liu and Y Zhang ldquoA new local-enhancedcuckoo search algorithmrdquo International Journal of Computa-tional Science and Mathematics vol 8 no 2 pp 175ndash182 2017

[15] S Wang S Y Song Y Yu Z Xu H Yachi and S C GaoldquoMultiple chaotic cuckoo search algorithmrdquo in Proceedings ofthe 8th International Conference on Swarm Intelligence (ICSIrsquo17) vol 10385 pp 531ndash542 Springer International PublishingFukuoka Japan 2017

[16] S-S Wang J-J Yang and S Chai ldquoArtificial bee colonyalgorithm with chaotic catfish effect and its applicationrdquo ActaElectronica Sinica vol 42 no 9 pp 1731ndash1737 2014

[17] C T Brown L S Liebovitch and R Glendon ldquoLevy flights indobe Juhoansi foraging patternsrdquoHuman Ecology vol 35 no 1pp 129ndash138 2007

[18] A M Reynolds and M A Frye ldquoFree-flight odor tracking inDrosophila is consistent with an optimal intermittent scale-freesearchrdquo PLoS ONE vol 2 no 4 p e354 2007

[19] I Pavlyukevich ldquoCooling down Levy flightsrdquo Journal of PhysicsAMathematical andTheoretical vol 40 no 41 pp 12299ndash123132007

[20] P Barthelemy J Bertolotti andD SWiersma ldquoA Levy flight forlightrdquo Nature vol 453 no 22 pp 495ndash498 2008

[21] L Y Chuang S W Tsai and C H Yang ldquoFuzzy adaptive catfishparticle swarm optimizationrdquo Artificial Intelligence Researchvol 1 no 2 pp 149ndash170 2012

[22] W Z Ju K W Xia and S D Dai ldquoImproved cloud particleswarm optimization algorithm and its application on circuitbreaker optimizationrdquo Application Research of Computers vol35 no 7 2018

[23] L Yi X C Diao J J Cao and B Zhang ldquoLocal EnhancedCatfish Bat Algorithmrdquo in Proceedings of the 2016 InternationalConference on Robots amp Intelligent System (ICRIS rsquo16) pp238ndash245 Institute of Electrical and Electronics Engineers IncZhangJiaJie China August 2016

[24] K James and E Russell ldquoParticle swarm optimizationrdquo inProceedings of the 1995 IEEE International Conference on NeuralNetworks pp 1942ndash1948 IEEE Publication Perth Australia1995

[25] S Gao C Vairappan Y Wang Q Cao and Z Tang ldquoGravita-tional search algorithm combinedwith chaos for unconstrainednumerical optimizationrdquo Applied Mathematics and Computa-tion vol 231 pp 48ndash62 2014

[26] N V Chawla and G Karakoulas ldquoLearning from labeled andunlabeled data An empirical study across techniques anddomainsrdquo Journal of Artificial Intelligence Research vol 23 pp331ndash366 2005

[27] J Bai K Xia Y Lin and P Wu ldquoAttribute Reduction Based onConsistent Covering Rough Set and Its Applicationrdquo Complex-ity vol 2017 Article ID 8986917 9 pages 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom