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Energy-Aware Multicast Routing in MANETs: A Genetic Algorithm Approach Dilip Kumar S.M., and Vijaya Kumar B.P., Member, IEEE Abstract—Energy-aware multicasting in mobile ad hoc networks (MANETs) is an important issue due to the energy constraint of battery in each mobile node. In this paper, we propose an energy-aware source-based multicast routing algorithm for MANET, that ﬁnds a path for each node-pair (s, di ) consisting of minimum number of links, that passes through common links and extend the lifetime of an ad hoc network using optimization techniques, where s is a source node and di is a member of the destination set. A linear programming and genetic algorithm approach is used for optimization. The simulation results demonstrate the computational power of the proposed algorithm and shows that this approach is efﬁcient and robust for constructing an optimized multicast tree1 . Keywords—Mobile ad hoc networks; energy-aware; multicast routing; optimization; genetic algorithm 2) Establishing the MCT as quickly as possible 3) Minimize the number of links and nodes from the source node to mutlicast receivers 4) Computing the MCT as and when required to hide the mobility of the host from applications 5) Ensuring the end-to-end reliable multicast delivery 6) Satisfying the energy requirement of nodes along the routing path Several works has been done on energy-aware unicast and multicast routing in mobile ad hoc networks [3], [4], [5], [6], [7], [9]. Motivated by the increasing importance of real-time and multimedia applications with different Quality-of-Service (QoS) requirements, e.g., VoIP and video conferencing, several multicast routing algorithms in wireless/ mobile networks have also been proposed [10], [11], [12]. Such multimedia applications will be popular in high speed ad hoc networks in the near future. Real-time trafﬁc is usually bandwidth and energy extensive and requires QoS guarantees from the underlying network. Hence we need efﬁcient multicast routing algorithms capable of constructing optimized multicast trees that satisﬁes the constraints imposed by the QoS requirements. In this paper, we propose an energy-aware multicast routing algorithm using genetic algorithm that constructs a multicast tree such that the number of links connecting the source node and destination set is minimized and optimizes the energy cost simultaneously. A Genetic Algorithm (GA) based solution is proposed in this work. The GA provide robust and efﬁcient search in complex spaces and are used to solve an optimization problem based on the principle of evolution. The main advantages of GA include: (1) since solutions are coded as bit strings, referred to as chromosomes, large problems can be easily handled using long strings; (2) genetic operations, such as crossover and mutation, are easy to implement; (3) with a pool of chromosomes (candidate solutions), GA search the solution space at different corners in parallel; (4) randomized genetic operations, such as mutation, can keep the search from being trapped by local-optima. GA have been successfully applied by researchers to solve unicast and multicast routing problems in wireless/mobile networks [8], [15], [16], [17], [20]. The rest of the paper is organized as follows. In Section II, some previous multicast routing algorithms relevant to this work are reviewed. An ad hoc network model and the problem statement is presented in Section III. In Section IV, the proposed multicast routing algorithm is discussed. Section V presents the solution for the energy-aware multicast routing problem using GA. Simulation results and concluding remarks are presented in Sections VI I. I NTRODUCTION In the recent literature, mobile ad hoc networks have gained much attention, due to the convenience of building mobile wireless networks without any need for pre-existing infrastructure. The nodes in an ad hoc network cooperatively maintain network connectivity. Each node acts as a router and forwards packets to the next hop in order to reach the ﬁnal destination via multiple hops. The MANET environment is typically characterized by energy-constrained nodes, variablecapacity, bandwidth-constrained wireless links and dynamic topology, leading to frequent and unpredictable connectivity changes. A critical issue for MANETs is that the activity of nodes are energy constrained. However, signiﬁcant energy savings can be obtained at the routing level by designing minimum energy routing protocols that take into consideration the energy