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Zone Routing Protocol In Mobile Ad Hoc Network Using an Estimation Of Distribution Algorithm
M. Masud Karim, Mst. Farhana Rahman and Md. Iqbal Hossain suvo Computer Science and Engineering Discipline Khulna University Khulna-9208, Bangladesh mmkcseku@yahoo.com, farha_cseku@yahoo.com, suvo_rgbd@yahoo.com Abstract An ad hoc network is a collection of mobile nodes that dynamically form a temporary network. Unlike traditional network, that the nodes use the infrastructure to form the network, an ad hoc network operates without the support of any infrastructure. Zone routing protocol is a widely used protocol for ad hoc network and it is the most promising and widely accepted protocol in mobile ad hoc network (MANET). Genetic algorithm (GA) that uses the zone routing protocol as an application and performs better than the traditional method. Estimation Of Distribution algorithm is a probabilistic model building GA based on the probabilistic model for searching and optimization which could be used in ZRP for optimizing the network and to find the finest path for the nodes.
Keywords: EDA, GA, MANET ;
1. Introduction Among all the protocols used in MANETs, Zone Routing Protocol (ZRP) [1] is the most popular and widely accepted routing protocol. ZRP was the first hybrid routing protocol with both a proactive and a reactive routing component. ZRP is formed by two sub-protocols, Intra-zone Routing Protocol (IARP) and Inter-zone Routing Protocol (IERP). A route to a destination within the local zone can be established from the proactively cached routing table of the source by IARP; therefore, if the source and destination is in the same zone, the packet can be delivered immediately. For routes beyond the local zone, route discovery happens reactively. The source node sends a route requests to its border nodes, containing its own address, the destination address and a unique sequence number. GAs[2] are adaptive heuristic search algorithms premised on the evolutionary ideas of natural selection and genetic. The basic concept of GAs is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. As such they represent an intelligent exploitation of a random search within a defined search space to solve a problem. Not only GAs provide alternative methods to solving problem, it consistently outperform other traditional methods in most of the problem links. Many of the real world problems involved finding optimal parameters, which might prove difficult for traditional methods but ideal for GAs. Estimation of Distribution Algorithms (EDAs) [6], sometimes called Probabilistic Model-Building Genetic
Algorithms (PMBGA), are an outgrowth of GAs. In a GA, a population of candidate solutions to a problem is maintained in order to search for an optimum solution. In EDA the population is typically represented explicitly as an array of objects. In an EDA, this explicit representation of the population is replaced with a probability distribution over the choices available at each position in the vector that represents a population member. 1.1 Objective of our Thesis Recently genetic algorithm has been used in [3][4][5], mobile ad hoc network to find the optimized solution. This gives a better performance than the traditional zone routing protocol. Estimation of distribution algorithms are widely being accepted by the researcher around the world as an alternative for Genetic algorithms. EDA is based on probabilistic model, thus converges faster than genetic algorithm. Hence, when we studied the Genetic Zone Routing Protocol (Known as when genetic algorithm is used to solve ZRP), we considered EDA as an alternative of Genetic algorithms and found it very interesting for research. Our objective of research can be summarized as follows: • To implement the traditional Zone Routing Protocol. • To implement and compare the Genetic Zone Routing Protocol with the traditional Zone Routing Protocol.
2 • To survey the scope of using Estimation of Distribution Algorithms as an alternative of Genetic algorithm. To apply the Univariate Marginal Distribution Algorithm (UMDA) as an Estimation of Distribution Algorithm. To compare and analyze the performance of EDA and GA in ZRP To find the reasonable solution that stands for the comparison result of GA and EDA. routing zone. By employing query control mechanisms, route requests can be directed away from areas of the network that already have been covered. In order to detect new neighbor nodes and link failures, the ZRP relies on a Neighbor Discovery Protocol (NDP) provided by the Media Access Control (MAC) layer. NDP transmits “HELLO” beacons at regular intervals. Upon receiving a beacon, the neighbour table is updated. Neighbours, for which no beacon has been received within a specified time, are removed from the table. If the MAC layer does not include a NDP, the functionality must be provided by IARP. The relationship between the components is illustrated in Figure 2. Route updates are triggered by NDP, which notifies IARP when the neighbour table is updated. IERP uses the routing table of IARP to respond to route queries. IERP forwards queries with BRP. BRP uses the routing table of IARP to guide route queries away from the query source. Detailed of ZRP can be found in [1].
