OPTIMIZATION OF ROUTING AND WAVELENGTH

ASSIGNMENT IN PASSIVE OPTICAL NETWORKS

A PROJECT REPORT

Submitted by

ROSHNI .V.V

Register No:14MAE015

in partial fulfillment for the award of the degree

of

MASTER OF ENGINEERING

in

APPLIED ELECTRONICS

Department of Electronics and Communication Engineering

KUMARAGURU COLLEGEOF TECHNOLOGY

(An autonomous institution affiliated to Anna University, Chennai)

COIMBATORE-641049

ANNA UNIVERSITY: CHENNAI 600 025

APRIL 2016

ii

BONAFIDE CERTIFICATE

Certified that this project report titled “OPTIMIZATION OF ROUTING AND

WAVELENGTH ASSIGNMENT IN PASSIVE OPTICAL NETWORKS” is the

bonafide work of ROSHNI .V.V. [Reg. No. 14MAE015] who carried out the research

under my supervision. Certified further, that to the best of my knowledge the work

reported here in does not form part of any other project or dissertation on the basis of

which a degree or award was conferred on an earlier occasion on this or any other

candidate.

SIGNATURE

SIGNATURE

Ms.R.HEMALATHA Dr. A.VASUKI

PROJECT SUPERVISOR PROFESSOR AND HEAD

Associate Professor Department of ECE

Department of ECE Kumaraguru College of Technology

Kumaraguru College of Technology Coimbatore-641 049

Coimbatore-641 049

The Candidate with Register No. 14MAE015 was examined by us in the project

viva –voice examination held on............................

INTERNAL EXAMINER EXTERNAL EXAMINER

iii

ACKNOWLEDGEMENT

First, I would like to express my praise and gratitude to the Lord, who has

showered his grace and blessings enabling me to complete this project in an excellent

manner.

I express my sincere thanks to the management of Kumaraguru College of

Technology and Joint Correspondent Mr. Shankar Vanavarayar for the kind support

and for providing necessary facilities to carry out the work.

I would like to express my sincere thanks to our beloved Principal

Dr.R.S.Kumar Ph.D., Kumaraguru College of Technology, who encouraged me in each

and every steps of the project.

I would like to thank Dr. A. Vasuki Ph.D., Head of the Department, Electronics

and Communication Engineering, for her kind support and for providing necessary

facilities to carry out the project work.

In particular, I wish to thank with everlasting gratitude to the Project

Coordinator Ms.S.Umamaheswari M.E.(Ph.D), Associate Professor, Department of

Electronics and Communication Engineering ,for her expert counseling and guidance to

make this project to a great deal of success.

I am greatly privileged to express my heartfelt thanks to my Project Guide

Ms.R.Hemalatha M.E.(Ph.D), Associate Professor, Department of Electronics and

Communication Engineering, throughout the course of this project work and I wish to

convey my deep sense of gratitude to all teaching and non-teaching staff of ECE

Department for their help and cooperation.

Finally, I thank my parents and my family members for giving me the moral

support and abundant blessings in all of my activities and my dear friends who helped me

to endure my difficult times with their unfailing support and warm wishes.

iv

ABSTRACT

Routing and Wavelength Assignment (RWA) problem is one of the important

optimization problems in optical networks. RWA problem are of two types, static and

dynamic. In static RWA the set of connections is known in advance where as in dynamic

RWA connection request arrive sequentially. In the proposed work the dynamic routing

and wavelength assignment problem is examined. The goal is to minimize the number of

wavelengths and blocking probability. Evolutionary programming algorithms are used

to optimize the routing and wavelength assignment. The RWA problem can be fixed by

number of algorithms like PSO, ACO etc.

Genetic Algorithm and Shuffled Frog Leaping Algorithm (SFLA) have been

implemented in optical networks to fix the RWA problem. Cost, number of wavelengths,

hop count and blocking probability are the optimization parameters. In WDM network,

for the given set of connection requests, routing and wavelength assignment problem

involves the task of establishing lightpaths (routing) and assigning a wavelength to each

connection request.

The problem is analyzed for different wavelength assignment methods such as

first fit, random, round robin, wavelength ordering and FWM priority based assignment.

Fitness function is calculated in terms of cost, number of wavelengths, hop count and

setup time. The experimental result shows that the network has better blocking

performance when using Shuffled Frog Leaping Algorithm with FWM aware priority

based wavelength assignment. SFLA algorithm produces less blocking probability, less

cost and less computational complexity than existing methods.

v

TABLE OF CONTENTS

CHAPTER NO. TITLE PAGE NO.

ABSTRACT iv

LIST OF TABLES vii

LIST OF FIGURES viii

LIST OF ABBREVIATIONS ix

1. INTRODUCTION 1

1.1 OPTICAL AMPLIFIERS 1

1.2 WDM 2

1.3 ROUTING AND WAVELENGTH

ASSIGNMENT 3

1.4 GENETIC ALGORITHM 3

1.5 SHUFFLED FROG LEAPING ALGORITHM 4

2. LITERATURE SURVEY 5

3. EVOLUTIONARY PROGRAMMING METHOD 10

3.1 BLOCK DIAGRAM 10

3.2 NETWORK MODEL 10

3.3 ROUTING MODEL 12

3.3.1 Fixed Path Routing 14

3.3.2 Fixed Alternate Routing 15

3.3.3 Adaptive Routing 15

3.3.4 Traditional Adaptive RWA 16

3.3.5 Physically Aware Adaptive RWA 16

3.4 WAVELENGTH ASSIGNMENT MODEL 17

3.5 GENETIC ALGORITHM 19

3.5.1 Flow Chart of Genetic Algorithm 20

vi

3.5.2 Create a Random Initial Population 20

3.5.3 Evaluate Fitness 21

3.5.4 Produce Next Generation 21

3.5.5 Next Generation or Termination 21

3.5.6 Advantages of Genetic Algorithm 22

3.6 SHUFFLED FROG LEAPING ALGORITHM 23

4. RESULTS AND DISCUSSIONS 25

4.1 FITNESS FUNCTION 25

4.2 MEAN BLOCKING PROBABILITY(W.R.T.

CHANNEL REJECTION RATIO) 26

4.3 AVERAGE FITNESS SCORE 29

4.4 MEAN BLOCKING PROBABILITY(W.R.T.

GENERATIONS) 30

4.5 MEAN EXECUTION TIME 33

4.6 COMPARISON OF PERFORMANCE

MEASURES IN GA AND SFLA 37

5. CONCLUSION 39

REFERENCES 40

LIST OF PUBLICATIONS 43

vii

LIST OF TABLES

TABLE NO. TITLE

PAGE NO.