costs of a route when choosing an optimized route. Multicasting, which is a one-to-many communication enables a number of e-services whose applications cover a wide spectrum including audio/video conferencing, distance learning, news programmes, software distribution, replicated database update, distributed interactive simulation, etc. A multicast group consists of a source host (server) that is responsible for transmitting data packets to the other hosts (clients) in the same group. Apparently, building a multicast tree is more efﬁcient than sending the same packets from the server to each client individually, which results in signiﬁcant savings in source host processing and network bandwidth. Some of the features of such multicast routing algorithms must have are: 1) Constructing a multicast tree (MCT) from one source to multicast destinations/receivers. 1 This paper is an extended/improved version of our works in [1] and [2]. and VII respectively. II. R ELATED W ORKS In this section, we present a brief review of some heuristic algorithms used to construct the multicast tree. In [15], a heuristic dynamic algorithm for handling group membership which constructs a least cost multicast tree is proposed. The paper in [16], discussed the multicast routing problem with multiple QoS constraints in MANETs and proposed an energy efﬁcient genetic algorithm mechanism to resolve the problem. A source-tree-based routing algorithm is designed and a shortest path multicast tree is constructed to minimize delay by using a small population size in genetic algorithm. A genetic based solution for the multicast routing problem in ad hoc networks is proposed in [19] considering link cost and delay metrics. In [20], a static least cost multiple constrained multicast routing algorithm based on genetic algorithm is proposed. In [21], a multicast routing algorithm that minimizes the end-to-end path cost and maximizes the utilization of path bandwidth. Ref. [1] proposes an energyaware multicast routing problem for MANETs using genetic algorithm, that ﬁnds a path for each node-pair connecting the source node and the destination set such that any node in each path does not run out of its power during the transmission of packets. In [2], the use of the genetic algorithm which considerably reduce the number of solutions to be evaluated is proposed. The algorithm selects a single path from the set of paths between each node-pair. The routes are computed using the on-demand source routing principle considering the reliability of the nodes. Based on the above related works and the literature in the area of multicast routing, energy-based routing and the application of GA in wireless, mobile and ad hoc networks, the observations made are as follows: • The algorithms produce good results, however, their execution time grows exponentially when the size of the network grows and do not provide guarantee for optimal convergence solutions. • The GA encoding scheme is complex and could not be able to adapt to the dynamic changes. • The algorithms construct the least cost multicast tree under bandwidth and delay constraints. However, realtime multimedia applications that uses mobile nodes require the optimization of energy in addition to the above constraints. • Less attention is paid to the issues related to the energybased QoS requirement of a route, i.e., to provide guaranteed battery power for the transmission of packets along the path from a source node to the destination such that any node in the path does not run out of its power during the transmission of packets. In general, the design of QoS multicast routing protocols with multi-constrained metrics has not always taken the nodes’ energy into consideration. • Most of the existing energy-aware routing protocols are designed primarily only to maximize the lifetime of AHNs. To mitigate these problems and to provide an improvement to our previous works in [1] and [2], this paper is proposed. We propose an energy-aware multicast routing using genetic algorithm for MANETs that selects a single path for each node-pair while the number of links connecting the source and multicast receivers are minimized and subject to energy optimization. III. N ETWORK M ODEL AND P ROBLEM D EFINITION In this section, we ﬁrst introduce a mobile ad hoc network model, give some deﬁnitions and then present the problem statement precisely. A. Mobile Ad Hoc Network Model The wireless mobile ad hoc network is modeled by an undirected graph G = (V, E), where V is the set of verticies representing the mobile nodes and E is the set of edges representing full-duplex wireless links connecting the nodes. There is an edge (u, v) ∈ E, if nodes u and v are within the transmission range of each other and its endpoints u and v are called neighboring nodes. B. Deﬁnitions 1) Multicast Group (MCG): A set of destination nodes (or multicast receivers), Γ = {d1 , d2 , ..., dM } excluding the source node (s) participating in the multicast operation is called the Multicast Group. 