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As EDA is still a growing field of research and so far no one came out of trying to solve ZRP with EDA, we hope that this research will contribute a bit in analyzing the performance of EDA in a new application area, which is already solved by Genetic algorithm. The observations will surely be interesting one. 2. Background 2.1 Zone Routing Protocol (ZRP) The Zone Routing Protocol, as its name implies, is based on the concept of zones. A routing zone is defined for each node separately, and the zones of neighbouring nodes overlap. The routing zone has a radius r expressed in hops. The zone thus includes the nodes, whose distance from the node in question is at most r hops. An example routing zone is shown in Figure 1, where the routing zone of S includes the nodes A–I, but not K. In the illustrations, the radius is marked as a circle around the node in question. It should however be noted that the zone is defined in hops, not as a physical distance. ZRP refers to the locally proactive routing component as the IntrA-zone Routing Protocol (IARP). The globally reactive routing component is named IntEr-zone Routing Protocol (IERP). IERP and IARP are not specific routing protocols. Instead, IARP is a family of limited-depth, proactive link-state routing protocols. IARP maintains routing information for nodes that are within the routing zone of the node. Correspondingly, IERP is a family of reactive routing protocols that offer enhanced route discovery and route maintenance services based on local connectivity monitored by IARP. The fact that the topology of the local zone of each node is known can be used to reduce traffic when global route discovery is needed. Instead of broadcasting packets, ZRP uses a concept called bordercasting.Bordercasting utilizes the topology information provided by IARP to direct query request to the border of the zone. The bordercast packet delivery service is provided by the Bordercast Resolution Protocol (BRP). BRP uses a map of an extended routing zone to construct bordercast trees for the query packets. Alternatively, it uses source routing based on the normal
Figure 2: ZRP Architecture 2.2 Genetic Algorithm (GA) A genetic algorithm is a type of searching algorithm. It searches a solution space for an optimal solution to a problem. The key characteristic of the genetic algorithm is how the searching is done. The algorithm creates a "population" of possible solutions to the problem and lets them "evolve" over multiple generations to find better and better solutions. The generic form of the genetic algorithm is found in Algorithm bellow. The items in bold in the algorithm are defined here. Algorithm: a General Genetic Algorithm BEGIN 1. Create a population of random candidate solutions named pop. 2. Until the algorithm termination conditions are met, do the following (each iteration is called a generation): (a) Create an empty population named new-pop. (b) While new-pop is not full, do the following: i. Select two individuals at random from pop so that individuals which
3 are more fit are more likely to be selected. ii. Cross-over the two individuals to produce two new individuals. (c) Let each individual in new-pop have a random chance to mutate. (d) Replace pop with new-pop. 3. Select the individual from pop with the highest fitness as the solution to the problem. END The population is the collection of candidate solutions that we are considering during the course of the algorithm [5]. Over the generations of the algorithm, new members are "born" into the population, while others "die" out of the population. A single solution in the population is referred to as an individual. The fitness of an individual is a measure of how "good" the solution represented by the individual is. The better the solution, the higher the fitness - obviously, this is dependent on the problem to be solved. The selection process is analogous to the survival of the fittest in the natural world. Individuals are selected for "breeding" (or cross-over) based upon their fitness valuesthe fitter the individual, the more likely that individual will be able to reproduce [5]. The cross-over occurs by mingling the two solutions together to produce two new individuals. During each generation, there is a small chance for each individual to mutate, which will change the individual in some small way. 2.3 Estimation of Distribution Algorithm (EDA) In EDAs the problem specific interactions among the variables of individuals are taken into consideration. In Evolutionary Computations the interactions are kept implicitly in mind whereas in EDAs the interrelations are expressed explicitly through the joint probability distribution associated with the individuals of variables selected at each generation. The probability distribution is calculated from a database of selected individuals of previous generation. The selections methods used in Genetic Algorithm may be used here. Then sampling this probability distribution generates offspring. Neither crossover nor mutation has been applied in EDAs. But the estimation of the joint probability distribution associated with the database containing the selected individuals is not an easy task. The following is a pseudo-code for EDA approach: Step 1: D0 ← Generate M individuals (the initial population) at random Step 2: Repeat steps 3-5 for l=1, 2 … until the stopping criteria met Step 3: Select N<=M Dlse1 ← − individuals from Dl-1 according to selection method Step 4: pl ( x) = p(x | Dl − 1 ) ← Estimate the probability distribution of an individual being among the selected individuals Step 5: Dl ← Sample M individuals (the new population) from pl(x)
se
The easiest way to calculate the estimation of probability distribution is to consider all the variables in a problem as univariate. Then the joint probability distribution becomes the product of the marginal probabilities of n variables, i.e, . Univariate Marginal Distribution Algorithm (UMDA) (Mühlenbein, 1998), Population Based Incremental Learning (PBIL) (Baluja, 1994) and Compact Genetic Algorithm (cGA) (Harik et al., 1998) consider no interaction among variables. In UMDAs the joint probability distribution is factorized as a product of independent univariate marginal distribution, which is estimated from marginal frequencies:
pl (x) =
∏
n i= 1
p ( xi )
pl ( xi ) =
∑
N j=1
δ j ( X i = x i | Dlse1 ) −
N
with
δ j ( X i = x i | Dlse1 ) = 1 −
if in the jth case of
Dlse1 −
,
Xi=xi ; =0, otherwise.