4.1 Fitness function of GA and SFLA with

respect to time

26

4.2 Mean blocking probability (wr.t. channel

rejection ratio) of GA

27

4.3 Mean blocking probability (wr.t. channel

rejection ratio) of SFLA

28

4.4 Average fitness score for GA and SFLA 30

4.5 Mean blocking probability (wr.t.

Generations) of GA

31

4.6 Mean blocking probability (wr.t.

Generations) of SFLA

32

4.7 Mean execution time of GA 34

4.8 Mean execution time of SFLA 36

4.9 Comparison of different wavelength

assignment techniques with respect to four

performance measures in GA

37

4.10 Comparison of different wavelength

assignment techniques with respect to four

performance measures in SFLA

38

viii

LIST OF FIGURES

FIGURE NO. TITLE PAGE NO.

1.1 Principle of AON 1

1.2 Principle of PON 2

1.3 Principle of WDM 2

3.1 Block diagram of evolutionary method 10

3.2 Architecture of a wavelength routing node 11

3.3 Model of a transmission lightpath 11

3.4 Flow chart of GA 20

3.5 Flow chart of SFLA 24

4.1 Fitness function of GA and SFLA 25

4.2 Mean blocking probability(w.r.t. channel

rejection ratio) of GA

26

4.3 Mean blocking probability(w.r.t. channel

rejection ratio) of SFLA

28

4.4 Average fitness for fixed network 29

4.5 Mean blocking probability(w.r.t. generations) of

GA

31

4.6 Mean blocking probability(w.r.t. generations) of

SFLA

32

4.7 Mean execution time of GA 33

4.8 Mean execution of SFLA 35

ix

LIST OF ABBREVIATIONS

AON Active Optical Network

PON Passive Optical Network

WDM Wavelength Division Multiplexing

OLT Optical Line Terminal

ONT Optical Network Terminal

RWA Routing and Wavelength Assignment

DRWA Dynamic Routing and Wavelength Assignment

EDFA Erbium Doped Fiber Amplifier

ABC Artificial Bee Colony

GA Genetic Algorithm

GASP Grooming Adaptive Shortest Path Algorithm

FA Firefly Algorithm

GOF Generic Objective Function

SFLA Shuffled Frog Leaping Algorithm

WRN Wavelength Routing Node

XCS Cross Connect Switch

ILP Integer Linear Program

PABR Physically Aware Backward Reservation

FWM Four Wave Mixing

1

CHAPTER 1

INTRODUCTION

1.1 OPTICAL NETWORKS

Optical networks are high capacity telecommunication networks based on

optical technologies and components that provide routing, grooming and restoration at

the wavelength level as well as wavelength based services. Fiber optics uses light

signals to transmit data. As this data moves across a fiber, there needs to be a way to

separate it so that it gets to the proper destination.

There are two important types of systems that make fiber-to-the-home

broadband connections possible. These are active optical networks and passive optical

networks. Each offers ways to separate data and route it to the proper place, and each

has advantages and disadvantages as compared to the other [12].

An active optical system uses electrically powered switching equipment, such

as a router or a switch aggregator, to manage signal distribution and direct signals to

specific customers. This switch opens and closes in various ways to direct the

incoming and outgoing signals to the proper place. In such a system, a customer may

have a dedicated fiber running to his or her house. Fig 1.1 shows the principal of

Active Optical Network (AON).

A passive optical network, on the other hand, does not include electrically

powered switching equipment and instead uses optical splitters to separate and collect

optical signals as they move through the network. A passive optical network shares

fiber optic strands for portions of the network. Powered equipment is required only at

the source and receiving ends of the signal. Fig 1.2 shows the principle of Passive

Optical Network (PON).

Fig 1.1 Principle of AON

2

Fig 1.2 Principle of PON

1.2 WDM

In fiber-optic communications, wavelength division multiplexing (WDM) is a

technology which multiplexes a number of optical carrier signals onto a single optical

fiber by using different wavelengths (i.e., colors) of laser light. This technique enables

bidirectional communications over one strand of fiber, as well as multiplication of

capacity. The term wavelength-division multiplexing is commonly applied to an

optical carrier (which is typically described by its wavelength).

Fig 1.3 Principle of WDM

A WDM system as shown in Fig 1.3 uses a multiplexer at the transmitter to

combine the signals together from different sources operating at different wavelengths

and a demultiplexer at the receiver to split them apart. With the right type of fiber it is

possible to have a device that does both simultaneously and can function as an optical

add-drop multiplexer. Wavelength-division multiplexing (WDM) have high band

width demand. Traffic grooming, Optimal routing and wavelength assignment,

3

survivability, Quality of service (QoS) routing, physical layer impairment aware (PLI

aware) routing and wavelength assignment are different problems that exist in optical

wavelength division multiplexing (WDM) [1].

1.3 ROUTING AND WAVELENGTH ASSIGNMENT (RWA)

In the WDM networks, there is a tight coupling between routing and

wavelength selection. A path of links between the source and destination nodes is

selected and a particular wavelength on each of these links is reserved for the

lightpath. Thus for establishing an optical connection select a suitable path and

allocate an available wavelength for the connection. The resulting problem is called

routing and wavelength allocation (RWA) problem. The routing and wavelength

allocation problem is subject to the following two constraints: Wavelength continuity

constraint and distinct wavelength constraint.

There are two variations in the problem:

1.3.1 Static RWA : The traffic requirements are known in advance.

1.3.2 Dynamic RWA: The sequence of lightpath requests arrive in some random

fashion.

The methods that have been employed to solve RWA problem include classical

approaches and heuristics or metaheuristics-based approaches. Conventional

techniques are able to give accurate results for simple problems. But to solve complex

problems, these techniques have too much computational time [3]&[6]. Multiobjective

evolutionary algorithms are used to solve the RWA problem which is based on swarm

intelligence in real-world optical networks [4]&[5].

1.4 GENETIC ALGORITHM

Genetic algorithm (GA) is a search algorithm based on the mechanics of

natural selection and natural genetics. GA works with individuals, each representing a

solution to the problem being tackled. A fitness function is defined in order to

estimate the goodness of a solution. An initial population of individuals is created and

then evolved by means of genetic operators, such as cross over and mutation, to form

a new population (the next generation) that is hoped to be fitter than the last one. The

evolution process is repeated a predefined number of iterations or until another

criterion is met [2]&[7].

4

The crossover operator is applied to pairs of individuals in order to

interchange their genetic material, imitating natural reproduction. By applying this

operator to the fittest individuals, good properties should propagate down the

generations. The mutation operator makes a random change in genetic material of a

single individual, allowing the GA to explore new corners of the search space. Since

individuals from the population become fitter throughout the generations, the final

population will contain an optimal or near optimal solution.