2) Multipath Set (MPS): The set of paths from s to a destination di (i.e., node-pair (s, di )), is termed as Multipath Set and is denoted by Λ. 3) Node-pair Set (NPS): We deﬁne a node-pair set Υ = {Λ1 , Λ2 , ..., ΛM } for M destinations, where each Λi is the M P S for the ith node-pair and the total number of M paths in Υ = i=1 |Λi |. C. Problem Deﬁnition Based on the notations and deﬁnitions, we now formally deﬁne the problem of this work. Given a graph G = (V, E), s, Γ and Υ, select a single path for each node-pair such that the number of links connecting s and Γ is minimized, passes through common links and the lifetime of the path increases. D. An Example Consider an example of a mobile ad hoc network with nine nodes as shown in Fig. 1. s is a source node, Γ = {d1 , d2 , d3 } is the set of multicast destination nodes belonging to MCG (here M = 3). Given s and Γ, the corresponding node-pair set NPS, Υ = {Λ1 , Λ2 , Λ3 } = {(s, d1 )1 , (s, d2 )2 , (s, d3 )3 }. The multipath set MPS Λ for each node-pair is as follows: • Path set for the node-pair (s, d1 )1 is: {P11 = (s, A, D, d1 ), P12 = (s, B, D, d1 )} • Path set for the node-pair (s, d2 )2 is: {P21 = (s, A, D, d2 ), P22 = (s, B, D, d2 ), P23 = (s, B, E, d2 ), P22 = (s, C, E, d2 )} A D d1 with routing operations with current trafﬁc conditions. The corresponding cost function is deﬁned as: Ci = RBPi DRi (2) s B E d2 C d3 During the route discovery process, when a source node has data to send to its multicast receivers, it broadcasts a route request packet to its neighbors. It is assumed that each node inserts its Ci value to the route request packet that it forwards. The maximum lifetime of a given path P is determined by the minimum value of Ci over the path, that is: LP = min∀ni ∈P Ci (3) Fig. 1. A graph representing an ad hoc network with three destination nodes (d1 , d2 and d3 ). Path set for the node-pair (s, d3 )3 is: {P31 = (s, B, E, d3 ), P32 = (s, C, E, d3 )} where Pik = the k th path of the ith node-pair (s, di ). Now the routing problem is the selection of a single best path (i.e., having minimum number of links, passes through common links and is energy efﬁcient) from the set of paths for each node-pair using optimization techniques. • IV. P ROPOSED MULTICAST ROUTING ALGORITHM In this section, we propose the routing algorithm for constructing a multicast tree in MANETs. The description of the algorithm is given in three steps. Step 1. Finding a set of node-pair paths: This task involves the computation of a set of paths from a source node to each destination belonging to M CG and calculate the lifetime of each path. The number of possible routes depends on the network topology. If the network is densely connected and/or the size of the network is large, the number of routes between source and the destination will be large. So the size of the routing table should be set to a upper bound limit. During this step, we assume that each node vi monitors its energy consumption caused by transmission, reception, and overhearing activities and computes the energy drain rate, denoted by DRi , every T seconds sampling interval by averaging the amount of energy consumption and estimating the energy dissipation per second during the past T seconds2 . The actual value of DRi is calculated by utilizing the well-known exponential weighted moving average method applied to the drain rate values DRold and DRsample , which represent the previous and newly calculated values [3], [4]. DRi = α × DRold + (1 − α) × DRsample (1) Step 2. Optimizing the set of paths for each node-pair using linear programming: In this step, a subset of paths between each node-pair which minimizes the number of links is computed from the set of paths obtained in step 1. In other words, we ﬁnd Υ ⊆ Υ, where |Λi | ≤ |Λi |, Λi ∈ Υ and Λi ∈ Υ using optimization technique formulated as follows. Let (s, di )i = ith node-pair of the multicast group where i = {1, 2, ..., M }, and N P (i) = the number of paths of the ith node-pair (s, di )i , which can be ﬁxed based on the requirement, Pik = the k th path of the ith node-pair (s, di )i , Xik = 1 0 if path Pik is chosen; if path Pik is not chosen; From the set of paths connecting the node-pair (s, di )i where i = {1, 2, ..., M }, select a subset of paths Υ for each node-pair, so that the number of links connecting s and Γ is minimized, passes through common links and the number of such paths in Υ is limited to a certain limit3 . Rmin 1 = minimize 2 N P (i) N P (j) ψ(Pik , Pjl )Xik Xjl k=1 l=1 (4) ∀i, j ≤ M , i = j and (i, j) = (j, i) where ψ(Pik , Pjl ) = |Pik | + |Pjl | − |Pik ∩ Pjl |, |Pik | = number of links in Pik path, |Pik ∩ Pjl | = the number of common links shared by paths Pik and Pjl and Rmin is the list of minimum objective function values produced by the RHS of the Eq. 4 and it is upper-bounded. The paths that are responsible to produce such minimum values are considered to form the set Υ = {Λ1 , Λ2 , ..., ΛM }. Step 3. Optimizing the subset of paths using GA: Once the set Υ is computed in step 2, this step involves the selection of a single path from the subset of paths between each node-pair by considering the lifetime of each node along the path. This optimization problem is solved by using a genetic algorithm approach and is described in Section V. 3 This limit can be ﬁxed based on the topology and total number of paths computed. To better reﬂect the current condition of energy expenditure of nodes, higher priority to the current sample drain rate may be given by setting α between 0.2 and 0.4. The ratio RBPi , DRi where RBPi denotes the residual battery energy of node ni , indicates when the remaining battery of node ni can keep up 2 Such drain rate metric were successfully applied in works such as [3], [4], etc., and their advantages are highlighted. START Initial Population (minimum no. of links & common links) representation of a chromosome is shown in Fig. 3, in which the ith gene, gi = 2 indicates that the second path from the routing table of s to di is chosen. Also shown the lifetime of the k th path of the ith node-pair, for i = 1 to M and k = 1 to S, represented by LPik . Crossover Mutation Fitness Evaluation (based on the lifetime of each path in the chromosome j) No Generate criterion is true? New Offsprings B. Initialization of Chromosomes The initial procedure generates N different chromosomes at random, which forms the ﬁrst generation. This set of chromosomes is called the chromosome pool (or population), and N is the size of the chromosome pool. C. Evaluation of Chromosomes The ﬁtness value of a chromosome is the value of the objective (ﬁtness) function for the solution represented by the chromosome. Given a chromosome pool H = {h0 , h1, ..., hN −1 }, the ﬁtness value of each chromosome is computed as follows. Let LPik be the lifetime of the k th path in the ith node-pair as derived in Eq. 3. The ﬁtness value of the chromosome hj , is given by M Yes STOP Fig. 2. The GA ﬂowchart q 1 q Chromosome 2 q i q M g i= 2 Routing table for s −> d i Route No. Sequence of nodes in Path F (hj ) = i=1 LPik , j = 0, N − 1 (5) 1 2 S s −> d i s−>−−−>d i s−>−−−−−>d i Lifetime LP 12 LP 22 LP After evaluating the ﬁtness values of all chromosomes, the chromosomes are then sorted according to their ﬁtness values such that F (h0 ) ≥ F (h1 ) ≥ ... ≥ F (hN −1 ). That is, the ﬁrst chromosome is the best solution found so far. D. Discarding the duplicate Chromosomes In the chromosome pool, there may exists two or more duplicate chromosomes. These duplicate chromosomes are discarded and they are replaced by new randomly generated chromosomes. E. Reproduction Based on the computed ﬁtness values, some of the chromosomes are selected in order to generate more offspring using crossover and mutation operations and others are removed from the chromosome pool. Hence, chromosomes with large ﬁtness values will survive and reproduce more for the next generation and those with small ﬁtness values will die off. Thus reproduction increases the number of good solutions in the population in every iteration of the algorithm. F. Crossover In this process, two chromosome strings with larger ﬁtness values are picked from the chromosome pool ﬁrst. The start point and length of the portion to be exchanged are randomly selected. Two new offsprings created are put back into the pool. G. Mutation Here one bit in the chromosome string is changed with a certain mutation probability. This process gives the GA an opportunity to search for new, more feasible, chromosomes in new corners of the solution spaces. S2 Fig. 3. Representation of a chromosome V. S OLVING E NERGY- AWARE M ULTICAST ROUTING P ROBLEM USING