2.3.1 Univariate Marginal Distribution Algorithm (UMDA) In UMDA it is assumed that is there is no interrelation among the variables of the problems. Hence the ndimensional joint probability distribution is factorized as a product of n univariate and independent probability distribution. That is: . Each univariate marginal distribution is estimated from marginal frequencies:
pl ( x) = p ( x | Dlse1 ) = −
∏
n
pl ( xi )
i= 1
pl ( xi ) =
∑
N j= 1
δ j ( X i = xi | Dlse1 ) −
N
with
δj(Xi=x|Ds−le)11
if in the jth case of
Dlse1 −
, Xi=xi =0, otherwise.
The pseudo code for UMDA is as follows: Step-1:D0¬Generate M individuals (the initial population) at random Step-2: Repeat steps 3-5 for l=1,2,… until stopping criteria is met
4 Step-3: Dl-1← Select N£M individuals from Dl-1 according to selection method Step-4: Estimate the joint probability distribution for slow convergence because of the “counting-to-infinity” problem. To address the problem, the DestinationSequenced Distance-Vector routing (DSDV) [7] protocol was proposed for ad-hoc networks. On the other hand, link-state protocols, as represented by OSPF [10], have become standard in wired IP networks. They converge more rapidly, but require significantly more control traffic. Since ad-hoc networks are bandwidth limited and their topology changes often, an Optimized Link-State Protocol (OLSR) [10] has been proposed. While being suitable for small networks, some scalability problems can be seen on larger networks. The need to improve convergence and reduce traffic has led to algorithms that combine features of distance-vector and link-state schemes. Such a protocol is the wireless routing protocol (WRP) [10], which eliminates the counting-to-infinity problem and avoids temporary loop without increasing the amount of control traffic. On the other hand, reactive or on-demand protocols attempt to find a route to the destination, only when the source has a packet to send to the destination. Reactive routing does not attempt to continuously determine the network connectivity. Instead, a route determination procedure is invoked on demand when a packet needs to be forwarded. The technique relies on queries that are flooded throughout the network. In Dynamic Source Routing (DSR) and Adhoc On-demand Distance Vector (AODV), a reply is sent back to the query source along the reverse path that the query traveled. The main difference is that DSR performs source routing with the addresses obtained from the query packet, while AODV uses next-hop information stored in the nodes of the route. In contrast to these protocols, Temporally Ordered Routing Algorithm (TORA) [11] creates directed acyclic graphs rooted at the destination by flooding the route replies in a controlled manner. Proactive protocols maintain the routing information of one node to the other using routing tables. Whenever there is a need for the route to the destination, it is readily available incurring minimum delay. But, at the same time, they may lead to a lot of wastage of the network resources if a majority of these available routes are never used. Reactive protocols are usually associated with less control traffic in a dynamic network; nodes have to wait until replies to the route queries are received. Also reactive protocols resort to frequent flooding of the network, which may cause network congestion. In between the above two extremes, there are the hybrid protocols. As seen, proactive routing uses excess bandwidth to maintain routing information, while reactive routing involves long route request delays. Reactive routing also inefficiently floods the entire network for route determination. The Zone Routing Protocol (ZRP) [1] [7] aims to address the problems by combining the best properties of both approaches. ZRP can be classed as a hybrid reactive/proactive routing protocol. The Zone Routing Protocol (ZRP) [7] is a hybrid proactive / reactive protocol. It is a routing framework composed of the proactive Intra-zone Routing Protocol (IARP) [12], reactive
p l ( x) = p ( x | D ) =
Se l−1
∏
n
i= 1
pl ( xi )
Step-5: Dl¬Sample M individuals (the new population) from pl(x) 2.3.2 Convergence of UMDA by Laplace correction González et al. has shown that some instances with pl(x)³d>0 visits populations of D* which contains global optimum infinitely with probability 1 and if the selection is elitist, then UMDA may converge to a population that contains the global optimum. But the joint probability distribution of UMDA can be zero for some x; for example, when the selected individuals at the previous steps are such that ji −l1 for all j=1, 2,…, N. Hence pl(x)=0. So UMDA sometimes may not visit a global optimum (González et al.). To overcome the problems the way of calculating the probabilities should be changed. One possible solution is to apply Laplace correction (Cestnik, 1990). Now