1.5 SHUFFLED FROG LEAPING ALGORITHM

Shuffled frog leaping algorithm (SFLA) is a meta-heuristic optimization

method which is based on observing, imitating and modeling the behavior of a group

of frogs when searching for the location that has the maximum amount of available

food. Shuffled frog leaping algorithm is a population based random search algorithm

inspired by nature memetics. Instead of using genes in GA, SFLA uses memes to

improve spreading and convergence ratio. Meme is a contagious information pattern

that alters human/animal behavior. The actual contents of a meme, called memotype,

are analogous to the genes of a chromosome. The main difference between a gene and

a meme is related to its transmission ability. Genes can only be transmitted from

parents or a parent in the case of asexual reproduction to offspring. Memes can be

transmitted between any two individuals. SFLA combines the benefit of the local

search tool of Particle Swarm Optimization (PSO) and the idea of mixing information

from parallel local searches, to move towards a global solution [8].

The whole population of frogs is distributed within a different subset called a

memeplex. Each memeplex is considered a different culture of frogs, performing an

independent local search. After a defined number of memetic evolutionary steps, frogs

are shuffled among memeplexes, enabling frogs to interchange messages among

different memeplexes and ensuring that they move to an optimal position, similar to

particles in PSO. The local search and the shuffling processes continue until defined

convergence criteria are satisfied [9].

5

CHAPTER 2

LITERATURE SURVEY

This chapter deals with review of literature about routing and wavelength

assignment using several natural inspired algorithms and comparisons in terms of

performance and computational complexity.

[1] A Metaheuristic Approach for Optical Network Optimization Problems

Urmila Bhanjaa et al proposed a metaheuristic approach for optical network

optimization problems such as QoS routing and DRWA problems in their paper. Genetic

algorithm is used to solve different optimization problems by designing problem specific

fitness functions. The initial search space is very small since the initial population

consists of only a single chromosome. The evolutionary algorithm depends on the

mutation operator alone for creating and exploring the search space .Encodings of the

chromosomes are random and simple and these are of variable length.

[2] Distributed Grooming, Routing, and Wavelength Assignment for Dynamic

Optical Networks Using Ant Colony Optimization

X. Wang et al made a comparison between ant colony optimization algorithm and

a centralized heuristic algorithm, a grooming adaptive shortest path algorithm (GASP) for

routing and wavelength assignment in optical networks. In their examination although

GASP shows better efficiency in terms of blocking probability, ACO shows great

robustness and adaptivity to varying network and traffic conditions.

6

[3] A Comparative Study on Multi objective Swarm Intelligence for the

Routing and Wavelength Assignment Problem

A lvaro Rubio-Largo presented a comparative study on swarm intelligence to

solve the RWA problem. They have evaluated three multi objective metaheuristic based

on the behavior of honey bees (MO-ABC), on the law of gravity and mass interactions

(MO-GSA), as well as on the flash pattern of fireflies (MO-FA) .They concluded that

MO-FA is a very suitable approach to solve the RWA problem.

[4] Routing and wavelength assignment in optical networks using Artificial

Bee Colony algorithm

Yousef S. Kavian et al introduced Artificial Bee Colony algorithm for routing and

wavelength assignment. Every food source represented one of the K possible and feasible

paths between each node pair in optical network. The positions of food sources were

modified by artificial bees and evaluated by the fitness function. In their analysis ABC is

faster than GA to solve RWA problem in real-world EUROPEAN and NSFNET optical

networks.

[5] Evolutionary Algorithms for Solving Routing and Wavelength Assignment

Problem in Optical Networks: A Comparative Study

Arash Rashedi et al described applications of some intelligent algorithms such as

GA, PSO and ABC algorithms for solving routing and wavelength assignment problem in

optical networks. The performances of proposed algorithms were compared for both

convergence speed and accuracy using NSFNET test-bench network considering

randomly generated connection requests. The convergence speed of ABC algorithm is

much better than other two algorithms to reach near-optimum solution in acceptable

processing time.

7

[6] A New Proposal of an Efficient Algorithm for Routing and Wavelength

Assignment in Optical Networks

Afonso Jorge F. Cardoso presented a RWA algorithm based on a Generic

Objective Function (GOF) which aims to establish a base from which it is possible to

develop a standard or multiple standards for optical networks. The GOF algorithm

introduces the concept of implicit constraint, which guarantees a simple solution to a

problem not as trivial as the RWA. In GOF no restriction point is considered, i.e. no

explicit restrictions are considered. RWA is solved and creates the possibility that the

algorithm GOF serve as a standard for optical WDM networks.

[7] Shuffled Frog-Leaping Algorithm: A Memetic Meta-heuristic for Discrete

Optimization

Muzaffar et al proposed a new efficient natural inspired metaheuristic approach,

called Shuffled Frog Leaping Algorithm (SFLA) for discrete optimization. SFLA is a

population-based method and uses a population of solutions to proceed to the global

solution. SFLA is a population-based cooperative search metaphor inspired by natural

memetics. The algorithm contains elements of local search and global information

exchange. The SFLA consists of a set of interacting virtual population of frogs

partitioned into different memeplexes. The virtual frogs act as hosts or carriers of memes

where a meme is a unit of cultural evolution. The algorithm performs simultaneously an

independent local search in each memeplex. SFLA performance was compared with a

GA for a series of test problems. The results for 11 theoretical test problems (functions)

and two applications show that the SFLA performed better than or at least comparable

with the GA for almost all problem domains and was more robust in determining the

global solution. Four realistic engineering problems were also solved and results

compared with literature results from several optimization algorithms.

8

[8] A Modified Shuffled Frog Leaping Algorithm for Long-Term Generation

Maintenance Scheduling

G. Giftson Samuel et al discussed a modified Shuffled frog leaping algorithm to

Long term Generation Maintenance Scheduling to Enhance the Reliability of the units.

The algorithm has been tested on thirty two generating unit system. The proposed method

has been compared with other methods. The result obtained is compared with the results

of other method such as DP, LR and PSO. From the result it is shown that the proposed

algorithm provides true optimal solution for minimum fuel cost and computation timing

in all cases.

[9] An Ant-Based Algorithm for Distributed Routing and Wavelength Assignment

in Dynamic Optical Networks

Joan Triay et al proposed the use of an ant colony optimization (ACO) algorithm

to solve the intrinsic problem of the routing and wavelength assignment (RWA) on

wavelength continuity constraint optical networks. In optical burst switching the forward

ants are implemented as burst control packets, whereas feedback ants, which gather

information about the positive or negative delivery of the bursts, are a special type of

acknowledgment control packet. The algorithm takes into account both the path length

and the congestion in the network to update the values of the pheromone trails. It has

been evaluated through extensive simulations with very promising results, particularly on

highly congested scenarios where the load balancing capabilities of the protocol become

especially efficient.

9

[10] A Genetic Algorithm for Shortest Path Routing Problem and the Sizing of

Populations

C.W. Ahn et al presented a genetic algorithmic approach to the shortest path (SP)

routing problem. Crossover and mutation together provide a search capability that results

in improved quality of solution and enhanced rate of convergence. The crossover is

simple and independent of the location of crossing site. Consequently, the algorithm can

search the solution space in a very effective manner. The mutation introduces, in part, a

new alternative route. The population-sizing equation appears to be a conservative tool to

determine a population size in the routing problem.