GA The GA maintain a population of chromosomes, each of which has a ﬁtness value. The ﬁtness value deﬁnes the quality of a chromosome. Beginning with a set of random chromosomes, a process of evolution can be simulated. The main components of this process are reproduction, crossover and mutation. The energy-efﬁcient GA ﬂowchart for the proposed multicast routing is shown in Fig. 2. In this section, we use the principle of GA to construct an energy-aware multicast tree for routing in MANETs. The aim of this GA is to select a single path for each node-pair after the preliminary optimization done using Eq. 4, so that the multicast tree is energy-efﬁcient. Thus the number of possible solutions is signiﬁcantly reduced by preferring routes with minimum number of links leading to reduced search space. In this context, the GA approach is structured around the following functional processes. A. Representation of Chromosomes For a given source node s and MCG Γ = {d1 , d2 , ..., dM }, a chromosome can be represented by a string of integers of length M. A gene gi , 1 ≤ i ≤ M , of the chromosome is an integer in {1, 2, ..., S} which represent a possible route between s and di , where di ∈ Γ and S represents the total number of possible paths constructed for each node-pair. The X 10 5 3 X 10 5 16/64 4 3 4 Fitness values Fitness values 3 2 1 8/32 4/16 3 2 1 20 40 60 80 100 120 140 160 180 200 10 20 30 40 50 60 70 80 90 100 Generations Population size Fig. 4. Fitness values for different generations. Fig. 5. Fitness values with respect to the size of the chromosome pool. 1.0 H. Termination Criteria Convergence speed The execution of the GA is terminated when the number of generations exceed an upper bound speciﬁed by the user. VI. S IMULATION R ESULTS The computational simulation was carried out in an 2.71GHz, 1GB RAM PC with LINUX Operating System and implemented using C++. It is assumed that the network is well dimensioned and nodes are distributed. The experiment is carried out by considering 16-, 24-, 32- and 64- node networks with change in topology in different situations. The source node and the multicast group are randomly selected in the network. The size of the multicast group participating in the multicast operation are varied from 10 to 50 percent nodes of the total number of nodes in a given network topology. The ﬁtness function formula in Eq. 5 is used to obtain the objective function. The parameters of the genetic algorithm, such as size of the chromosome pool, crossover probability, mutation rate, and the number of generations must be properly selected to obtain best performance. The initial energy of all mobile nodes is set to 1000 Joule units and the drain rate(mA) is varied between 2 to 10. Fig. 4 shows the changes in ﬁtness values during generations for three network sizes. The label on the curves in the graph of the form a/b represents the number of multicast receivers/total number of nodes in the network. The maximum runtime was limited to 200 generations; population size is set to 50; crossover probability = 0.8; and mutation rate = 0.02. Fig. 5 shows the ﬁtness value observed after 50 generations under different population size. It is observed that as the size of the population increases, better solutions emerge that could keep the genetic algorithm from falling into the local optimum. The convergence speed taken by the algorithm w.r.t. the number of generations for different crossover probabilities when the mutation rate is 0.02 is shown in Fig. 6. It is observed that the convergence speed is much related to the crossover probability which has a tendency to converge towards 1 after 80 generations for crossover probability: CO prob = 0.9. Fig. 7 shows the efﬁciency of the multicast tree by the number of occurrences of common links with respect to the number of multicast receivers. It is found that as the number 0.8 0.6 0.4 0.2 CO_prob = 0.9 CO_prob = 0.8 CO_prob = 0.7 0 20 40 60 80 100 120 140 160 180 200 Generations Fig. 6. Convergence speed for different crossover rates. of multicast receivers increases and/or density of the nodes increases and/or the multicast receivers are located closely to each other, the number of common links in the multicast tree increases. VII. C ONCLUSION In this paper, an energy-aware multicast routing algorithm for MANETs using genetic algorithm for constructing an optimized multicast tree that connects the source node and the participants of M CG is proposed. The multicast tree consists of minimum number of links (to reduce end-to-end delay) and passes through