δ(X=x|DSe)0
p ( X i = xi | D ) =
Se l− 1
∑
N j= 1
δ j ( X i = xi | DlSe1 ) + 1 −
N + ri
where ri is the number of different values that variable Xi may take. Detailed of EDA can be found in [6]. 3. Related Work In recent past, a lot of attention has been shown by the research community to various issues related to ad hoc networks [9]. Many protocols have been proposed for routing in such an environment. These protocols can broadly be classified into two types: proactive and reactive routing protocols. Proactive or table-driven protocols try to maintain routes to all the nodes in the network at all times by broadcasting routing updates in the network. Proactive routing protocols attempt to keep an up-to-date topological map of the entire network. With this map, the route is known and immediately available when a packet needs to be sent. The approach is similar to the one used in wired IP networks, for example in open Shortest Path First (OSPF) [10], Topology Broadcast based on Reverse Path Forwarding (TBRPF), Optimized Link State Routing (OLSR) and Wireless Routing Protocol (WRP). Proactive protocols are traditionally classified as either distancevector or link-state protocols. The former are based on the distributed Bellman-Ford (DBP) algorithm, which is known
5 Inter-zone Routing Protocol (IERP) [26], and the Border cast Resolution Protocol (BRP) [13] [16]. Despite the use of zones, ZRP has a flat view over the network. In this way, the organizational overhead related to hierarchical protocols can be avoided. Hierarchical routing protocols [17] depend on the strategic assignment of gateways or landmarks, so that every node can access all levels, especially the top level. Nodes belonging to different subnets must send their communication to a subnet that is common to both nodes. This may congest parts of the network. ZRP can be categorized as a flat protocol because the zones overlap. Hence, optimal routes can be detected and network congestion can be reduced [14] [15]. ZRP is proved to work well compared to either table-driven protocols or on-demand protocols [18] [19]. Shortest Path Routing [25] is used in mobile ad-hoc network and it determines the effective of application of genetic algorithm in terms of performance. [27] Investigate using a genetic algorithm to create routing tables for an under-water ad hoc network and look at how to use a genetic algorithm to cluster network nodes into subnetworks. The application of Genetic Algorithms in ZRP was first investigated by [25]. But the problem lies whenever the source and destinations reside in different zone. These algorithms failed to work solve the problem of ZRP. [20] [25] give better performance using GA rather than traditional methods. 4. Proposed Method Figure 13: Chromosome representation (arbitrary) Zone routing protocol is a wide area of research in Mobile ad hoc network.GA and EDA both cover a huge selection of theory and application. Thus we need to limit our view in making a liaison between ZRP, GA and EDA. There are various types of EDA [6] both in discrete and continuous domain. We will consider the discrete domain in our case. Specifically, we want to use UMDA [1] to apply EDA in ZRP. UMDA is the simplest of all EDA and use univariate distribution to generate new population. Therefore, the implementation will be easier and this can be compared to the result of GA in ZRP. Our focus can be summarized as follows: • Find a good encoding strategy that will represent the chromosome as the contents of source to destination routing. To solve the increasing complexity of time, delay and congestion for large number of nodes in ZRP. To solve the source to destination routing where the destination is outside the zone. To compare the performance of EDA and GA and traditional ZRP for large number of nodes. S and D represent the source and destination nodes, Bi represents the border nodes of a zone. 5.2 Initial Population The initial population will be generated randomly using uniform random distribution. The size of the population will be a parameter of the network. As the number of population increases (as well as the chromosome length), the complexity of the problem increases. For small number of population and chromosome length, the difference may not be proved significant, but the time consumption will become low. This is the biggest trade off between the real time network and simulated approach. So we will try to choose this parameter as close as possible to a real life network. 