[11] A Novel Solution to the Dynamic Routing and Wavelength Assignment Problem

in Transparent Optical Networks

Urmila Bhanjaa et al discussed an evolutionary programming algorithm for

solving the dynamic routing and wavelength assignment (DRWA) problem in optical

wavelength-division-multiplexing (WDM) networks under wavelength continuity

constraint. They assume an ideal physical channel and therefore neglect the blocking of

connection requests due to the physical impairments. They implemented three types of

wavelength assignment techniques, such as First fit, Random, and Round Robin

wavelength assignment techniques.

10

CHAPTER 3

EVOLUTIONARY PROGRAMMING METHOD

3.1 BLOCK DIAGRAM

Fig 3.1 Block Diagram of Evolutionary Programming Method

The evolutionary programming method is organized in four models namely

Network model, Routing model, Wavelength Assignment model and Optimization

Algorithm [10] as shown in Fig 3.1.

3.2 NETWORK MODEL

The N node network can be modeled as a graph G (V, E), in which V is the set of

nodes representing routers or switches and E is the set of edges representing connectivity

between the nodes. The link existing between a pair of nodes is assumed to be

bidirectional in nature, that is, the existence of a link e = (i,j) from node i to j implies the

existence of another link e‟ = (j,i) for any pair of nodes (i,j)∈E.

For the DRWA problem with ideal as well as non-ideal physical layers, V is the

set of nodes representing routers or WRNs, and E is the set of fiber links representing

physical connectivity between the nodes. Each link is assumed to be bidirectional with

fixed number of wavelengths per fiber. For the physical impairment aware DRWA

problem, each wavelength routing node (WRN) consists of a cross connect switch (XCS),

11

transmitter and receiver arrays, optical taps and erbium doped fiber amplifiers (EDFA) as

in Fig.3.2.

Fig 3.2 Architecture of a wavelength routing node

The wavelength routing switches (WRSs) in the XCS are assumed to employ non-

blocking active splitter/combiner architecture. The XCSs transfer each wavelength in an

input fiber into the same wavelength in one of the output fibers. A tap is present at the

input and output of each XCS to monitor the signal condition [16]. The EDFA at the

input side compensates for the fiber loss and the tap loss and the EDFA at the output side

compensates for the switch loss.

Fig 3.3 Model of a transmission lightpath

12

In Fig. 3.3, WRN (1) represents the source node, WRN (m) represents the

destination node, and WRN (k) represents the kth intermediate node. Array of

transmitters and receivers are present in each of the nodes for locally adding or dropping

the traffic. In the adopted network model, each XCS consists of an array of

demultiplexers followed by a set of WRSs and a set of multiplexers. All the signals that

are demultiplexed and have identical wavelengths are directed to the corresponding WRS

tuned to the same wavelength and the switch redirects the signal to the desired output

port; the multiplexers then combine signals with different wavelengths and redirect them

to the output fibers. The number of WRSs in an XCS depends on the number of input

wavelengths, and the number of input and output ports of a WRS depends on the number

of input and output fibers.

3.3 ROUTING MODEL

The routing and wavelength assignment (RWA) problem is an optical

networking problem with the goal of maximizing the number of optical connection. Each

connection request must be given a route and wavelength. The wavelength must be

consistent for the entire path, unless the usage of wavelength converters is assumed. Two

connection requests can share the same optical link, provided a different wavelength is

used [11]&[17].

The routing models used for all the four problems are nearly identical. For the QoS

constrained routing problem F is assumed to be the set of flows existing at any time and f

is any unicast flow or request belonging to F. The variable Ifi,j is set to 1 if link (i,j) is

used by flow f; otherwise, it is set to 0. A Path from the source S to destination D for a

flow f is represented as Path (f) and is the collection of all the links belonging to the flow

from S to D. Any link e ∈ E has a bandwidth, bandwidth (e): E→R+, associated with it,

R+ being the set of positive real numbers. The bandwidth from any source to any

destination, for a flow f, is denoted by bandwidth(f), and is defined as:

13

bandwidth (f) = min {bandwidth (e)|e∈Path(f )}, f∈ F

Fitness function is to maximize

1

,( ), ( 1) ( , )

1

x

x x xx k x

i j xgx j gx j i j E

j

W W Wf

H TC

(3.1)

In the fitness function, Wx is the free wavelength factor. If the same wavelength is

available in all links of the path x then it is one and zero otherwise. The other term in the

fitness function defines the sum of the link costs in the path. The denominator of the

second term represents the total number of hops the path passes through. The variable

Hxi,j equals one if link (i, j) is a part of path x; otherwise, it is equal to zero. The variable

Tx represents the set up time of path x. The variable kx represents the length of the x-th

chromosome or number of memeplexes. A route is considered to be optimal when it

maximizes this objective function while satisfying the following constraints:

( , ) ( , )

1,lp lp

ij ij

i j E j i E

I I

if i=S, lpLP (3.2)

( , ) ( , )

1lp lp

ij ij

i j E j i E

I I

, if i=D, lpLP (3.3)

( , ) ( , )

0lp lp

ij ij

i j E j i E

I I

, if i≠S, i≠D, lpLP (3.4)

( , )

1lp

ij

i ji j E

I

, if i≠D, lpLP (3.5)

( , )

0lp

ij

i ji j E

I

, if i=D, lpLP (3.6)

0

( , )

lp

ij

i j E

I h

, for t ≤ T (3.7)

14

0

( , )

( 1)lp

ij

i j E

h I N

, for t > T (3.8)

The flow conservation constraint, given from equation (3.2) to (3.4) and the loop

constraint from equation (3.5) to (3.6) guarantee that the solutions obtained represent

valid paths from S to D and that the lightpath has no loops. Equations (3.7) and (3.8)

represent the hop count constraint, which, however, is a soft constraint. For a threshold

time T, the number of hops traversed by the lightpath is initially limited to prevent

excessively long paths causing delay and is required to be less than or equal to an upper

bound h0. However after this time, the bound is relaxed up to a maximum value of

(N - 1). In the initialization phase of the proposed algorithm, the threshold time is set to

T1 and during the mutation phase, the threshold time is set to T2 [18]. The variable, t

represents the algorithm execution time.

Since dynamic RWA is more complex than static RWA, it must be the case that

dynamic RWA is also NP-complete. The RWA problem is further complicated by the

need to consider signal quality. Many of the optical impairments are nonlinear, so a

standard shortest path algorithm can't be used to solve them optimally even if we know

the exact state of the network. This is usually not a safe assumption, so solutions need to

be efficient using only limited network information.

