Multidepot UAV Routing Problem with Weapon Configuration ...

Research ArticleMultidepot UAV Routing Problem withWeapon Configuration and Time Window

Tianren Zhou1 Jiaming Zhang1 Jianmai Shi 12 Zhong Liu1 and Jincai Huang 1

1Science and Technology on Information Systems Engineering Laboratory National University of Defense TechnologyChangsha 410073 China2School of Traffic and Transportation Engineering Central South University Changsha 410075 China

Correspondence should be addressed to Jianmai Shi jianmaishigmailcom

Received 23 January 2018 Accepted 15 April 2018 Published 23 May 2018

Academic Editor Juan-Antonio Escareno

Copyright copy 2018 Tianren Zhou 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

In recentwars there is an increasing trend that unmanned aerial vehicles (UAVs) are utilized to conductmilitary attackingmissionsIn this paper we investigate a novel multidepot UAV routing problem with consideration of weapon configuration in the UAV andthe attacking time window of the target A mixed-integer linear programming model is developed to jointly optimize three kindsof decisions the weapon configuration strategy in the UAV the routing strategy of target and the allocation strategy of weapons totargets An adaptive large neighborhood search (ALNS) algorithm is proposed for solving the problem which is tested by randomlygenerated instances covering the small medium and large sizes Experimental results confirm the effectiveness and robustness ofthe proposed ALNS algorithm

1 Introduction

With the development of information technologies artificialintelligence and new materials as well as their wide appli-cation in unmanned aerial vehicles (UAVs) the abilities ofUAVs on autonomously flying endurance and stealth havebeen greatly improved There are many advantages of UAVsto conduct military operations such as low cost high agilitygood stealth and no risk of casualties Thus in several recentlocal wars there was an increasing trend to employ UAVsfor completing military missions During the Gulf War [1 2]the US army deployed the ldquoPioneerrdquo and the ldquoPointerrdquo UAVsto conduct military tasks such as battlefield reconnaissancesurveillance artillery support and target damage assessmentIn the Kosovo war [3 4] NATO employed over 200 UAVsduring the war In the Afghanistan war [5] the UAV namedldquoGlobal Hawkrdquo was used to directly destroy enemy targetsThe outstanding performance of UAVs in current wars hasproved their military value and more UAVs are introducedand used to replace manned aircrafts for carrying out variousmilitary missions

When UAVs are used to perform attack missions onenemy targets commanders need to consider the constraints

on UAV load and the hanging points for weapons and shoulddetermine the type and quantity of weapons equipped inthe UAV while optimizing the flight path for visiting thetargets In the UAV mission planning process commandersalso have to determine the type and quantity of weaponsthat the UAV delivers to each target ensuring that theseweapons can cause sufficient damage on the target and meetthe missionrsquos damage requirements Modern wars are usuallyjoint operations of multiple services (army navy air forceetc) and there are many cooperative actions among differentmilitary unitsThus formost of the targets attacked byUAVsthe attacking actions are required to complete in specifictime windows In the military operations research field mostliteratures related to UAV mission planning focused on taskassignment path planning and routing separately To the bestof our knowledge the UAV routing problem with weaponconfiguration and time window has not been studied

The UAV routing problems were usually solved based onmodels and algorithms utilized in vehicle routing problem(VRP) The weapon configuration in the UAV and allo-cation to the targets are quite different from the productdelivery to customer in the common VRP For a targetthe attacking effect is different if it is attacked by different

HindawiJournal of Advanced TransportationVolume 2018 Article ID 7318207 15 pageshttpsdoiorg10115520187318207

2 Journal of Advanced Transportation

Table 1 Weapon-target combat ability matrix

Small smartbomb

Small precisionguided bomb

Laser-guidedbomb

Bridge 035 065 095Communicationstation 04 055 075

weapons Table 1 presents the combat ability matrix of threedifferent weapons on two targets It can be seen that ifthe destroy requirement for the bridge target is restrictedover 90 in the mission there are a number of combinationsof weapons that can satisfy the requirement such as 3small smart bombs 1 small smart bomb 1 small precisionguided bomb and 1 laser-guided bomb Thus the weaponsdelivered to a target are not deterministic and are impactedby the weapon configuration and routing strategies of theUAV while the types and quantities of products deliveredto each customer are deterministic in the general VRPproblem

Motivated by the practical requirement in military mis-sion planning of UAV we investigated the multidepot UAVrouting problem with weapon configuration and time win-dow (MD-URP-WCampTW) which can be viewed as a newextension on the traditional VRP In MD-URP-WCampTWthree kinds of decisions should be cooperatively optimizedwhich are the weapon configuration strategy in the UAVthe routing strategy of target and the allocation strategy ofweapons to targets The interaction among these decisionsmakes the modelling and solution of the problem morecomplex In this paper a mixed-integer linear program-ming model is developed to formulate the problem anda powerful adaptive large neighborhood search (ALNS)based metaheuristic is proposed to obtain better feasiblesolutions

The paper is organized as follows In Section 2 the relatedliteratures are reviewed The formulated model is developedin Section 3 and the proposed ALNS algorithm includingits main steps is presented in Section 4 The computationalresults are reported and analyzed in Section 5 Section 6concludes the paper

2 Literature Review

Multidepot UAV routing problem with consideration ofweapon configuration and time window is related to mainstreams of literatures which are UAV path planningroutingandUAV task assignment A review of the literatures on thesetwo fields is summarized below

The earlier studies in the field of UAV flight path opti-mization mainly focused on optimizing the UAV flight pathfrom the control level It is necessary to consider the influ-ence of the turning angle obstacle avoidance and weatherconditions (such as wind power level) on the UAV Based onthese constraints an optimal flight path is found for the UAV[6] Edison and Shima [7] studied the mission planning andpath planning ofmulti-UAV inmilitary operationsThey fullyconsidered flight parameters such as the minimum turningradius in the proposed mathematical model and solved the

problem using a genetic algorithm Zhang et al [8] studiedmulti-UAV path planning considering mobility collisionavoidance and flight information sharing and proposed theCooperative and Geometric Learning Algorithm (CGLA)to solve the above problem Moon et al [9] developed amultilevel planning model for multi-UAV task assignmentand path planning taking into account practical constraintssuch as collision avoidance between UAVs and solved theproblem by the Alowast algorithm Yang et al [10] studied the pathplanning problem of UAV in terms of obstacle avoidancedecomposed the original goal and constraint function ofUAV path planning into a new set of evaluation functionsand proposed the evolutionary algorithm for solving theproblem

With the improvement in intelligent control technologyfor UAVs UAVs can independently complete the flightbetween the target points In recent years studies on UAVpath planning have begun to focus on tactical optimizationin order to minimize the overall minimum flight distance byoptimizing the sequence of UAV to visit the target Shettyet al [11] studied multi-UAV task assignment and routingproblems based on target priority and distinguished thetargets by their degrees of importance using the Tabu searchalgorithm Mufalli et al [12] studied the multi-UAV routingproblem for target reconnaissance considering the load con-straints of the UAV and solved the problem by the columngeneration and heuristic algorithm Liu et al [13] studiedthe UAV deployment and routing problem for road-trafficinformation collection Subject to the number of UAVs andthe maximum cruise distance a multiobjective optimizationmodel was developed Moyo and Plessis [14] studied theinspection path optimization problem for the cable networkof UAVs and described it as a traveling salesman problem(TSP) Guerriero et al [15] proposed a system of UAVs thatare able to communicate self-organize and cooperate Amulticriteria optimizationmodelwas developed to determinethe distributed dynamic schedule of UAVs and ensure bothspatial coverage and temporal coverage of specific targetsEvers et al [16] studied multi-UAV path planning with targetreconnaissance time windows Luo et al [17] studied thetwo-echelon routing problem of mounting UAV on a groundvehicle (GV) where the GV acts as the mobile depot forlaunching and recycling the UAV while the UAV visits thetargets for information collection

In order to facilitate multi-UAV collaborative task alloca-tion during mission planning Ghalenoei et al [18] proposedthe Discrete Invasive Weed Optimization Algorithm for spe-cific target attributes and geographical locations George etal [19] proposed an online task assignment algorithm basedon UAV task alliance to deal with unexpected tasks whichinvolves requesting adjacent UAVs to form task alliances andreplanning the tasks Zhong et al [20] studied the UAV taskassignment problem with dynamic changes in target valueover time taking into account various constraints includingUAV flight altitude maximum climb height and maximumturning radius Hu et al [21] studied the assignment ofUAV collaborative tasks using the hierarchical assignmentmethod and solved the problem by an improved ant colonyalgorithm Yin et al [22] described the UAV collaborative

