A Proposed Genetic Algorithm for Multicast Routing

Many I nternet applications (such a s video conferences) are one-to-ma ny or many-to-many, where one or multiple sources are sending to multiple receivers. These applications need certain Quality of Services to be guaranteed in underlying network. This paper presents a genetic multicast routing algorithm which finds the low-cost multicasting tree from a designated source t o multiple destinations with Quality of S ervice ( QoS ) ( i


A) Background
Kadaba Bharath-Kumar and Jeffrey M. Jaffe [1] studied algorithms for effectively routing messages from a source to multiple destination nodes in a store-andforward computer network.The focus was on minimizing the Network Cost, its measure is also compared to the Destination Cost.M. Hamdan and M.E.El-Hawary [2] presented a constrained multicast routing scheme based on GA.They considered two constraints, a constraint on end-to-end delays and a bounded delay variations.Lin Chen et al [3] proposed a new multicast routing algorithm based on GA that takes delay and also degree constraints into account to construct Degree-Delay Constrained least-cost multicast routing Tree.It is clear from the wide variety of anticipated multicast applications that no single tree can satisfy requirement of all of them, therefore the proposed GA is capable of providing QoS to their members and play an important role in future communications networks.

B) Objectives
The objectives of this paper are to propose a genetic multicast routing algorithm that discovers a multicast tree from a designated source to a set of destinations that discovers a minimum cost multicast tree and satisfies the bandwidth and end-to-end delay constraints.Then building a simulator to implement and study the designed algorithm.Results show that the algorithm is capable of being implemented practically on real world networks.

C) Organization
The rest of the paper is organized as follows; In Section II, a network model, QoS constraints and Objective Function are explained.The proposed GA for the multicast routing with several key components is described in Section III.In Section IV, Experimental Results with various network topologies and the performances of the proposed GA are explicated.After that, Analysis of Results is discussed in Section V. Finally, Section VI presents Conclusions and Suggestions for Future Work.

II. Network Model
The network can be represented as the undirected and connected weighted graph G = (V,E) where V is the set of network nodes (vertices), E is the set of connected links (edges).A link e ij Є E connecting nodes v i and v j will be denoted by (v i ,v j ).It is characterized by an ordered triple ( B ij ,D ij ,C ij ) representing capability of bandwidth, delay and cost between nodes v i and v j .A multicast tree is defined by T = (V T ,E T ), where V T ⊆ V, E T ⊆ E, and T ⊆ G, and there exists a path P T (s,v k ) from the source node s to each destination node

A) Initial Whole Population
In order to generate good solutions, random initialization is used to initialize the population.Physically, the random initialization chooses genes (nodes) from the topological information database in a random manner during the encoding process.When initializing the population, the algorithm starts from the source.Source is a constant in the program.The algorithm selects one of the neighbors provided that it has not been picked before.It keeps doing this operation until it reaches all destinations.

B) Encoding and Representation
A chromosome consists of sequences of positive integers that represent the Identifications ( IDs) of nodes through which a routing path passes and variable-length chromosomes are employed.Each locus of the chromosome represents an order of a node (indicated by the gene of the locus) in a routing path.The gene of first locus in each chromosome is always reserved for the source node.Each chromosome in population denotes a multicast tree.Obviously, a chromosome represents a candidate solution for the multicast routing problem since it guarantees a path between the source node and any of the destination nodes.

C) Fitness Function
The (in the tournament selection, individuals of a population are divided into sub-groups and next the individual with the best fitness is selected out of each of the subgroups [5]) is preferable in this regard to prevent premature convergence.

E) Mixing
A dimensional mixing model was interrelated with a selection model to identify regions of the proposed GA parameter combinations where the proposed GA is predicted to reliably converge to the global optimum.By mixing operation, the crossover operator now transfers complete multicast trees from both parents to form an offspring that has a higher number of multicast trees than either one of its parents.

F) Crossover
The crossover operator is used to reorganize the arrangement of genes in the chromosome for the next generation.It processes the current solutions so as to find better ones.In the proposed GA, the crossover produces diverse chromosomes by exchanging the partial chromosomes (i.e., sub-trees) without positional consistency of potential crossing sites between two chromosomes.This dictates onepoint crossover as a good candidate scheme for the proposed GA.Two (dominant) chromosomes chosen for crossover should have at least one common gene (node) except for source and a set of destination nodes.

G) Repair Function
The repair function treats infeasible chromosomes that contain lethal genes that possibly form loop. Infeasible chromosomes may occur by variation operator (i.e., crossover), that violates the constraints and tree conditions and thus it needs fixing.It must be denoted that none of the chromosomes of the initial population or after the mutation is infeasible because once a node is chosen, it is excluded from the candidate nodes forming the rest of the multicast tree.