5.3 Fitness Function This is another challenge of our research. As our objective is to minimize the distance of the path (find SP), we will design such a fitness function, that will give the best fitness value to the chromosome which represents the shortest path of the network. The fitness function is same for both EDA and GA and will be used to evaluate all the chromosomes of the population. Thus, we can see that there are two main non-conflicting challenges in our research. One is to solve the problem of increasing complexity and the other is to solve the source to destination routing outside the zone, using the border nodes of that particular zone. In both the cases, we will use GA and EDA to solve the problems. 5. Our Approach 5.1 Encoding of Chromosome Arbitrarily, a chromosome consists of sequences of positive integers that represent the IDs of border nodes through which a route path passes. Each locus of the chromosome represents an order of a border node (indicated by the gene of the locus) in a routing path. The gene of the first locus is always reserved for the source node. It never needs more than N number of nodes in a network to form a routing path (Since the chromosome length will never be over the capacity of network). Hence, the maximum size of a chromosome length can be N. A chromosome (routing path) encodes the problem by listing up border node IDs from its source node to destination node based on topological information (routing table) of the network. The chromosome will look like the following figure. However, this is an arbitrary figure and can be changed in future according to the need of the problem domain. This is given just to give the reader an idea about the chromosome.
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6 5.4 Selection Another issue is the number of selected sub population. How can we know, which ‘magical’ number is most appropriate? Unfortunately there is no perfect answer. So, for simplicity, we will consider 50 percent of the initial population whose fitness values are higher. 5.5 Crossover and Mutation The above four sections are common to GA and EDA. This section applies only to GA. Crossover examines the current solutions in order to find the better ones. Physically, crossover in the SP routing problem plays the role of exchanging each partial route of two chosen chromosomes in such a manner that the offspring produced by the crossover represents only one route. This dictates selection of one-point crossover as a good candidate scheme for the proposed GA. One partial route connects the source node to an intermediate node, and the other partial route connects the intermediate node to the destination node. But the mechanism of the crossover is not the same as that of the conventional one-point crossover. In the proposed scheme, two chromosomes chosen for crossover should have at least one common gene (node) except for the source and destination nodes, but there is no requirement that they be located at the same locus. That is, the crossover does not dependent on the position of nodes in routing paths. 5.6 Probabilistic Model This section applies to EDA only. As described in 2.3.2, we will use only UMDA as EDA. Hence we will use that equation for calculating the joint probability distribution of UMDA. This will give us N number of probabilities where N is the chromosome length. Using this vector we will generate the new population of chromosome length N. 5.7 Comparison Parameters Firstly, we will compare the time complexity of ZRP, GA and EDA. Then we will calculate the convergence velocity of EDA and GA. Another parameter may be the number of generations of population needed to reach the optimal point. Our proposed method can be summarized as follows: • • To find a good encoding strategy that will represent the ad hoc network. This encoding will give us the vector which we will try to convert into a binary representation. Then the representation will act as a chromosome of the population. To randomly generate the initial population. • To calculate the fitness value for each chromosome. Use the same fitness function for both GA and EDA. To perform crossover and mutation for GA to generate new population. To perform Probabilistic model for EDA to generate new population. Select the subpopulation with elitism and without elitism. Continue until the result converges.