Journal of Advanced Transportation 3

1 2

610

3

12

4

5

8

9

7 11

Depot

Target

Route

Figure 1 An illustration of the MD-URP-WCampTW

task assignment problem as a multiobjective optimizationproblem and solved it using a Pareto-dominated multiob-jective discrete particle swarm optimization algorithm Jin[23] studied the distributed UAV task allocation problemwhere the tasks are divided into detection attack andverification

As far as current UAV mission planning and path plan-ning studies are concerned no study has focused on theintegrated optimization of UAV flight path for target attackand airborne weapons configuration Taking into accountthe type and quantity of weapons on board during theUAV path planning process there exists a new direction fortraditional path planning which is of great significance forimproving the efficiency of UAV mission planning in themilitary

3 Model Formulation

The MD-URP-WCampTW considers a set of targets each ofwhich must be attacked once by one UAV The weaponsdelivered to the target must be able to destroy it over arequired destroy levelThere are multiple depots for the UAVwhere the weapons are configured for each UAV subjectto the UAVrsquos constraints on payload and hanging pointsAn illustration of the MD-URP-WCampTW is presented inFigure 1 In the MD-URP-WCampTW the commander has tooptimize the decisions onwhich depot the UAV leaves whichtargets are visited in what sequence what type and howmanyweapons are configured on the UAV and what type and howmany weapons are delivered to each target The objectiveis to minimize the number of UAVs employed the overallweapons consumed for destroying all the targets and the totalcost (timedistance) traveled by all UAVs

31 Symbol Description The notations and symbols utilizedin the model formulation are presented as follows

(1) Sets

119873 the set of targets and119873 = 1 2 119899119872 the set of depots and119872 = 119899+1 119899+2 119899+119898119880 the set of UAVs and 119880 = 1 2 119906119882 the set of different weapon types and 119882 =1 2 119908

(2) Parameters

119886119894 damage demand of target 119894 and 119894 isin 119873119888 the payload capacity of the UAV119892 the number of hanging points of the UAV119905119894119895 the time of UAV flying from target 119894 to target119895 and 119894 119895 isin 119873 119894 = 119895119891ℎ the cost of a weapon of type ℎ and ℎ isin 119882119902ℎ the weight of a weapon of type ℎ and ℎ isin 119882119887119894ℎ the combat ability of weapon ℎ on target 119894and 119894 isin 119873 ℎ isin 119882119903 the duration time of UAV119890119894 the earliest allowed hitting time of target 119894and 119894 isin 119873119897119894 the latest allowed hitting time of target 119894 and119894 isin 119873119904119894 the spent time of UAV hitting target 119894 and 119894 isin119873119908119896119894 the waiting time of UAV 119896 hovering abovetarget 119894 and 119896 isin 119880 119894 isin 119873119871 a large enough number

(3) Decision Variables

119909119894119895119896 binary variable which is equal to 1 if atarget 119895 is attacked after target 119894 by UAV 119896 and0 otherwise119905119896119894 continuous variable the moment of UAV 119896reaching target 119894119910119896ℎ119894 integer variable which denotes the numberof weapons ℎ on UAV 119896 used to attack target 119894and 119910119896ℎ119894 ge 0

32 Mathematical Model The MD-URP-WCampTW can beformulated as the following mixed-integer programmingmodel

min 119885

= 1198751119899+119898

sum119894=119899+1

119899

sum119895=1

119906

sum119896=1

119909119894119895119896 + 1198752119908

sumℎ=1

119906

sum119896=1

119899

sum119894=1

119891ℎ119910119896ℎ119894

+ 1198753119899+119898

sum119894=1

119899+119898

sum119895=1

119906

sum119896=1

(119905119894119895 + 119908119896119894 + 119904119894) 119909119894119895119896

(1)

subject to119906

sum119896=1

119899+119898

sum119894=0119894 =119895

119909119894119895119896 = 1 forall119895 isin 119873 (2)


119906

sum119896=1

119899+119898

sum119895=0119894 =119895

119909119894119895119896 = 1 forall119894 isin 119873 (3)

119899+119898

sum119894=1

119909119894119901119896 minus119899+119898

sum119895=1

119909119901119895119896 = 0

forall119901 isin 119873 cup119872 119896 isin 119880

(4)

119908

sumℎ=1

119902ℎ119899

sum119894=1

119910119896ℎ119894 le 119888 forall119896 isin 119880 (5)

119908

sumℎ=1

119899

sum119894=1

119910119896ℎ119894 le 119892 forall119896 isin 119880 (6)

V

sum119896=1

119908

sumℎ=1

119887ℎ119894119910119896ℎ119894 le 119886119894 forall119894 isin 119873 (7)

119910119896ℎ119894 le 119871119899

sum119895=1

119909119894119895119896

forall119894 isin 119873 119896 isin 119880 ℎ isin 119882

(8)

119899+119898

sum119894=0

119899+119898

sum119895=0

(119905119894119895 + 119904119894 + 119908119896119894) 119909119894119895119896 le 119903

forall119896 isin 119880

(9)

119905119896119894 + 119905119894119895 + 119908119896119894 + 119904119894 minus 119871 (1 minus 119909119894119895119896) le 119905119896119895

forall119894 isin 119873(10)

119905119896119894 + 119908119896119894 ge 119890119894 forall119894 isin 119873 (11)

119905119896119894 + 119908119896119894 + 119904119894 le 119897119894 forall119894 isin 119873 (12)

119905119896119894 ge 0 forall119894 isin 119873 119896 isin 119880 (13)

119910119896ℎ119894 ge 0 forall119896 isin 119880 ℎ isin 119882 119894 isin 119873 (14)

119909119894119895119896 isin 0 1 forall119894 isin 119873 119895 isin 119873 119896 isin 119880 (15)

The objective function consists of three parts The firstpart represents the total number of UAVs used in combatoperations the second part shows the total cost of theweapons used in combat operations and the third partexpresses the total flight time for all UAVs in combatoperations 1198751 1198752 and 1198753 are the weight coefficients of eachpart to adjust the three parts of the objective function to thesame number of units Constraints (2) and (3) define thatevery target can be hit by one UAV Flow conservation isguaranteed by constraints (4) Constraints (5) ensure that thatthe total weight of category 119897 weapons carried by each UAVcannot exceed its load limit Constraints (6) ensure that thenumber of weapons mounted on each UAV does not exceedthe number of weapons hanging on the UAV Constraints(7) regulate that the damage demand of each target mustbe fulfilled Constraints (8) ensure that the UAV can only

Input119904initial initial solutionsix neighborhood structuresOutput the best solution 119904lowast119904lowast larr 119904initial119904current larr 119904initialinitialize scores on neighborhood structureswhile acceptance standards not meet do

select a neighborhood structuremodify 119904current by chosen structure to generate 119904newif 119904new is accepted then

119904current larr 119904newendif 119885(119904new) le 119885(119904lowast) then119904lowast larr 119904new

endupdate scores on neighborhood structures

endReturn 119904lowast

Algorithm 1 Procedure of the ALNS

drop off weapons to the target visited by it Constraints(9) guarantee that the endurance of the UAV must not beexceeded Constraints (10) ensure that the arriving time ofUAV 119896 at target 119894 is no later than the arriving time at target 119895 ifUAV 119896 attacks target 119894 after target 119895 Constraints (11) and (12)are time window constraints for the UAV to perform a taskConstraints (13) (14) and (15) are the constraints of decisionvariables

4 Algorithm

ALNS is an extension of the large neighborhood searchalgorithm and is first proposed by Ropke and Pisinger [24]which has been widely employed for solving complex vehiclerouting problems [25 26] The main procedure of ALNS isillustrated in Algorithm 1 The ALNS starts from an initialfeasible solution and conducts iteratively search for bettersolutionsThe initial feasible solution is usually generated by aconstructive heuristic In each iteration the current solutionis destroyed and repaired by heuristics which are selectedbased on their past performances

41 The Heuristic Algorithm for Constructing an InitialSolution The heuristic algorithm for generating an initialsolution aims to rapidly construct a feasible solution whichincludes four main steps First weapons are assigned to eachtarget according to its damage requirements based on someheuristic rules Second the targets are clustered to the depotsthrough the clustering strategies Third a complete tour isconstructed to visit all the targets assigned to a depot Finallythe feasible flight path for each UAV is constructed

411 Weapon Allocation Strategy The weapon assignmentstrategy is to determine the type and quantity of weaponsused to attack the target and meet its damage requirement