H) Mutation
The population undergoes mutation by an actual change or flipping of one of the genes of the candidate chromosomes.Physically, it generates an alternative partial route from the mutation node to the chosen destination according to PDF created with pdfFactory Pro trial version www.pdffactory.com

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mutation probability.After mutation, the upper partial route represents the surviving portion of the previous route and it produces a new path from the mutation node to the selected destination.

IV. Experimental Results
The proposed GA initializes the population size according to the equation: k × | V | 1.5 , where k is a fixed number and is set to 3 and if the value of | V | 1.5 is not positive integer, the proposed GA takes the integer number from it and will be increased by one.
Pair-wise tournament selection (i.e., tournament size = 2) without replacement is employed [6].In all the experiments, the crossover probability is set to 0.75 and the mutation probability is set to 0.15.Each experiment is terminated when all the chromosomes in the population have converged to the same solution [7].Both bandwidth and delay constraints are set to 10.
Network topologies with 10 nodes and 30 links, 20 nodes and 118 links, and 40 nodes and 472 links are generated to test the proposed GA.Each link has a bandwidth, a delay, and a cost is associated with them.The performances of it with 10, 20, and 40 nodes and increasing number of destination nodes from 2 to 7, 2 to 11 and 4 to 17 are shown in Figures (2), ( 3) and ( 4) respectively.

V. Analysis of Results
The quality of solution is taken into account in Figures (2), (3), and (4) for a range of networks with 10, 20, and 40 nodes.This algorithm finds a multicast routing tree in a limit time.The multicast group is randomly selected in the graph and the size of it is considered 20%-70%, 10%-55%, and 10%-42.5% for 10, 20, and 40 nodes network topologies respectively.
In most cases, the bandwidth is increased and the delay is decreased as the number of destinations increases.Sometimes the cost of tree is decreased because there are the same intermediate nodes among the destination nodes which can be used to reach these destination nodes.The number of generations is increased as the number of destination nodes increases which is a normal case.The results show that the proposed GA gets close to optimum very quickly.This is a promising result for the proposed GA because the encoding method does not allow of any redundancy when constructing a multicast tree due to preventing reentry of the nodes that are already included in the current sub-tree, the genetic operators newly designed provide higher exploratory power and a fair measure of genetic diversity.

VI. Conclusions and Suggestions for Future Work
The proposed GA reaches a good solution much faster than initialized randomly when the initial chromosomes are generated with preference for genes of shorter routes and can be easily extended to solve the multiple constrained multicast problems.It can find a minimumcost multicast tree with QoS constraints from a designated source to multiple destinations.The synergy achieved by integrating the new components (i.e., representation, Here, D is the set PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal,Vol.28,No.15, 2010 A Proposed Genetic Algorithm for Multicast Routing .4994ofdestinations and n is the number of destinations.-QoSconstraints 1 -Bandwidth: It is required that the minimum value of link bandwidth in the multicast tree T must be greater than or equal to the required bandwidth (B req ),[4] along the path from a source node s to each destination node v k Є D. That is:2 -Delay bound: The maximum value of path delays (from a source to each destination) is smaller than or equal to the acceptable path delay (D acc ), i.e.,-Objective FunctionTree Cost: The total cost ( T c ) of multicast tree must be minimized (while satisfying the above two QoS constraints):III.The Proposed GA for Multicast RoutingThe proposed GA technique for multicast routing is described in this section.It consists of several key componentsvariation operators (i.e., mixing, crossover, repair function, and mutation).Fitness function and genetic operators iterate until the termination conditions are satisfied.Overall procedures of the proposed GA are depicted in Figure (1).
proposed fitness function only involves network link costs, in other words, the objective function (3) is considered.The QoS constraints are directly incorporated PDF created with pdfFactory Pro trial version www.pdffactory.comEng.& Tech.Journal,Vol.28,No.15, 2010 A Proposed Genetic Algorithm for Multicast Routing .4995 in the course of constructing and assembling the trees.Given an initial population H = { h 1 , h 2 ,…h N }, the fitness value of each chromosome is computed as follows: Let T k be a multicast tree represented by the chromosome h k , and C T k be the sum of the link costs of the tree T k .The fitness value of the chromosome h k , F(h k ), is given by D) Selection The selection (reproduction) plays an important role in improving the average quality of the population by giving the high-quality chromosomes a better chance to get copied into the next generation.The selection of chromosome is based on the value of fitness function.Ordinal selection such as tournament selection