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6. Numerical Analysis and Simulation 5. Acknowledgement This research was supported by the Computer Science and Engineering Discipline, Khulna University. 8. Conclusion In this paper we have proposed an efficient routing protocol called Zone Routing Protocol. The major difference between ZRP and other routing protocol is it work both in IARP and IERP. Thus such routing protocol using GA and EDA could be more efficient for mobile node clustering. 9. Reference [1] H J Haas, M.R Pearlman, “The performance of query control schemes for the zone routing protocol”, ACM/IEEE Transaction. On Networking, 9(4), 2001, pp. 427–438. [2] H J Holland, “Adaptation in Natural and Artificial Systems”, University of Michigan Press, Ann Arbor, 1975. [3] J M Kin, T H Cho, “Genetic Algorithm Based Routing Method for Efficient Data Transmission in Sensor Networks”, in proceeding of ICIC 2007, pp.273-282. [4] H Cheng, J Cao, X Fan, “GMZRP: Geography-aided Multicast Zone Routing Protocol in Mobile Ad Hoc Networks.” in proceeding of Mobile Networks and Applications Conference 2008. [5] J Inagaki, M Haseyama, H Kitajima, “A genetic algorithm for determining multiple routes and its applications”, in proceeding of IEEE Int. Symp. Circuits and Systems, 1999, pp. 137-140. [6] M Pelican, D Goldberg, F Lobo,” A Survey of Optimization by Building and Using Probabilistic Models”,
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7 Illinois: Illinois Genetic Algorithms Laboratory (IlliGAL), University of Illinois at Urbana-Champaign . [7] H J Haas, “A new routing protocol for the reconfigurable wireless networks”, in proceeding. of IEEE 6th International Conference on Universal Personal Communications 97, 1997, pp. 562-566 [8] D. Whitley,”A Genetic Algorithm Tutorial”, Statistics and Computing, Vol. 4, No. 2. 1994, pp. 65-85. [9] M Frank, M Gerome, P Don, S Steve, ”The Performance of Ad hoc Networking Protocols in Highly Mobile Environments”, Spring 2000, Washington. [10] C E Perkins, P Bhagwat,”Highly Dynamic Destination Sequenced Distance Vector Routing (DSDV) for Mobile Computers”, Computer Communications, 1994, pp234-244 [11] D B Johnson, D A Maltz, “Dynamic Source Routing in Ad hoc Wireless Networking, Mobile node Computing”, T. Imielinski and H.Korth Eds. Norwell, MA,Kluwer, 1996, pp 153-181. [12] H J Haas, M R Pearlman, P Samar, “Intrazone Routing Protocol (IARP)”, IEFT internet Draft, draft-ietf-manetiarp-01.txt, 2001. [13] H J Haas, M R Pearlman, P Samar, “Bordercast Resolution Protocol (BRP)”, IEFT internet Draft, draft-ietfmanet-brp-01.txt, 2001. [14] M R Pearlman, H J Hass, “Determining the Optimal Configuration for the Zone Routing Protocol”, IEEE Journal on Selected Areas in Communications, Vol 17, No. 8, 1999. [15] M R Pearlman, H J Hass, “Providing ad-hoc Connectivity With Reconfigurable Wireless Networks”, Ad Hoc Network 2000. [16] M R Pearlman, H J Hass, “The Performance of Query Control Schemes for the Zone Routing Protocol”, IEEE/ACM Transactions on Networking, Vol 9 No. 4, 2001. [17] P Sinha, S Krishnamurthy, S Dao: “Scalable Unidirectional Routing with Zone Routing Protocol (ZRP) Extensions for Mobile Ad hoc Networks”. [18] P S Kumar, S Ramachandram , C R Rao, “Effect of Transmission Range on the Performance of Zone Routing Protocol in MANETs”, In Proceedings of ICACC, 2007,pp. 627-630. [19] P S Kumar, S Ramachandram, “Performance Studies on the various routing protocols in Ad hoc Networks”, Internationall Journal of Scientific Computing, vol.2, No.1, 2008, pp. 83-91. [20] M Munemoto, Y Takai, Y Sato, “A migration scheme for the genetic adaptive routing algorithm”, in Proceeding of. IEEE International. Conference Systems, Man, and Cybernetics, 1998, pp 2774-2779. [21] D J Baker, A Ephremides, “The architectural organization of a mobile radio network via a distributed algorithm”. [22] I I E Wnston, K G Seah, “Mobility-based d -Hop Clustering Algorithm for Mobile Ad Hoc Networks”. [23] C Y Chiu, E H kuang , G H Chen, “Stability Aware Cluster Routing Protocol for mobile Ad-Hoc Networks”. [25] C W Ahn, R S Ramakrishna, “A Genetic Algorithm for Shortest Path Routing Problem and the Sizing of Populatioon”, IEEE Transaction. On Evolutionary Computation Vol.6, No.6, 2002. [26] C S R Marthy, B S Manoj,”Ad Hoc Wireless Networks Architecture & Protocols, ISBN 81-297-0945-7, Pearson Education Pte. Ltd, Singpore”. [27] D Turgut, S Das, R Elmasri, B Turgaut, “Optimizing clusturing algorithm in mobile ad hoc networks using genetic algorithm approach”, in proceeding of IEEE Global Telecommunications Conference, 21(1), 2002, pp.62-66.