Input 119886119894 119887119894119898 for 119894 isin 119873 119898 isin 119882Output 119908119886119905119894119898 the number of weapon119898 assigned to target 119894

Set 119908119886119905119894119898 = 0 (119898 isin 119882)119898lowast = argmax119887119894119898 119898 isin 119882119908119886119905119894119898lowast = lfloor119886119894119887119894119898lowastrfloor1198981015840 = argmin119891119898 | 119898 isin 119882 and 119886119894 minus 119908119886119905119894119898lowast119887119894119898lowast minus 119887119894119898 le 01199081198861199051198941198981015840++

Return 119908119886119905119894119898 (119898 isin 119882)

Algorithm 2 Procedure of the assigning strategy based on destroy effect

Inputeff119894119898 the cost-effectiveness ratio of weaponm against target 119894119902119898 the weight of weapon119898119898 isin 119882119888 the UAVrsquos payload119892 the number of hanging points in the UAVOutput119908119886119905119894119898 the number of weapon119898 assigned to target 119894Set 119862119882119867 = minus1 119908119886119905119894119898 = 0 (119898 isin 119882)while (119862119882119867 lt 0) do

119898lowast = argmaxeff119894119898 119898 isin 119882119908119886119905119894119898lowast = lceil119886119894119887119894119898lowastrceilif (sum119872119898=1 119902119898119908119886119905119894119898 le 119888 and sum

119872119898=1 119908119886119905119894119898 le 119892) then

119862119882119867 = 1endelse

119908119886119905119894119898lowast = 0119882 = 119882119898lowast

endendReturn 119908119886119905119894119898 (119898 isin 119882)

Algorithm 3 Procedure of the assigning strategy based on cost-effectiveness

Two strategies are designed to dispose and assign weapons tothe targets

(a) Assigning Strategy Based on Destroy Effect The assigningstrategy based on destroy effect is to select the weapon withthe highest destroy effect on the target and assign it to thetarget The main procedure is illustrated in Algorithm 2

(b) Assigning Strategy Based on Cost-Effectiveness In theassigning strategy based on cost-effectiveness a measure-ment named as ldquocost-effectivenessrdquo is introduced as follows

eff119894119898 =119887119894119898119891119898

(16)

The weapon with the highest ldquocost-effectivenessrdquo is pref-erentially selected and assigned to the target The main pro-cedure for the assigning strategy based on cost-effectivenessis illustrated in Algorithm 3

412 Target Clustering Strategy Three target clusteringstrategies are designed for assigning targets to each depot

which are distance based clustering greedy search clusteringand virtual feedback clustering

(a) Distance Based Clustering (DC) The basic idea of theDC strategy is to assign each target to its closest depot Thedistance between each target point and each depot is firstcalculated and then the targets are clustered to their closestdepot

(b) Greedy Search Clustering (GSC) In the GSC strategy eachdepot is first allowed to select one target randomly and thenthe target closest to the selected target is addedThe operationis repeated until all targets are assigned to the appropriatedepots The GSC strategy is illustrated in Figure 2

(c) Virtual Feedback Clustering (VFC) The basic idea of theVFC strategy is to assume that there is a virtual depot aroundthe known depots and all UAVs performing the strikingtask are from the virtual depot We can obtain 119878 a set ofpath planning schemes for multiple UAVs departing fromthe virtual depot In addition 119878 = 1199041 1199042 119904119906 where 119906denotes the quantity of UAVs usedThen the virtual depot ischanged to the actual depot for each route in 119878The total flying


Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Figure 2 The operation process for the GSC strategy

distance is computed every time after the depot is changedThe targets corresponding to the changing scheme with theshortest distance are assigned to the appropriate depots Theabove operation is repeated until all elements in set 119878 areassigned

413 Target Sequencing Strategy The target sequencing strat-egy aims to determine the sequence in which the UAV visitsthe targets subject to their time windows There are fourstrategies for sequencing the targets which are sequencingbased on distance (SD) sequencing based on earliest strikingtime (SEST) sequencing based on latest striking time (SLST)and sequencing based on time window width (STWW) TheSD strategy aims to sort all targets by the distance to the depotin an ascending order AUAVfirst visits the closest target andthen the next target at a longer distance after departing fromthe depot The UAV visits the remaining targets in the samemanner until all targets are visited The SEST strategy is tovisit all targets in an ascending order by the earliest strikingtime of the target that is the targets with earlier striking timeshould be attacked earlier In the SLST strategy all targets arevisited in a descending order of the latest striking time The

STWW strategy is to visit all targets in an ascending order ofthe time window width

414 Feasible Route Construction (FRC) In this step afeasible route for each UAV is constructed while consider-ing the constraints on endurance payload the number ofhanging points in UAV and the time window of the targetThe main procedure of the FRC algorithm is presented inAlgorithm 4

The basic idea of FRC is to let a UAV depart from thedepot and visit the targets one by one The total weight andquantity of the weapons carried by the UAV and its totalactual flight time are calculated when it arrives at a targetThen constraints (5) (6) (9) (11) and (12) are checked andthe target is added to the UAVrsquos route if all these constraintsare satisfied If any constraint is not met the UAV returns tothe depot and the target is assigned to a new UAV and itsroute The operation is repeated until all targets are visited

42 Neighbourhood Structures In ALNS the neighborhoodstructures are employed to slightly diversify the starting point


Input119899 the total number of targets119864(5+119882)times119899 the basic information matrix related with the target The firstline (119864[0 119899]) of the matrix is the targetrsquos number The second line (119864[1 119899]) ofthe matrix stores the earliest allowed strike time of the target The third line(119864[2 119899]) of the matrix stores the targetrsquos latest hit time The fourthline (119864[3 119899]) of the matrix stores the target time that UCAV hit the goal Thefifth line (119864[4 119899]) of the matrix stores the time it takes UCAV to fly to thetarget The sixth line (119864[5 119899]) of the matrix stores the time it takes UCAV to flyfrom the previous target to the target The seventh line (119864[6 119899]) of the matrixstores the total number of weapons assigned to the target The eighthline (119864[7 119899]) stores the total weight of the weapon assigned to the target point119888119906119898119898119879119900119863119890119901119900119905 time accumulated from depot to target 119894 and 1198941015840 to depot119888119906119898119898119879119900119873119890119909119905 time accumulated from target 119894 to target 1198941015840119888119906119898119898119864119909119890119888119906119905119890 total time for all target points visited by UAV119888119906119898119898119882119890119886119901119900119899 the total numbers of weapons after visiting all targets119888119906119898119898Weight The total weight of weapons after visiting all targets119890119899119889119906119903 UAV endurance119901119886119910119897119900119886119889 UAV maximum payloadℎ119886119903119889119901119900119894119899119905 The number of UAV hanging points119899119906119898119880119862119860119881 The number of UAVOutput120577 A matrix set containing 119899119906119898119880119862119860119881 number of new information matrix119864V4times(119886minus119887) where V = 1 2 119899119906119898119880119860119881

Set 119886 = 119899 119887 = 0 119899119906119898119880119860119881 = 1 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0 119888119906119898119898119864119909119890119888119906119905119890 = 0while (119887 lt 119899 minus 1) do

while (119888119906119898119898 lt 119890119899119889119906119903) dofor (119894 = 119887 119894 lt 119886 119894 + +) do

119888119906119898119898119864119909119890119888119906119905119890 = 119888119906119898119898119864119909119890119888119906119905119890 + 119864[3 119894] 119888119906119898119898119879119900119863119890119901119900119905 = 119864[4 119887] + 119864[4 119886 minus 1]119888119906119898119898119879119900119873119890119909119905 = 119888119906119898119898119879119900119873119890119909119905 + 119864[5 119894] 119888119906119898119898119882119890119886119901119900119899 = 119888119906119898119898119882119890119886119901119900119899 + 119864[6 119894]119888119906119898119898Weight = 119888119906119898119898Weight + 119864[7 119894]

end119888119906119898119898 = 119888119906119898119898119864119909119890119888119906119905119890 + 119888119906119898119898119879119900119863119890119901119900119905 + 119888119906119898119898119879119900119873119890119909119905If (119888119906119898119898119882119890119886119901119900119899 gt ℎ119886119903119889119901119900119894119899119905 or 119888119906119898119898Weight gt 119901119886119910119897119900119886119889 or

119888119906119898119898 ge 119890119899119889119906119903 or 119888119906119898119898-119864[4 119886 minus 1] lt 119864[1 119886 minus 1] or 119888119906119898119898-119864[4 119886 minus 1] gt 119864[2 119886 minus 1])do