Given the complexity of RWA, there are two general methodologies for solving the

problem:

The first method is solving the routing portion first, and then assigning a

wavelength. Three types of route selection are Fixed Path Routing, Fixed

Alternate Routing and Adaptive Routing.

The second approach is to consider both route selection and wavelength

assignment jointly.

15

3.3.1 Fixed path routing

Fixed path routing is the simplest approach to find a lightpath. The same fixed

route for a given source and destination pair is always used. Typically this path is

computed ahead of time using a shortest path algorithm, such as Dijkstra's Algorithm.

While this approach is very simple, the performance is usually not sufficient. If resources

along the fixed path are in use, future connection requests will be blocked even though

other paths may exist.

The SP-1 (Shortest Path, 1 Probe) algorithm is an example of a Fixed Path

Routing solution. This algorithm calculates the shortest path using the number of optical

routers as the cost function. A single probe is used to establish the connection using the

shortest path. The running time is the cost of Dijkstra's algorithm: 𝑂(𝑚 + 𝑛𝑙𝑜𝑔 𝑛) ,

where is the number of edges and is the number of routers. The running time is just

a constant if a predetermined path is used. This definition of SP-1 uses the hop count as

the cost function. The SP-1 algorithm could be extended to use different cost functions,

such as the number of EDFAs.

3.3.2 Fixed alternate routing

Fixed alternate routing is an extension of fixed path routing. Instead of having just

one fixed route for a given source and destination pair, several routes are stored. The

probes can be sent in a serial or parallel fashion. For each connection request, the source

node attempts to find a connection on each of the paths. If all of the paths fail, then the

connection is blocked. If multiple paths are available, only one of them would be utilized.

The SP-p (Shortest Path, p Probes, p>1) algorithm is an example of Fixed

Alternate Routing. It calculates the p shortest paths using the number of optical routers as

the cost function. The running time using is 𝑂(𝑝𝑛 𝑚 + 𝑛𝑙𝑜𝑔 𝑛 ) where m is number of

edges, n is the number of routers, and p is the number of paths. The running time is a

constant factor if the paths are precomputed.

16

3.3.3 Adaptive routing

The major issue with both fixed path routing and fixed alternate routing is that

neither algorithm takes into account the current state of the network. If the predetermined

paths are not available, the connection request will become blocked even though other

paths may exist. Fixed Path Routing and Fixed Alternate Routing are both not quality

aware. For these reasons, most of the research in RWA is currently taking place in

Adaptive algorithms. Adaptive algorithms fall into two categories: traditional and

physically aware. Traditional adaptive algorithms do not consider signal quality,

however, physically aware adaptive algorithms do.

3.3.4 Traditional adaptive RWA

The routing algorithm is to route connection requests away from congested areas

of the network, increasing the probability that connection requests will be accepted. This

is accomplished by setting the cost of each link to be 𝑐𝑜𝑠𝑡 𝑙 = 𝛽𝑢𝑠𝑎𝑔𝑒 (𝑙) where is

parameter that can be dynamically adjusted according to the traffic load and usage(l) is

the number of wavelengths in use on link . A standard shortest path algorithm can then

be used to find the path. This requires each optical switch to broadcast recent usage

information periodically. Note that LORA does not consider any physical impairment.

When is equal to one, the LORA algorithm is identical to the SP algorithm.

Increasing the value of will increase the bias towards less used routes. The optimal

value can be calculated using the well-known hill climbing algorithm. The optimal values

of were between 1.1 and 1.2 in the proposal.

3.3.5 Physically aware adaptive RWA

The physically aware backward reservation algorithm (PABR) is an extension of

LORA. PABR is able to improve performance in two ways: considering physical

impairments and improved wavelength selection. As PABR is searching for an optical

path, paths with an unacceptable signal quality due to linear impairments are pruned. In

17

other words, PABR is LORA with an additional quality constraint. PABR can only

consider linear impairments. The nonlinear impairments, on the other hand, would not be

possible to estimate in a distributed environment due to their requirement of global traffic

knowledge. PABR also considers signal quality when making the wavelength selection. It

accomplishes this by removing from consideration all wavelengths with an unacceptable

signal quality level. The approach is called Quality First Fit.

3.4 WAVELENGTH ASSIGNMENT MODEL

Two of the most common methods for wavelength assignment are First Fit and

Random Fit. First Fit chooses the available wavelength with the lowest index. Random

Fit determines which wavelengths are available and then chooses randomly amongst

them. The complexity of both algorithms is ( )O w , where w is the number of wavelengths.

First Fit outperforms Random Fit.

An extension to First Fit and Random Fit was proposed in to consider signal

quality. Quality First Fit and Quality Random Fit eliminate from consideration

wavelengths which have an unacceptable signal quality. The complexity of these

algorithms is higher though, as up to calls to estimate the Q-factor are required.

There are several other wavelength assignment algorithms: Least Used, Most

Used, Min Product, Least Loaded, Max Sum, and Relative Capacity Loss. Most Used

outperforms Least Used significantly, and slightly outperforms First Fit. Min Product,

Least Loaded, Max Sum, and Relative Capacity Loss all try to choose a wavelength that

minimizes the probability that future requests will be blocked.

A significant disadvantage of these algorithms is that they require a significant

communication overhead, making them impractical to implement unless you have a

centralized network structure.

In the proposed fitness function, a free wavelength factor, WX, is updated after the

wavelength assignment phase. In the wavelength assignment model, the variable Iijlp

is

equal to one when the link (i, j) is used by the lightpath lp, and zero otherwise. The

18

additional variables used are, Iijwlp

, the lightpath wavelength indicator that shows whether

the lightpath lp uses wavelength „W‟ on link (i, j) and Iijwlp(x,y)

, the lightpath wavelength

link indicator that is one when the lightpath uses wavelength „W‟ on link (i, j) between

the nodes x and y, and, l(x,y)

which equals one if a physical link exists between the nodes

x and y.

The wavelength continuity constraints are

1

0

Wlp lp

ij ijw

w

I I

, (i,j) (3.9)

( , )lp x y lp

ijw ijwI I , (i,j), (x,y) , w (3.10)

( , )

,

1lp x y

ijw

i j

I , (x,y), w (3.11)

1 1( , ) ( , ) ( , ) ( , )

0 0

W Wlp x y x y lp y x y x lp

ijw ijw ij

w x w x

I l I l I

, y=j (3.12)

1 1( , ) ( , ) ( , ) ( , )

0 0

W Wlp x y x y lp y x y x lp

ijw ijw ij

w x w x

I l I l I

, y=i (3.13)

1 1( , ) ( , ) ( , ) ( , )

0 0

0W W

lp x y x y lp y x y x

ijw ijw

w x w x

I l I l

, y≠i, y≠j (3.14)

The binary variable lp

ijwI is the lightpath wavelength indicator, which is one

whenever the lightpath lp uses wavelength w on link (i, j); ( , )lp x y

ijwI is another binary

variable called the lightpath wavelength link indicator, which is one when the lightpath lp

between the nodes x and y uses wavelength w on link (i, j); and the variable ( , )x yl is one if

a physical link exists between nodes x and y; otherwise, it is zero. Equations (3.9) and

(3.10) together imply that the wavelength used by a lightpath is unique. Equation (3.9)

dictates that the same wavelength is used in all the links traversed by a lightpath. On the

19

other hand, equation (3.10) implies that only a single lightpath using the link (i, j) can use

the wavelength w. Equation (3.11) guarantees that two lightpaths using the same link are

not assigned the same wavelength, and equations from (3.12) to (3.14) ensure the

conservation of wavelengths at the end nodes of the physical links traversed by a

lightpath.