common links (to use minimum bandwidth). We also adopted a strategy to balance the energy consumption 24 20 16 12 8 4 16−node network 24−node network 32−node network # of common links 2 3 # of multicast receivers 4 5 6 7 Fig. 7. Number of common links occurred with respect to number of multicast receivers for different network sizes. in the multicast tree to extend its lifetime. The number of generations required to reach a good solution has been reduced signiﬁcantly by preferring routes with minimum number of links in initializing the chromosome pool and reusing the past solutions as the initial chromosomes for the new search. This work also presents the capability of the genetic algorithm as a computational tool for solving constrained optimization problem. The proposed work facilitates a possible multicast routing algorithm for future high-speed mobile ad hoc networks, since the hardware implemented genetic algorithm can achieve an extremely high response speed. The proposed algorithm can be extended to multicast routing problems with multiple QoS constraints and may be applied to other types of networks. R EFERENCES [1] Dilip Kumar S.M. and Vijaya Kumar B.P., ”An efﬁcient multicast routing in MANETs: a genetic algorithms approach”, in Proc. of the TENCON’ 08, IEEE Region 10 Conference, Hyderabad, India, Nov. 2008. [2] Dilip Kumar S.M. and Vijaya Kumar B.P., ”Energy-aware multicast routing in MANETs based on genetic algorithms”, in Proc. of the 16th IEEE International Conference on Networks (ICON’ 08), New Delhi, India, Dec. 2008. [3] D. Kim, J.J. Garcia L-A, K. Obraczka, K-C Cano, & P. Manzoni, ”Routing mechanisms for mobile ad hoc networks based on the energy drain rate”, IEEE Trans. on Mobile Computing, 2(2), 2003. [4] K. Murugan & S. Shanmugavel, ”Trafﬁc-dependent and energy-based time delay routing algorithms for improving energy efﬁciency in mobile ad hoc networks”, EURASIP Jr. on Wireless Communications and Networking, no. 5, pp. 625-634, 2005. 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Jr. Network Manage, vol. 13, 1-15, 2003. [15] T.C. Chiang, C.H Liu and Y.M. Huang, ”A near-optimal multicast scheme for mobile ad hoc networks using a hybrid genetic algorithm”, Expert systems with applications, vol. 33, no. 3, pp. 734-742, Oct. 2003. [16] Y-S. Yen, Y-K. Chan, H-C. Chao and J.H. Park, ”A Genetic Algorithm for Energy-efﬁcient based Multicast Routing on MANETs”, Elsevier Computer Communications, no. 31, pp. 858-869, 2008. [17] A.T. Haghighat, K. Faez, and M. Dehghan, ”GA-based heuristic algorithms for QoS based multicast routing”, Jr. of Knowledge-based Systems, vol. 16, no. 5-6, pp. 305-312, 2003. [18] Gelenbe E., A Ghanwani and V. Srinivasan, ”Improved Neural Heuristics for multicast routing”, IEEE JSAC, vol. 15, pp. 147-155, 1997. [19] Piotr S., Maciej P., and Piotr Z, ”The implementation of genetic multicast algorithms in ad-hoc networks”, Poznan University of Technology Academic Journals, 2007. [20] Sun, Q. and L. Li, ”Optimizing on multiple constrained QoS multicast routing algorithms based on GA”, Jr. Sys. Engg. Elect., vol. 15, pp. 677683, 2004. [21] M. R. Islam, M. F. Rahman and M. A. G. Khan, ”An approach to implement the multicast multiconstrained routing based on genetic algorithm”, Bangaladesh Research Journal, vol. 1, no. 1, pp. 101-112, 2008. [22] K. F. Man, K. S. Tang and S. Kwong, ”Genetic Algorithms - Concepts and Designs”, Springer-Verlag, London, 1999. Dilip Kumar S.M. received the B.E degree in Computer Science and Engineering, Kuvempu University and M. Tech degree in Computer Science and Engineering, Visvesvaraya Technological University in 1996 and 2001 respectively. Currently, he is the assistant professor in the Department of Computer Science and Engineering, University Visvesvaraya College of Engineering (UVCE), Bangalore University, Bangalore, INDIA. His research interests are in mobile computing, ad hoc networks and computational intelligence. Vijay Kumar B.P. received the B.E degree in Electronics and Communication from Mysore University in 1986. He received the M. Tech degree in Computer Technology from Indian Institute of Technology, Roorkee with honors in 1992 and Ph. D degree from Indian Institute of Science, Bangalore in 2002. Currently he is the professor and principal research scientist at the wireless information systems laboratory, Reva institute of technology and management, Bangalore, INDIA. His current research interests include mobile computing, ad hoc networks, wireless sensor networks, and neural networks for wireless mobile networks.