119886 minus minus 119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0119888119906119898119898119882119890119886119901119900119899 = 0 119888119906119898119898Weight = 0

endelse

119887 = 119886 119899119906119898119880119862119860119881 + + 119886 = 119899Output a new encoding matrix 119864V

4times(119886minus119887)end

end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577

Algorithm 4 Procedure of the FRC algorithm

of local search In this section six neighborhood structuresare designed for effectively searching the solution space

(a) Depot Exchanging (DE) In the DE operator firstly onedepot is selected randomly and one flight route is alsoselected from the routes starting at this depot In this way weselect119898 depots and119898 routesThen the depots corresponding

to the 119898 selected routes are exchanged We further verifywhether the new routes satisfy the constraints on enduranceof the UAV and the time windows of the targets If theconstraints aremet a new solution is obtainedThedepots areexchanged again if any constraint is not satisfied The abovesteps are repeated until a new feasible solution is obtainedIt should be noted that it is impossible to guarantee that


eachDE operation obtains an improved feasible solution andsometimes it is even not possible to obtain a feasible solution

(b) Targets Reclustering (TRC) The TRC operator is toconstruct a new feasible solution by reclustering all targetnodes When the targets are reclustered target sequencingand feasible route construction strategies in the above sectionare conducted to generate a new solution

(c) Weapons Reconfiguration (WR) The basic idea of the WRoperator is to first delete the weapon assignment schemes for119896 (1 le 119896 lt 119899) targets and invoke the appropriate weaponallocation strategies to reassign weapons for these targets Anew weapon assignment scheme follows the ldquodeletionrdquo andldquoreassignmentrdquo operations

(d) Reducing the Number of Weapons (RNW) The basic ideaof the RNW structure is to reduce the total cost by adjustingthe quantity of weapons assigned to the target In the RNWstructure we first select the target with the most weaponsThen the type and number of weapons assigned to this targetare changed in an attempt to reduce the quantity of weaponsIf the RNW operation successfully reduces the quantity ofweapons at a target it provides potentials for reducing thecost ofweapons the quantity ofUAVs and the flying distance

(e) Reducing the Cost ofWeapons (RCW)The basic idea of theRCW structure is to reduce the total cost by replacing high-cost weapons with low-cost weapons In the RCW structurewe first select the target with the highest cost of weaponsin the weapon assignment schemes and then attempt toreplace the high-cost weapons with combination of low-costweapons It should be noted that the RCW operation cannotguarantee that the weapon exchange always reduces the totalcost For example the cost of weapons at a target may belowered and in the same time the weight and number of theweapons at this target may increase which may make thevalue of the objective increase

(f) Reducing the Weight of Weapons (RWW) The RWWstructure is a variant of the RCW structure Its basic ideais to reduce the quantity of weapons and thus improvethe objective by replacing the heavy weapons with relativelylighter weapons in the weapon assignment schemes In theRWW structure we first select the target with the highestweight of weapons and then attempt to replace the heav-iest weapons with relatively lighter weapons The damagerequirements for the target point must be verified when theweapons are being replaced In other words the adjustedweapon assignment schemes shouldmeet Constraints (5) and(7)

43 Adaptive Learning Strategy The six neighborhood struc-tures provide potentials to improve a solution from differentperspectives The first neighborhood structure DE mayimprove the solution by adjusting the UAV flight loopThe second neighborhood structure TRC may improvethe solution by changing the depot The third to sixthneighborhood structures WR RNW RCW and RWW

may improve the solution by adjusting the weapon assign-ment scheme Different neighborhood structures may leadto different improvement results To achieve more exten-sive neighborhood search this section presents an adap-tive learning strategy to dynamically adjust the weightsof the six structures during the neighborhood searchprocess

The six neighborhood structures are randomly selectedto adjust the solution under the ldquorouletterdquo principle Giventhe weights of the neighborhood structures119908119894 (119894 = 1 6)the probability of structure 119895 to be selected is 120596119895sum

ℎ119894=1 120596119894

Theweights of the six neighborhood structures are adaptivelyupdated every 120593119890V119900 iteration by evaluating their performancein these earlier 120593119890V119900 iterations We note 120593119890V119900 iterations asan evaluation segment Assuming the initial weight of everyneighborhood structure is 1 in the 119895th evolution the weightof structure 119894 is as follows

120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)

where 119903 (119903 isin [0 1]) is a constant 120576119894119895 is the number of timesthe neighborhood structure 119894 is invoked in the 119895th evolutionand 120590119894119895 is the score of the neighborhood structure 119894 in the 119895thevolution

The neighborhood structure 119894 in the 119895th evolution isscored according to the following scoring rules

(1) 1205900119894119895 = 0 the initial score of structure 119894 (119894 = 1 2 6)at the beginning of the 119895th evaluation is set to be 0

(2) 1205901119894119895 = 30 30 scores are added to structure 119894 if the newsolution is the best one generated in the 119895th evolution

(3) 1205901119894119895 = 20 20 scores are added to structure 119894 if the newsolution is better than the average one generated in the 119895thevolution

(4) 1205901119894119895 = 10 10 scores are added to structure 119894 if the newsolution is worse than the average one generated in the 119895thevolution

(5) 1205901119894119895 = 5 5 scores are added to structure 119894 if the newsolution is better than the worst one generated in the 119895thevolution but can be accepted by the algorithm

44 Acceptance Standard and Criteria for Termination

441 Acceptance Standard for Solutions In the ALNS algo-rithm the acceptance standard for the generated solutionsis defined on the basis of the record-to-record algorithmproposed by Dueck [27] It is assumed that 119892lowast is the objectivefunction value of the current optimal solution called recordIt is assumed that 120575 is the difference between the objectivefunction value of the current solution and 119892lowast called devia-tion

It is assumed that119877 is the solution1198771015840 is the neighborhoodsolution to 119877 and 1198921198771015840 is the objective function value of1198771015840

When 1198921198771015840 lt 119892lowast + 120575 the neighborhood solution 1198771015840 can beaccepted where 120575 = 01 times 119892lowast And 119892lowast is only allowed to beupdated when 1198921198771015840 lt 119892lowast


Table 2 Experimental scale

Number oftargets

Area(km2)

Number ofstations 120593learn

Small scale 10 500 times 300 2 200020 500 times 300 3 10000

Medium scale 50 800 times 500 5 15000Large scale 100 1200 times 800 10 20000

Table 3 UAV-related parameters

Name Value of parameter sPayload capacity (kg) 600 900 1200Number of hanging points 4 6 8Weapons W1W2W3Cruising speed (kmh) 180Endurance (h) 20

442 Criteria for Termination of Algorithm Search In thestudy there are two criteria for termination of the ALNSalgorithm

(1)The iteration process should be terminated when thequality of the solution does not improve after the number ofiterations reaches a given value

(2)The iteration process should be terminated when thenumber of iterations reaches a given value

5 Experiments

In this section computational experiments are conductedto test the performance of the proposed algorithms Allthe algorithms are coded with Visual C 40 and the testenvironment is set up on a computer with Intel Core i7-4790CPU 360GHz 32GB RAM running on Windows 7

51 Experimental Design In order to fully test the perfor-mance of the proposed algorithms instances with four dif-ferent sizes are randomly generated respectively 10 targets20 targets 50 targets and 100 targets Three different types ofUAVs were utilized which are UAVs with 4 hanging pointsand 600 kg loads 6 hanging points and 900 kg loads and8 hanging points and 1200 kg loads Three sizes of combatareas 500times 300 km2 800times 500 km2 and 1200times 800 km2 areutilizedThe experimental scale settings are shown in Table 2The values of parameters for the weapons are illustratedin Tables 3 and 4 In the experiment the service time oftargets (unit hours) is generated randomly in (0 1] Thetargetrsquos time window is also generated randomly between 0hours and 12 hours Meanwhile the following restrictions areconsidered in the random generation process (1) the earliestallowed strike time 119890119894 for target 119894 is no less than the time-consumed by the UAV flying from the depot to the target 1199050119894

Table 4 Value of parameters for the weapons

W1 Weight (kg) 75Cost ($ thousand) 68



(2) the difference between the latest required strike time oftarget 119894 119897119894 and its earliest allowed attack time 119890119894 is no morethan 120591 (120591 = 5 hours) and is no less than the service time119878119894

In practical battlefields there is usually a safe distancebetween the depot and the enemy targetThus the depots andthe enemy targets are randomly generated in different combatzones which can ensure that the distance between each depotand any enemy target is over 100 km