3.5 GENETIC ALGORITHM

In the field of artificial intelligence, genetic algorithm (GA) is

a search heuristic that mimics the process of natural selection. This heuristic (also

sometimes called a metaheuristic) is routinely used to generate useful solutions

to optimization and search problems. Genetic algorithms belong to the larger class

of evolutionary algorithms (EA), which generate solutions to optimization problems

using techniques inspired by natural evolution, such as inheritance, mutation, selection,

and crossover [13]. Genetic algorithms are not too hard to program or understand, since

they are biological based. Thinking in terms of real-life evolution helps.

The general algorithm for a GA is:

• Generate a large set of possible solutions to a given problem (initial population)

• Evaluate each of those solutions, and decide on a "fitness level" ("survival of the

fittest")

• From these solutions breed new solutions (the next generation) o The parent solutions

that were more "fit" are more likely to reproduce o While those that were less "fit" are

more unlikely to do so

• Solutions are evolved over time, by repeating the process each generation.

• Terminate when a solution has been found or other termination criteria has been met

20

3.5.1 Flow Chart of Genetic Algorithm

Fig 3.4 Flow chart of Genetic Algorithm

Fig.3.4 shows the flow of the genetic algorithm to solve the routing and wavelength

assignment problem.

3.5.2 Create a Random Initial Population

An initial population is created from a random selection of solutions. These

solutions have been seen as represented by chromosomes as in living organisms .The

genetic information defines the behaviour of the individual. A chromosome is a packet of

Creation of Initial Population (single

chromosome generation)

Mutation (Offspring generation from

single chromosome)

Selection of one best chromosome

depending on the fitness function

Is termination criteria reached?

Stop

21

genetic information organized in a standard way that defines completely an individual

(solution). The genetic principles (way in which that information encodes the individual)

enable the individuals to evolve in a given environment. The genetic structure (way in

which that information is packed and defined) enables the solutions to be manipulated.

The genetic operands (way in which that information can be manipulated) enable the

solutions to reproduce and evolve [14]&[15].

3.5.3 Evaluate Fitness

A value for fitness is assigned to each solution (chromosome) depending on how

close it actually is to solve the problem. Therefore, define the problem, model it and

simulate it or have a data set as sample answers. Each possible solution has to be tested

in the problem and the answer is evaluated (or marked) on how good it is. The overall

mark of each solution relative to all the marks of all solutions produces a fitness ranking.

3.5.4 Produce Next Generation

Those chromosomes with a higher fitness value are more likely to reproduce

offspring. The population for the next Generation will be produced using the genetic

operators. Reproduction is by Copying or Crossing Over and Mutation is applied to the

chromosomes according to the selection rule. This rule states that the fitter and individual

is, the higher the probability it has to reproduce.

3.5.5 Next Generation or Termination

If the population in the last generation contains a solution that produces an output that

is close enough or equal to the desired answer then the problem has been solved. This is

the ideal termination criterion of the evolution. If this is not the case, then the new

generation will go through the same process as their parents did and the evolution will

continue. This will iterate until a solution is reached or another of the termination criteria

is satisfied. A termination criterion that always must be included is Time-Out (either as

computing time or as number of generations evaluated).Since one drawback of

22

Evolutionary Programming is that, it is very difficult (impossible most of the time) to

know if the ideal termination criterion is going to be satisfied and/or when.

3.5.6 Advantages of Genetic Algorithm

It can solve every optimisation problem which can be described with the

chromosome encoding.

It solves problems with multiple solutions.

Since the genetic algorithm execution technique is not dependent on the error

surface, it can solve multi-dimensional, non-differential, non-continuous, and even

non-parametrical problems.

Structural genetic algorithm gives the possibility to solve the solution structure

and solution parameter problems at the same time by means of genetic algorithm.

Genetic algorithm is a method which is very easy to understand and it practically

does not demand the knowledge of mathematics.

Genetic algorithms are easily transferred to existing simulations and models.

3.6 SHUFFLED FROG LEAPING ALGORITHM

Shuffled Frog Leaping Algorithm (SFLA) is a natural inspired metaheuristic

algorithm. The most distinguished benefit of SFLA is its fast convergence speed .The

Shuffled frog leaping algorithm combines the advantages of the both the genetic-based

memetic algorithm and the behavior-based Particle Swarm Optimization(PSO) algorithm.

In the Shuffled frog leaping algorithm, possible solutions are defined by a group of frogs

which is referred to as population. The group of frogs is partitioned into several

communities referred to as memeplexes. Local search is performed by each frog in the

memeplexes. The individual frog‟s behavior can be influenced by behaviors of other

frogs within each memeplex and it will develop through a process of memetic evolution.

The memeplexes are forced to mix together after a certain number of memetics evolution

23

steps and new memeplexes are formed through a shuffling process. The local search and

the shuffling processes continue until convergence criteria are satisfied. The flowchart of

Shuffled frog leaping algorithm is illustrated in Fig.3.5.

The various steps are as follows:

(1) The Shuffled frog leaping algorithm involves a population „P‟ of possible solution,

defined by a group of virtual frogs(n).

(2) Frogs are sorted in descending order according to their fitness and then partitioned

into subsets called as memeplexes (m).

(3) Frogs i is expressed as Xi = (Xi1, Xi2, …..Xi3) where S represents number of variables.

(4) Within each memeplex, the frog with worst and best fitness is identified as Xw and

Xb.

(5) Frog with global best fitness is identified as Xg.

(6) The frog with worst fitness is improved according to the following equation.

Di=rand ( ) (Xb -Xw) (3.16)

Xneww=X oldw+ Di (3.17)

where rand is a random number in the range of [0,1].

Di is the frog leaping step size of the i-th frog and Dmax is the maximum step allowed for

change in a frog‟s position.