52 Computational Results Analysis

521 Small-Scale Experiment The results of small-scaleexperimentswith 10 targets and 20 targets are shown inTables5 and 6 In the table column 3 presents the initial feasiblesolutions obtained by the constructive heuristic and column4 presents the final solutions obtained by ALNS Column5 presents the computational time consumed by the ALNSalgorithm and column 6 proposes the improvement (Impro)of the final solution relative to the initial solution In orderto further analyze the performance of the six neighborhoodstructures utilized in ALNS we calculated the percentageof the number of times that each neighborhood structureis invoked in the overall iterations of ALNS The resultsare shown in columns 7 to 12 respectively As we can seefrom Table 5 when the ALNS algorithm is used to solvethe instances with 10 targets the average computational timeis 1131 seconds and the average improvement of the finalsolution compared to the initial solution is 4366 As shownin columns 7 to 12 the percentages of six neighborhoodstructures invoked are quite different from each other andthere is no same situation for any two of the thirty instanceswhich indicates that the adaptive learning strategy can effi-ciently adjust the weights of the neighborhood structures inthe search process

The average computational time for instances with 20targets as shown in Table 6 is 2681 seconds and the averageimprovement on the initial solution is 2724 Compared tothe results for instances with 10 targets the ALNS consumesmore time and obtains lower improvement on the initialsolution

In order to show the experimental resultsmore intuitivelythe routing results of instance 51 in Table 6 are graphicallydisplayed in Figure 3 As shown in Figure 3 eight UAVs haveto be dispatched from three stations


Table5Ex

perim

entalresultsforinstances

with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]

Target[a b] Time window

Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X

Figure 3 An illustration of the routing results for instance 51

522 Medium-Scale and Large-Scale Experiments FromTables 5 and 6 we can see that the performance of ALNSon improving the initial solution decreases as the problemscale increases when the total number of iterations remainsunchanged In order to get better results the number ofiterations 120593learn is increased as the problem size increasesand we set 120593learn = 15000 for solving instances with 50 targetsand set cases 120593learn = 20000 for solving instances with 100targets

The results are presented in Tables 7 and 8 As we cansee from Table 7 when ALNS algorithm is used to solve theinstances with 50 targets the average computational time ofthe algorithm is 6055 seconds and the average improvementof the final solution compared to the initial solution is 1925The results for instances with 100 targets in Table 8 show thatthe average calculation time is 20613 seconds and the averageimprovement (Impro) of the final solution compared to theinitial solution is 1954

The computational time for the heuristic to constructinitial feasible solution is less than one second and thuswe donot report the detailed time for all instances The maximumcomputational time for the instance with 100 targets is 22837seconds which is acceptable for mission planning in currentwars For most of the instances the ALNS can make goodimprovement on their initial solutions which indicates thatthe solution obtained by the ALNS is relatively better andcan satisfy the requirement of practical mission planningWenote that the improvement on some instances is less than 10and the similarity of these instances is that the UAV utilizedin them has 4 hanging points and a payload of 600 kg Wecan see that the combination scale for solving these instancesis lower and the constructive heuristic can present a betterinitial solution which provides a better start point for theALNS Thus although the ALNS may find a relative goodsolution its improvement compared to the initial solution isnot so big

6 Summary

This paper focuses on the mathematical model and solutionalgorithm design for a multidepot UAV routing problemwith consideration of weapon configuration in UAV and timewindow of the target A four-step heuristic is designed toconstruct an initial feasible solution and then the ALNSalgorithm is proposed to find better solutions Experimentsfor instances with different scales indicate that the con-structive heuristic can obtain a feasible solution in onesecond and the ALNS algorithm can efficiently improve thequality of the solutions For the largest instances with 100targets the proposed algorithms can present a relative goodsolution within 4 minutes Thus the overall performance ofthe algorithm can satisfy the practical requirement of com-manders for military mission planning of UAVs in currentwars

The UAV routing problem with weapon configurationand time window is new extension on the traditionalvehicle routing problem and there are many new topicsrequired to study in future research More efficient algo-rithms should be developed and compared with the ALNSalgorithm which is a broad and hard research As theproblem considered in this paper is quite complicatedthere are no benchmark instances that consider exactlythe same situation in literatures Thus we generate ran-dom instance based on practical military operation rules totest the proposed algorithm In next research benchmarkinstances from practical military applications need to beconstructed and used to test the performance of differentalgorithms

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request


Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954


Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research is supported by the National Natural ScienceFoundation of China (no 71771215 no 71471174 and no71471175)

References

[1] C Kurkcu and K Oveyik ldquoUS Unmanned Aerial Vehicles(UAVs) and Network Centric Warfare (NCW) Impacts onCombat Aviation Tactics from Gulf War I Through 2007 IraqrdquoThesis Collection 2008

[2] RW FoxUAVs Holy Grail for Intel Panacea for RSTA orMuchAdo about Nothing UAVs for theOperational Commander 1998

[3] J R Dixon UAV Employment in Kosovo Lessons for theOperational Commander Uav Employment in Kosovo Lessonsfor the Operational Commander 2000

[4] D A Fulghum Kosovo Conflict Spurred New Airborne Technol-ogy Use Aviation Week amp Space Technology 1999

[5] J Garamone Unmanned Aerial Vehicles Proving Their Worthover Afghanistan Army Communicator 2002

[6] C Xu H Duan and F Liu ldquoChaotic artificial bee colonyapproach to Uninhabited Combat Air Vehicle (UCAV) pathplanningrdquo Aerospace Science and Technology vol 14 no 8 pp535ndash541 2010

[7] E Edison and T Shima ldquoIntegrated task assignment and pathoptimization for cooperating uninhabited aerial vehicles usinggenetic algorithmsrdquo Computers amp Operations Research vol 38no 1 pp 340ndash356 2011

[8] B Zhang W Liu Z Mao J Liu and L Shen ldquoCooperativeand geometric learning algorithm (CGLA) for path planning ofUAVs with limited informationrdquo Automatica vol 50 no 3 pp809ndash820 2014

[9] S Moon D H Shim and E Oh Cooperative Task Assignmentand Path Planning for Multiple UAVs Springer Amesterdamthe Netherlands 2015

[10] P Yang K Tang J A Lozano and X Cao ldquoPath planningfor single unmanned aerial vehicle by separately evolvingwaypointsrdquo IEEE Transactions on Robotics vol 31 no 5 pp1130ndash1146 2015

[11] V K Shetty M Sudit and R Nagi ldquoPriority-based assignmentand routing of a fleet of unmanned combat aerial vehiclesrdquoComputers amp Operations Research vol 35 no 6 pp 1813ndash18282008

[12] F Mufalli R Batta and R Nagi ldquoSimultaneous sensor selectionand routing of unmanned aerial vehicles for complex missionplansrdquo Computers amp Operations Research vol 39 no 11 pp2787ndash2799 2012

[13] X Liu Z Peng L Zhang and L Li ldquoUnmanned aerial vehicleroute planning for traffic information collectionrdquo Journal ofTransportation Systems Engineering amp Information Technologyvol 12 no 1 pp 91ndash97 2012

[14] T Moyo and F D Plessis ldquoThe use of the travelling salesmanproblem to optimise power line inspectionsrdquo in Proceedings ofthe 6th Robotics andMechatronics Conference pp 99ndash104 IEEEOctober 2013

[15] F Guerriero R Surace V Loscrı and E Natalizio ldquoA multi-objective approach for unmanned aerial vehicle routing prob-lem with soft time windows constraintsrdquo Applied MathematicalModelling vol 38 no 3 pp 839ndash852 2014

[16] L Evers T Dollevoet A I Barros and H Monsuur ldquoRobustUAVmission planningrdquoAnnals of Operations Research vol 222no 1 pp 293ndash315 2014

[17] Z Luo Z Liu and J Shi ldquoA two-echelon cooperated routingproblem for a ground vehicle and its carried unmanned aerialvehiclerdquo Sensors vol 17 no 5 2017

[18] M R Ghalenoei H Hajimirsadeghi and C Lucas ldquoDiscreteinvasive weed optimization algorithm application to coop-erative multiple task assignment of UAVsrdquo in Proceedings ofthe 48th IEEE Conference on Decision and Control held jointlywith 28th Chinese Control Conference pp 1665ndash1670 IEEEDecember 2009

[19] J George P B Sujit and J B Sousa ldquoSearch strategies formultipleUAV search and destroymissionsrdquo Journal of Intelligentamp Robotic Systems vol 61 no 1ndash4 pp 355ndash367 2011

[20] L Zhong Q Luo D Wen S-D Qiao J-M Shi and W-MZhang ldquoA task assignment algorithm formultiple aerial vehiclesto attack targets with dynamic valuesrdquo IEEE Transactions onIntelligent Transportation Systems vol 14 no 1 pp 236ndash2482013

[21] X Hu H Ma Q Ye and H Luo ldquoHierarchical method of taskassignment for multiple cooperating UAV teamsrdquo Journal ofSystems Engineering and Electronics vol 26 no 5 Article ID7347860 pp 1000ndash1009 2015

[22] G Y Yin S L Zhou J C Mo M C Cao and Y H KangldquoMultiple task assignment for cooperating unmanned aerialvehicles using multi-objective particle swarm optimizationrdquoComputer amp Modernization no 252 pp 7ndash11 2016

[23] L Jin ldquoResearch on distributed task allocation algorithmfor unmanned aerial vehicles based on consensus theoryrdquo inProceedings of the 28th Chinese Control andDecision Conferencepp 4892ndash4897 May 2016

[24] S Ropke and D Pisinger ldquoAn adaptive large neighborhoodsearch heuristic for the pickup and delivery problem with timewindowsrdquo Transportation Science vol 40 no 4 pp 455ndash4722006

[25] N Azi M Gendreau and J-Y Potvin ldquoAn adaptive large neigh-borhood search for a vehicle routing problem with multipleroutesrdquoComputers ampOperations Research vol 41 no 1 pp 167ndash173 2014

[26] A Bortfeldt T Hahn D Mannel and L Monch ldquoHybridalgorithms for the vehicle routing problem with clusteredbackhauls and 3D loading constraintsrdquo European Journal ofOperational Research vol 243 no 1 pp 82ndash96 2015

[27] G Dueck ldquoNew optimization heuristics the great delugealgorithm and the record-to-record travelrdquo Journal of Compu-tational Physics vol 104 no 1 pp 86ndash92 1993

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Submit your manuscripts atwwwhindawicom


Table 1 Weapon-target combat ability matrix

Small smartbomb

Small precisionguided bomb

Laser-guidedbomb

Bridge 035 065 095Communicationstation 04 055 075

weapons Table 1 presents the combat ability matrix of threedifferent weapons on two targets It can be seen that ifthe destroy requirement for the bridge target is restrictedover 90 in the mission there are a number of combinationsof weapons that can satisfy the requirement such as 3small smart bombs 1 small smart bomb 1 small precisionguided bomb and 1 laser-guided bomb Thus the weaponsdelivered to a target are not deterministic and are impactedby the weapon configuration and routing strategies of theUAV while the types and quantities of products deliveredto each customer are deterministic in the general VRPproblem

Motivated by the practical requirement in military mis-sion planning of UAV we investigated the multidepot UAVrouting problem with weapon configuration and time win-dow (MD-URP-WCampTW) which can be viewed as a newextension on the traditional VRP In MD-URP-WCampTWthree kinds of decisions should be cooperatively optimizedwhich are the weapon configuration strategy in the UAVthe routing strategy of target and the allocation strategy ofweapons to targets The interaction among these decisionsmakes the modelling and solution of the problem morecomplex In this paper a mixed-integer linear program-ming model is developed to formulate the problem anda powerful adaptive large neighborhood search (ALNS)based metaheuristic is proposed to obtain better feasiblesolutions

The paper is organized as follows In Section 2 the relatedliteratures are reviewed The formulated model is developedin Section 3 and the proposed ALNS algorithm includingits main steps is presented in Section 4 The computationalresults are reported and analyzed in Section 5 Section 6concludes the paper

2 Literature Review

Multidepot UAV routing problem with consideration ofweapon configuration and time window is related to mainstreams of literatures which are UAV path planningroutingandUAV task assignment A review of the literatures on thesetwo fields is summarized below

The earlier studies in the field of UAV flight path opti-mization mainly focused on optimizing the UAV flight pathfrom the control level It is necessary to consider the influ-ence of the turning angle obstacle avoidance and weatherconditions (such as wind power level) on the UAV Based onthese constraints an optimal flight path is found for the UAV[6] Edison and Shima [7] studied the mission planning andpath planning ofmulti-UAV inmilitary operationsThey fullyconsidered flight parameters such as the minimum turningradius in the proposed mathematical model and solved the

problem using a genetic algorithm Zhang et al [8] studiedmulti-UAV path planning considering mobility collisionavoidance and flight information sharing and proposed theCooperative and Geometric Learning Algorithm (CGLA)to solve the above problem Moon et al [9] developed amultilevel planning model for multi-UAV task assignmentand path planning taking into account practical constraintssuch as collision avoidance between UAVs and solved theproblem by the Alowast algorithm Yang et al [10] studied the pathplanning problem of UAV in terms of obstacle avoidancedecomposed the original goal and constraint function ofUAV path planning into a new set of evaluation functionsand proposed the evolutionary algorithm for solving theproblem

With the improvement in intelligent control technologyfor UAVs UAVs can independently complete the flightbetween the target points In recent years studies on UAVpath planning have begun to focus on tactical optimizationin order to minimize the overall minimum flight distance byoptimizing the sequence of UAV to visit the target Shettyet al [11] studied multi-UAV task assignment and routingproblems based on target priority and distinguished thetargets by their degrees of importance using the Tabu searchalgorithm Mufalli et al [12] studied the multi-UAV routingproblem for target reconnaissance considering the load con-straints of the UAV and solved the problem by the columngeneration and heuristic algorithm Liu et al [13] studiedthe UAV deployment and routing problem for road-trafficinformation collection Subject to the number of UAVs andthe maximum cruise distance a multiobjective optimizationmodel was developed Moyo and Plessis [14] studied theinspection path optimization problem for the cable networkof UAVs and described it as a traveling salesman problem(TSP) Guerriero et al [15] proposed a system of UAVs thatare able to communicate self-organize and cooperate Amulticriteria optimizationmodelwas developed to determinethe distributed dynamic schedule of UAVs and ensure bothspatial coverage and temporal coverage of specific targetsEvers et al [16] studied multi-UAV path planning with targetreconnaissance time windows Luo et al [17] studied thetwo-echelon routing problem of mounting UAV on a groundvehicle (GV) where the GV acts as the mobile depot forlaunching and recycling the UAV while the UAV visits thetargets for information collection

In order to facilitate multi-UAV collaborative task alloca-tion during mission planning Ghalenoei et al [18] proposedthe Discrete Invasive Weed Optimization Algorithm for spe-cific target attributes and geographical locations George etal [19] proposed an online task assignment algorithm basedon UAV task alliance to deal with unexpected tasks whichinvolves requesting adjacent UAVs to form task alliances andreplanning the tasks Zhong et al [20] studied the UAV taskassignment problem with dynamic changes in target valueover time taking into account various constraints includingUAV flight altitude maximum climb height and maximumturning radius Hu et al [21] studied the assignment ofUAV collaborative tasks using the hierarchical assignmentmethod and solved the problem by an improved ant colonyalgorithm Yin et al [22] described the UAV collaborative


1 2

610

3

12

4

5

8

9

7 11

Depot

Target

Route




3 Model Formulation



(1) Sets


(2) Parameters





min 119885

= 1198751119899+119898

sum119894=119899+1

119899

sum119895=1

119906

sum119896=1

119909119894119895119896 + 1198752119908

sumℎ=1

119906

sum119896=1

119899

sum119894=1

119891ℎ119910119896ℎ119894

+ 1198753119899+119898

sum119894=1

119899+119898

sum119895=1

119906

sum119896=1

(119905119894119895 + 119908119896119894 + 119904119894) 119909119894119895119896

(1)

subject to119906

sum119896=1

119899+119898

sum119894=0119894 =119895

119909119894119895119896 = 1 forall119895 isin 119873 (2)


119906

sum119896=1

119899+119898

sum119895=0119894 =119895

119909119894119895119896 = 1 forall119894 isin 119873 (3)

119899+119898

sum119894=1

119909119894119901119896 minus119899+119898

sum119895=1

119909119901119895119896 = 0


(4)

119908

sumℎ=1

119902ℎ119899

sum119894=1

119910119896ℎ119894 le 119888 forall119896 isin 119880 (5)

119908

sumℎ=1

119899

sum119894=1

119910119896ℎ119894 le 119892 forall119896 isin 119880 (6)

V

sum119896=1

119908

sumℎ=1

119887ℎ119894119910119896ℎ119894 le 119886119894 forall119894 isin 119873 (7)

119910119896ℎ119894 le 119871119899

sum119895=1

119909119894119895119896


(8)

119899+119898

sum119894=0

119899+119898

sum119895=0

(119905119894119895 + 119904119894 + 119908119896119894) 119909119894119895119896 le 119903


(9)