If the fitness value of new Xw is better than the current one, Xw will be accepted. If

it isn‟t improved, then the calculated frog leaping step size Di and new fitness Xneww are

repeated with Xb replaced by Xg. If no improvement becomes possible in the case, a new

Xw will be generated randomly. Repeat the update operation for a specific number of

iterations. After a predefined number of memetic evolutionary steps within each

memeplex, the solutions of evolved memeplexes are replaced into new population. This

is called the shuffling process. The shuffling process promotes a global information

exchange among the frogs. Then, the population is sorted in order of decreasing

performance value and updates the population best frog‟s position, repartition the frog

24

group into memeplexes and progress the evolution within each memeplex until the

conversion criteria are satisfied.

Start

Initialize parameters: Population size (P)

Number of memeplexes (m) Number of

iterations within each memeplex

Generate random population of P solutions (frogs)

Calculate fitness of each individual frog

Sorting population in descending order of

their fitness

Divide P solutions into m memeplexes

Local Search

Shuffle evolved memeplexes

Termination =

true

Determine the best solution

End

Yes

No

Fig 3.5 Flow chart of Shuffled Frog Leaping Algorithm

25

CHAPTER 4

RESULTS AND DISCUSSIONS

The optimization algorithms have been carried out in MATLAB R2012b. In the

simulation work, Fig.4.1 depicts the fitness of the genetic algorithm and shuffled frog

leaping algorithm with the execution time. The fitness function involves cost, number of

hop counts and holding time. Better fitness is achieved for a smaller execution time.

4.1 FITNESS FUNCTION

Fig 4.1 Fitness function of GA and SFLA

26

Table 4.1. Fitness function of GA and SFLA with respect to time

Parameter

Genetic Algorithm

Shuffled Frog Leaping

Algorithm

Fitness Function 0.330 9.900

The average fitness value in GA and SFLA for the execution time 0.4 seconds are

0.330 and 9.900 as given in Table 4.1.

4.2 MEAN BLOCKING PROBABILITY (w.r.t. CHANNEL REJECTION RATIO)

Fig.4.2 and 4.3 shows the variation in the blocking probability assuming different

values of adjacent wavelength rejection ratios for GA and SFLA respectively. In each

case by executing the program several times and then by computing the average, mean

blocking probability is estimated. In FWM aware priority based wavelength assignment,

the mean blocking probability decreases for a reduction in each of the adjacent

wavelength rejection ratio.

Fig 4.2 Mean blocking probability for a fixed network load using GA

27

Table 4.2. Mean blocking probability of GA using different wavelength assignment

techniques

Wavelength

Assignment

Techniques

Mean Blocking Probability (w.r.to Channel Rejection Ratio(dB)

-0.6898 -0.5853 -0.5772 -0.5707 -0.5617 -0.5445 -0.515 -0.219

First Fit

0.2514

0.8053

0.8885

0.9444

0.9890

1.0273

1.0737

1.14

Random

0.2307

0.7160

0.7657

0.8053

0.8417

0.904

0.9588

1.02

Round

Robin

0.0180

0.0348

0.0644

0.1000

0.1276

0.1452

0.1579

0.16

Wavelength

Ordering

0.0088

0.0291

0.0620

0.0928

0.1215

0.1461

0.1576

0.15

Table 4.2 shows the mean blocking probability of Genetic Algorithm with four

wavelength assignment techniques first fit, random, round robin and wavelength

ordering. Wavelength ordering gives less blocking probability for GA compared to other

wavelength assignment techniques.

28

Fig 4.3 Mean blocking probability for a fixed load using SFLA

Table 4.3. Mean blocking probability (w.r.to Channel Rejection Ratio) of SFLA using

different wavelength assignment techniques

Wavelength

Assignment

Techniques

Mean Blocking Probability (w.r.to Channel Rejection Ratio(dB))

-0.6898 -0.5853 -0.5772 -0.5707 -0.5617 -0.5445 -0.515 -0.219

First Fit

0.2638

0.8022

0.8861

0.9443

0.9881

1.0291

1.0748

1.14

Random

0.2307

0.7160

0.7657

0.8053

0.8417

0.904

0.9588

1.03

Round

Robin

0.0315

0.1490

0.3265

0.4785

0.6545

0.7650

0.8655

0.91

Wavelength

Ordering

0.0082

0.0284

0.0620

0.0915

0.1240

0.1401

0.1536

0.15

29

Table 4.3 shows the mean blocking probability of Shuffled Frog Leaping

Algorithm with four wavelength assignment techniques first fit, random, round robin

and wavelength ordering. For SFLA wavelength ordering gives less blocking probability

with respect to channel rejection ratio.

4.3 AVERAGE FITNESS SCORE

Fig.4.4. Average fitness score for GA and SFLA

Fig.4.4 depicts the rate of convergence of genetic algorithm and shuffled frog

leaping algorithm for first fit, random, round robin, wavelength ordering and FWM

aware priority based wavelength assignment techniques. By randomly selecting an

individual and fixing the best fitness value, the curves can be plotted. The average

fitness score decreases with increase in generations. Table 4.4 shows the average fitness

score for GA and SFLA using different wavelength assignment techniques. Average

fitness score for GA and SFLA are approximately same. FWM priority based

assignment has higher average fitness score.

30

Table 4.4.Average fitness score for GA and SFLA using different wavelength

assignment techniques

Wavelength

Assignment

Techniques

Average Fitness Score (w.r.to Generations)

1 2 3 4 5 6 7 8

First Fit

0.5529

0.9033

1.4961

1.9989

2.4849

2.9046

3.0270

3.58

Random

0.0470

0.2296

0.4452

0.6275

0.7575

0.8816

0.9312

0.95

Round Robin

0.0791

0.3148

0.6957

1.0565

1.3227

1.4842

1.6000

1.65

Wavelength

Ordering

0.0796

0.0804

0.0812

0.0820

0.0828

0.0836

0.0844

0.08

FWM priority

based

Assignment

1.179e

+07

1.1696

e+07

1.1752

e+07

1.183e

+07

1.18e-

07

1.186e+

07

1.188e

+07

1.193

+07

4.4 MEAN BLOCKING PROBABILITY (w.r.to GENERATIONS)

Fig.4.5 and 4.6 show the mean blocking probability exhibited by the Genetic

Algorithm and Shuffled Frog Leaping Algorithm which is a performance metrics of

dynamic routing and wavelength assignment. The mean blocking probabilities obtained by

GA and SFLA for the three wavelength assignment techniques are plotted assuming

exponential holding times distribution.

31

Fig.4.5. Mean blocking probability of GA

Table 4.5. Mean blocking probability (w.r.to Generations) of GA using different

wavelength assignment techniques

Wavelength

Assignment

Technique

Mean Blocking Probability(w.r.to Generations)

1 2 3 4 5 6 7 8

First Fit

0.0420

0.1610

0.3185

0.4900

0.6185

0.7715

0.8495

0.89

Random

0.0558

0.2164

0.4275

0.6062

0.7823

0.8662

0.924

0.95

Round

Robin

0.0345

0.0761

0.1419

0.1979

0.2484

0.2909

0.3126

0.3123

32

Fig.4.6. Mean blocking probability of SFLA

Table 4.5 and 4.6 show the mean blocking probability of Genetic Algorithm and

Shuffled Frog Leaping Algorithm for three wavelength assignment techniques first fit,

random and round robin. For both GA and SFLA round robin gives less blocking

probability with respect to generations.