119905119896119894 + 119905119894119895 + 119908119896119894 + 119904119894 minus 119871 (1 minus 119909119894119895119896) le 119905119896119895

forall119894 isin 119873(10)

119905119896119894 + 119908119896119894 ge 119890119894 forall119894 isin 119873 (11)

119905119896119894 + 119908119896119894 + 119904119894 le 119897119894 forall119894 isin 119873 (12)












4 Algorithm







Return 119908119886119905119894119898 (119898 isin 119882)




119872119898=1 119908119886119905119894119898 le 119892) then

119862119882119867 = 1endelse

119908119886119905119894119898lowast = 0119882 = 119882119898lowast






eff119894119898 =119887119894119898119891119898

(16)








Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12
















endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1 2

610

3

12

4

5

8

9

7 11

Depot

Target

Route




3 Model Formulation



(1) Sets


(2) Parameters





min 119885

= 1198751119899+119898

sum119894=119899+1

119899

sum119895=1

119906

sum119896=1

119909119894119895119896 + 1198752119908

sumℎ=1

119906

sum119896=1

119899

sum119894=1

119891ℎ119910119896ℎ119894

+ 1198753119899+119898

sum119894=1

119899+119898

sum119895=1

119906

sum119896=1

(119905119894119895 + 119908119896119894 + 119904119894) 119909119894119895119896

(1)

subject to119906

sum119896=1

119899+119898

sum119894=0119894 =119895

119909119894119895119896 = 1 forall119895 isin 119873 (2)


119906

sum119896=1

119899+119898

sum119895=0119894 =119895

119909119894119895119896 = 1 forall119894 isin 119873 (3)

119899+119898

sum119894=1

119909119894119901119896 minus119899+119898

sum119895=1

119909119901119895119896 = 0


(4)

119908

sumℎ=1

119902ℎ119899

sum119894=1

119910119896ℎ119894 le 119888 forall119896 isin 119880 (5)

119908

sumℎ=1

119899

sum119894=1

119910119896ℎ119894 le 119892 forall119896 isin 119880 (6)

V

sum119896=1

119908

sumℎ=1

119887ℎ119894119910119896ℎ119894 le 119886119894 forall119894 isin 119873 (7)

119910119896ℎ119894 le 119871119899

sum119895=1

119909119894119895119896


(8)

119899+119898

sum119894=0

119899+119898

sum119895=0

(119905119894119895 + 119904119894 + 119908119896119894) 119909119894119895119896 le 119903


(9)

119905119896119894 + 119905119894119895 + 119908119896119894 + 119904119894 minus 119871 (1 minus 119909119894119895119896) le 119905119896119895

forall119894 isin 119873(10)

119905119896119894 + 119908119896119894 ge 119890119894 forall119894 isin 119873 (11)

119905119896119894 + 119908119896119894 + 119904119894 le 119897119894 forall119894 isin 119873 (12)












4 Algorithm







Return 119908119886119905119894119898 (119898 isin 119882)




119872119898=1 119908119886119905119894119898 le 119892) then

119862119882119867 = 1endelse

119908119886119905119894119898lowast = 0119882 = 119882119898lowast






eff119894119898 =119887119894119898119891119898

(16)








Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12
















endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



119906

sum119896=1

119899+119898

sum119895=0119894 =119895

119909119894119895119896 = 1 forall119894 isin 119873 (3)

119899+119898

sum119894=1

119909119894119901119896 minus119899+119898

sum119895=1

119909119901119895119896 = 0


(4)

119908

sumℎ=1

119902ℎ119899

sum119894=1

119910119896ℎ119894 le 119888 forall119896 isin 119880 (5)

119908

sumℎ=1

119899

sum119894=1

119910119896ℎ119894 le 119892 forall119896 isin 119880 (6)

V

sum119896=1

119908

sumℎ=1

119887ℎ119894119910119896ℎ119894 le 119886119894 forall119894 isin 119873 (7)

119910119896ℎ119894 le 119871119899

sum119895=1

119909119894119895119896


(8)

119899+119898

sum119894=0

119899+119898

sum119895=0

(119905119894119895 + 119904119894 + 119908119896119894) 119909119894119895119896 le 119903


(9)

119905119896119894 + 119905119894119895 + 119908119896119894 + 119904119894 minus 119871 (1 minus 119909119894119895119896) le 119905119896119895

forall119894 isin 119873(10)

119905119896119894 + 119908119896119894 ge 119890119894 forall119894 isin 119873 (11)

119905119896119894 + 119908119896119894 + 119904119894 le 119897119894 forall119894 isin 119873 (12)












4 Algorithm







Return 119908119886119905119894119898 (119898 isin 119882)




119872119898=1 119908119886119905119894119898 le 119892) then

119862119882119867 = 1endelse

119908119886119905119894119898lowast = 0119882 = 119882119898lowast






eff119894119898 =119887119894119898119891119898

(16)








Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12
















endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Return 119908119886119905119894119898 (119898 isin 119882)




119872119898=1 119908119886119905119894119898 le 119892) then

119862119882119867 = 1endelse

119908119886119905119894119898lowast = 0119882 = 119882119898lowast






eff119894119898 =119887119894119898119891119898

(16)








Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12
















endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12

Depot(1) Depot(2)

T6

T9

T3

T10T11

T1 T2 T4

T5

T7

T8T12
















endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










endelse



end119888119906119898119898119864119909119890119888119906119905119890 = 0 119888119906119898119898119879119900119863119890119901119900119905 = 0 119888119906119898119898119879119900119873119890119909119905 = 0

endReturn 120577















ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












ℎ119894=1 120596119894


120596119894119895+1 = 120596119894119895 (1 minus 119903) + 119903120590119894119895120576119894119895 (17)














Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Number oftargets

Area(km2)









5 Experiments














Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table5Ex

perim


with

10targets

UAVcapacity

No

Initial

solutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

DE

TRC

WR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

1503times106

318times106

1320

3676

2080

1986

1778

1457

1390

1308

2580times106

360times106

1180

3799

1474

1946

1828

1608

1742

1402

3599times106

310times106

1342

4810

1533

1816

1973

1596

1565

1517

4495times106

305times106

1057

3839

1231

1651

1986

1936

1683

1511

5508times106

339times106

967

3322

1069

1698

1783

1840

1857

1754

6622times106

390times106

1270

3725

914

1718

1974

1574

1873

1946

7549times106

369times106

1058

3266

1483

1896

1866

1380

1841

1534

8589times106

383times106

1321

3492

1379

2173

1773

1441

1829

1405

9574times106

335times106

932

4160

1555

1597

1798

1559

1493

1998

10550times106

355times106

1169

3549

2157

1617

1952

1325

1438

1510

6hang

ingpo

ints

andload

of900k

g

11597times106

315times106

1009

4719

515

1991

1900

1729

1944

1922

12639times106

325times106

905

4906

1293

1582

1847

1982

1674

1622

13670times106

373times106

963

4431

1281

1909

1947

1744

1477

1643

1476

5times106

417times106

978

4550

2033

1884

1462

1417

1689

1515

15571times106

311times106

1223

4547

854

1836

1957

1728

1723

1902

16673times106

328times106

1374

5124

2204

1863

1687

1590

1306

1350

17644

times106

345times106

955

4635

1426

1492

1801

1389

1925

1968

18650times106

341times106

1127

4751

2364

1813

1466

1362

1588

1408

19608times106

313times106

972

4849

1621

1932

1631

1681

1431

1703

20639times106

347times106

934

4560

2063

1923

1830

1525

1346

1313

8hang

ingpo

ints

andd

load

of1200

kg

21662times106

347times106

946

4751

1701

1669

1802

1728

1588

1512

22664times106

385times106

1331

4201

1970

1729

1594

1325

1560

1822

2372

4times106

395times106

1174

4547

1760

1433

1603

1837

1980

1387

24668times106

397times106

1305

4045

1288

1421

1613

1923

1914

1840

2575

6times106

399times106

1197

4716

2057

1855

1364

1426

1945

1353

26654times106

344

times106

1312

4727

1919

1333

1644

1964

1517

1622

27632times106

359times106

1299

4315

2402

1715

1651

1355

1527

1350

2872

2times106

344

times106

1067

5234

1481

1932

1577

1746

1505

1759

29679times106

380times106

1091

4399

2274

1530

1349

1920

1592

1335

3076

3times106

356times106

1162

5325

1265

1363

1658

1886

1919

1909

Average

1131

4366


Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table6Ex

perim


with

20targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

3192

9times106

799times106

2508

1406

1496

1945

2251

1357

1261

1689

3299

5times106

786times106

2948

2095

1385

2327

1955

1619

1036

1679

3395

2times106

753times106

3099

2086

1681

2579

1906

1731

1147

956

3498

3times106

807times106

2295

1794

1511

2105

2503

1784

1196

900

3590

9times106

728times106

2739

1982

1211

2115

2534

1145

983

2012

3691

2times106

777times106

2727

1472

1526

2253

2528

1609

1420

663

3710

1times107

876times106

2581

1379

1549

2381

2207

1052

1149

1663

3898

4times106

820times106

3067

1673

1863

2215

2206

1750

883

1083

39889times106

801times106

2786

996

1365

2704

2204

1633

1036

1059

40847times106

729times106

2757

1390

1596

2204

2295

1618

1139

1148

6hang

ingpo

ints

andload

of900k

g

4112

0times107

960times106

3070

2060

1162

2700

1825

1718

1149

1446

4212

9times107

979times106

2409

2431

1692

2251

2538

1722

1360

438

4313

3times107

934times106

2289

3009

1846

2341

1280

1521

1779

1234

4413

3times107

826times106

2350

3828

1697

1844

2467

1607

1129

1257

45119times107

912times106

2676

2352

1607

2229

2309

1216

1154

1485

46110times107

850times106

3074

2307

1826

1921

2569

1615

1217

850

4712

7times107

856times106

2503

3266

1638

2177

2193

1711

1304

977

4812

6times107

101times

107

2480

2074

1449

2674

2269

1424

1199

985

49118times107

849times106

2608

2857

1857

2777

2250

1333

1457

326

5013

2times107

894times106

2454

3252

1615

2693

2009

1152

1144

1387

8hang

ingpo

ints

andload

of1200

kg

5114

3times107

995times106

2652

3051

1549

2587

2120

1128

1192

1424

5215

2times107

948times106

3054

3789

1806

2597

2402

800

1544

852

5314

5times107

101times

107

2407

3003

1664

2698

2241

1401

1148

849

5413

7times107

837times106

2708

3904

1672

2659

2111

1201

1221

1136

5514

5times107

905times106

2682

3754

1494

2446

2083

831

1315

1831

5614

4times107

957times106

2777

3348

1716

2476

2344

1091

1725

649

5715

7times107

884times106

2261

4382

1791

2526

1704

917

1160

1903

5815

2times107

709times106

2985

5348

1555

2712

1833

1731

1001

1169

5915

2times107

934times106

2419

3855

1810

2668

2302

971

1269

980

6015

7times107

101times

107

3057

3582

1822

2398

1740

948

1067

2027

Average

2681

2724


10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



10

1811

13

19

9

1612

14 2

205

177

6

4 3

1

158

Y

Depot(2)Depot(3)

[212 303]

[232 314]

[358 413]

[187 231]

[195 274]

[267 385]

[192 247]

[230 322]

[175 233]

[202 294] [307 391]

[221 307][192 245]

[221 297]

[241 351]

[221 298]

[202 291]

[227 302]

[247 341]


Depot

Depot(1)00

5000

10000

15000

20000

25000

30000

3000020000 40000 500001000000X





6 Summary



Data Availability



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table7Ex

perim


with

50targets

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

6133

5times107

320times107

5969

446

1050

2276

2244

1530

1143

1756

62372times107

344

times107

5695

745

1110

2407

1784

1308

1610

1780

63339times107

323times107

5732

454

1979

2075

1530

1266

1638

1512

64346times107

328times107

5696

504

2346

1937

1376

1306

1210

1825

65330times107

306times107

6817

741

2178

2011

1319

1278

1406

1808

6635

1times107

332times107

5477

550

1778

2041

1611

1390

1320

1859

67352times107

325times107

5630

756

1826

2486

1757

1140

922

1869

68345times107

327times107

6188

503

1437

2109

1857

1469

1244

1884

69327times107

303times107

6230

721

1300

2352

1874

1591

1364

1520

70347times107

333times107

5512

385

1730

2514

1669

1263

1535

1288

6hang

ingpo

ints

andload

of900k

g

71477times107

374times107

6875

2154

932

2579

2198

1409

1293

1588

72496times107

386times107

5685

2213

1547

2427

1560

1188

1443

1834

73487times107

399times107

5932

1815

2042

1993

1299

1379

1733

1553

74494times107

318times107

6199

3553

1355

2368

1231

1240

2002

1804

75515times107

377times107

5388

2677

1806

2424

1784

1295

1495

1195

76493times107

354times107

6040

2820

2248

2044

1856

1593

1002

1257

77469times107

326times107

6843

3050

1702

1907

1726

1346

1728

1591

78472times107

374times107

5520

2078

1115

2177

1802

1634

1978

1294

79496times107

345times107

5317

3054

2213

1885

1584

1679

1353

1285

80453times107

369times107

6845

1851

1285

2326

1622

1289

1182

2297

8hang

ingpo

ints

andload

of1200

kg

81610times107

430times107

5275

2944

848

2358

1594

1555

1753

1892

82593times107

409times107

6612

3098

2103

2470

1863

1164

1134

1266

83543times107

347times107

6299

3603

2270

1928

1433

1563

1399

1406

84596times107

472times107

7537

2084

2716

1819

1518

1437

1151

1360

85591times107

495times107

7327

1618

1692

2471

1361

1642

1041

1793

86605times107

490times107

5648

1909

1893

2375

1221

1604

1386

1520

87574times107

375times107

6469

3466

1446

2586

1352

1518

1305

1793

88557times107

416times107

5870

2533

2177

2012

1803

1446

1395

1167

89582times107

406times107

5846

3024

1871

1880

1179

1714

1696

1660

90592times107

449times107

5190

2417

2014

2280

1402

1389

1245

1670

Average

6055

1925


Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table8Ex

perim


with

100targets

Mou

ntingcapacity

No

Initialsolutio

nFinalsolution

Time

(s)

Impro

()

Invokedpercentageso

fneighbo

rhoo

dstructures

()

EDTR

CWR

RNW

RCW

RWW

4hang

ingpo

ints

andload

of60

0kg

91733times107

683times107

20443

676

2118

1528

1809

1289

1732

1524

92801times107

725times107

20593

935

1654

1649

1626

1645

1623

1803

93851times107

782times107

2117

0806

1948

1534

1449

1461

2155

1453

9478

9times107

737times107

22081

653

1471

2119

1430

1758

1508

1714

9579

1times107

729times107

2197

478

51644

1699

1839

1744

1953

1121

96804times107

731times

107

2173

491

21787

1310

1975

1545

1868

1517

97711times

107

650times107

19237

856

1344

2088

1749

1878

1349

1593

98755times107

688times107

19887

887

2091

1470

1429

1750

1319

1941

9977

1times107

699times107

19400

925

1553

1560

1796

1588

1779

1725

100

780times107

723times107

20240

727

1587

2067

1663

1769

1305

1609

6hang

ingpo

ints

andload

of900k

g

101

118times108

882times107

22535

2531

1843

1851

1448

1859

1209

1791

102

117times108

826times107

2199

12976

1323

2182

1290

1540

1713

1952

103

109times108

964times107

21312

1215

1509

1512

1707

1700

1722

1848

104

122times108

889times107

22837

2759

1845

1226

1970

1729

1378

1852

105

115times108

909times107

1914

52132

1963

1389

1766

1759

1763

1361

106

110times108

743times107

22258

3301

1578

2192

1489

1447

1988

1306

107

114times108

888times107

22252

2242

2129

2088

1736

1213

1423

1411

108

107times108

890times107

21535

1720

2116

1981

1218

1909

1202

1573

109

117times108

869times107

18088

2576

1427

2096

1956

1842

1960

718

110111times

108

741times

107

22802

3378

1523

1216

1577

2221

1909

1554

8hang

ingpo

ints

andload

of1200

kg

111

109times108

844

times107

18316

2287

1992

1884

1968

1615

1372

1169

112

118times108

954times107

21202

1954

1576

1467

1571

1965

1535

1885

113

123times108

786times107

1992

33635

1291

1266

1786

1513

1583

2561

114114times108

810times107

22206

2923

1814

1815

1313

1675

1649

1735

115

124times108

101times

108

19409

1898

1528

1908

1669

1503

1862

1530

116117times108

942times107

19235

2010

2179

1618

1502

1280

1889

1532

117111times

108

722times107

1817

93477

1487

1541

1475

2246

1544

1707

118118times108

957times107

2118

11930

1956

2063

1306

1444

1262

1969

119114times108

860times107

18632

2514

1696

2116

1386

1580

1913

1309

120

118times108

833times107

18589

2990

1688

1685

1806

1991

1456

1374

Average

20613

1954




Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Acknowledgments


References






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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