Table 4.6 Mean blocking probability (w.r.to Generations) of SFLA using different

wavelength assignment techniques

Wavelength

Assignment

Technique

Mean Blocking Probability(w.r.to Generations)

1 2 3 4 5 6 7 8

First Fit

0.0412

0.1543

0.3054

0.3780

0.5153

0.6215

0.7412

0.85

Random

0.0529

0.2013

0.3865

0.5234

0.7813

0.8669

0.922

0.91

Round

Robin

0.0017

0.0038

0.0071

0.0099

0.0124

0.0145

0.0156

0.0161

33

4.5 MEAN EXECUTION TIME

Fig.4.7.Mean execution time of GA

For all wavelength assignment techniques mean execution time exhibited by

Genetic Algorithm is depicted in Fig.4.7 and the values are shown in Table 4.7. FWM

aware priority based wavelength assignment technique provides the least mean

execution time for different network loads.

34

Table 4.7 Mean Execution Time of GA using different wavelength assignment

techniques

Wavelength

Assignment

Techniques

Mean Execution Time (w.r.to network load(Erlang))

0 0.75 1.4 2.7 3.2 3.6 3.7 4.4

First Fit

0.1200

0.011

0.0432

0.0689

0.1123

0.1038

0.1023

0.1019

Random

0.3000

0.043

0.2372

0.2328

0.3201

0.3155

0.3443

0.3762

Round

Robin

0.1200

0.000

0.1736

0.1613

0.2061

0.2004

0.2092

0.2251

Wavelength

Ordering

0.0500

0.013

0.0062

0.0123

0.0244

0.0302

0.0359

0.0415

FWM

priority

based

Assignment

0.0050

0.000

4.275e-

11

8.509e-

11

1.697e-

11

2.1167e-

10

2.525e-

10

2.94e-

10

35

Fig.4.8. Mean execution time of SFLA

Mean execution time exhibited by Shuffled Frog Leaping Algorithm is plotted in

Fig.4.8 and the values are shown in Table 4.8 for five types of wavelength assignment

techniques. For different network loads, FWM aware priority based wavelength

assignment technique provides the least mean execution time.

36

Table 4.8. Mean Execution Time of SFLA using different wavelength assignment

techniques

Wavelength

Assignment

Techniques

Mean Execution Time (w.r.to network load(Erlang))

0 0.75 1.4 2.7 3.2 3.6 3.7 4.4

First Fit

0.1191

0.010

0.0423

0.0654

0.1023

0.1018

0.1008

0.1003

Random

0.2987

0.043

0.2372

0.2328

0.3201

0.3155

0.3443

0.3762

Round

Robin

0.1198

0.005

0.1703

0.1610

0.2056

0.2001

0.2081

0.2248

Wavelength

Ordering

0.0490

0.011

0.0059

0.00117

0.0232

0.0295

0.0343

0.0409

FWM

priority

based

Assignment

0.038

0.001

4.257e-

11

8.503e-

11

1.6763e-

11

2.1068e-

10

2.55e-

10

2.85e-

10

37

4.6 COMPARISON OF PERFORMANCE MEASURES IN GA AND SFLA

From Table 4.9 and 4.10, it is observed that wavelength ordering and round robin

exhibits less mean blocking probability with respect to channel rejection ratio and

generations respectively. Average fitness score is higher for FWM aware priority based

wavelength assignment technique. Least mean execution time is achieved by use of

FWM priority based assignment.

Table 4.9.Comparison of different wavelength assignment techniques with respect to

four performance measures in GA

Wavelength

Assignment

Techniques

Mean Blocking

Probability

(w.r.to channel

rejection ratio)

Average

fitness score

Mean Blocking

Probability

(w.r.to

generations)

Mean

Execution

Time

First Fit 0.8910 2.1184 0.5176 0.0829

Random 0.7875 0.6087 0.6035 0.2711

Round Robin 0.5225 1.023 0.2018 0.1619

Wavelength

Ordering

0.0959 0.08175 - 0.0266

FWM based

Assignment

- 12.481 - 0.00070

38

Table 4.10.Comparison of different wavelength assignment techniques with respect to

four performance measures in SFLA

Wavelength

Assignment

Techniques

Mean Blocking

Probability

(w.r.to channel

rejection ratio)

Average

fitness score

Mean Blocking

Probability

(w.r.to

generations)

Mean

Execution

Time

First Fit 0.8899 2.1184 0.4508 0.008025

Random 0.7802 0.6087 0.5805 0.2709

Round Robin 0.1009 1.023 0.0010 0.1618

Wavelength

Ordering

0.0947 0.08175 - 0.0256

FWM based

Assignment

- 12.481 - 0.00067

Considering Genetic Algorithm and Shuffled Frog Leap Algorithm, Shuffled Frog

Leap Algorithm achieves least mean blocking probability and a mean execution time for

different wavelength assignment techniques such as First Fit, Random, Round Robin,

Wavelength Ordering and FWM aware priority based wavelength assignment. Average

fitness score is approximately same for GA and SFLA.

39

CHAPTER 5

CONCLUSION

Routing and Wavelength Assignment (RWA) problem is the most complex

optimization problem in optical networks. In the proposed work, Genetic Algorithm and

Shuffled Frog Leaping Algorithm are used to solve the RWA problem. The fitness

function minimizes the cost, number of hops and blocking probability. The five

wavelength assignment techniques such as first fit, random, round robin, wavelength

ordering and FWM aware priority based wavelength assignment are used while

evaluating the performance of GA and SFLA.

Fitness function of SFLA is improved compared to GA. FWM priority based

wavelength assignment technique gives maximum average fitness score and least mean

execution time than other techniques. Considering different wavelength assignment

techniques, SFLA is better than GA with minimum mean blocking probability, less mean

execution time and best average fitness score. SFLA approach has a lower time

complexity compared to Genetic Algorithm. The proposed scheme provides certain

degree of flexibility in the network design.

40

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LIST OF PUBLICATIONS

Presented a paper titled “Optimization of Routing and Wavelength Assignment in

Passive Optical Networks” in IEEE Sponsored 3rd

International Conference on

Innovations in Information Embedded and Communication Systems on 17th

and18th

March 2016 at Karpagam College of Engineering, Coimbatore.

The paper is accepted to be published in a Scopus Indexed (Anna University

Annexure-II) Journal, Pakistan Journal of Biotechnology (S.no: 15755, Print

ISSN: 18121837, University of Sindh).