Cooperative Particle Swarm Optimization for Layout Optimization in Wireless Sensor Networks

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1 Cooperative Particle Swarm Optimization for Layout Optimization in Wireless Sensor Networks Nathan Fortier Compute Science Department Montana State University Bozeman, Montana Agata Gruza Compute Science Department Montana State University Bozeman, Montana Russ Ericksen Compute Science Department Montana State University Bozeman, Montana Abstract Energy consumption and coverage are common design issues in Wireless Sensor Networks (WSNs). For that reason, it is vital to consider network coverage and energy consumption in the design of WSN layouts. Because selecting the optimal geographical positions of the nodes is usually a very complicated task, we propose a novel heuristic search technique to solve this problem. Our approach is a multi-population search algorithm based on Particle Swarm Optimization (PSO). The goal of this algorithm is to search for sensor network layouts that maximize both the coverage and lifetime of the network. Unlike traditional PSO, our algorithm assigns a swarm to each sensor in the network and a global network topology is used to evaluate the fitness of each particle. We hypothesize that the suggested method will improve upon the single population search algorithms that are often applied to this problem. I. INTRODUCTION A Wireless Sensor Network (WSN) is an assemblage of sensor nodes deployed in a target area and used to perform monitoring and surveillance tasks. Each sensor node is a small, low-priced sensor that transmits data to a central high-energy communication node (HECN). The devices communicate with each other wirelessly over a small distance and can remotely monitor a variety of situations. At present, WSNs have become a hot research topic because of their promising application in numerous fields including environmental monitoring, medicine, animal tracking, and military surveillance. Even though sensor networks have expeditiously become omnipresent in their applications, energy consumption and positioning of the sensor nodes is a major concern. Most sensors rely on batteries that have limited lifespan and need to be replaced regularly. The design of sensor layouts that account for both network coverage and power consumption is a difficult problem. Because WSN may have large number of nodes, the task of selecting the optimal geographical positions of the nodes can be very complicated. Therefore, we propose a cooperative particle swarm algorithm as a heuristic to address the problem of wireless sensor layout design. In our approach we assign a swarm to each node in the network. Each swarm will search for optimal x and y positions for its associated sensor. A global network layout, consisting of the coordinates found by the best particles, will be maintained by the algorithm. The lifetime and coverage of this global layout will be used to measure the quality of each particle s position. We call this algorithm SSplit. We hypothesize that by splitting the swarms across the set of sensors, our algorithm will obtain a finer-grained credit assignment, and reduce the chance of neglecting a good solution for a specific portion of the solution vector. We will verify this hypothesis by comparing our algorithm to several traditional single-population search techniques. A. Layout Optimization II. BACKGROUND Layout optimization for wireless sensor networks consists of finding the coordinates for a set of sensors that maximizes the lifetime and coverage for the sensor network. Placement of the sensors is bounded within a two-dimensional square region with an upper left corner at (0, 0) and a lower right corner at (M, M). Each sensor can monitor anything in the sensing radius R s and a sensor can communicate with any other sensor within the communication radius R c. Every sensor must periodically transmit its data to a high-energy communication node (HECN). In our model we assume that the HECN is placed in the center of the region. This assumption does not effect generalizability. Each sensor has an initial energy E and this energy decreases by one unit for each data transmission. The coverage for a given layout is computed as the area of the union of the circles of radii R s centered at each sensor, divided by the total area: Coverage = n i=1 R s(x i, y i ) 2 (1) Area The lifetime of a sensor layout is computed as the time to first sensor failure divided by the maximum lifetime of a sensor: Lifetime = min i=1...n(t failure,i ) (2) T max In our model, we assume that all sensors gather data at the same time and then relay the data to the HECN. This may require the data to be propagated by several sensors before it reaches the HECN. Thus, at each iteration, the sensors must transmit their own data along with the data from other sensors. At each iteration, the data from each sensor must be routed to the HECN along the path that maximizes the remaining energy in the sensors. To find these paths, we weight the

2 Algorithm 1 Particle Swarm Optimization repeat for each particle position x i P do Evaluate position fitness f(x i ) if f(x i ) > f(p i ) then p i = x i end if if f(x i ) > f(p g ) then p g = x i end if v i = ωv i + U(0, φ 1 ) (p i x i ) + U(0, φ 2 ) (p g x i ) x i = x i + v i end for until termination criterion is met outgoing edges of each sensor node by the inverse of the nodes remaining energy and use Dijkstra s algorithm to identify the minimum weight path. This procedure is repeated until the energy for one of the sensors is depleted, providing the time to first sensor failure. This method for estimating lifetime is commonly used in the literature by several population-based search techniques for topology design [1 3] and shortest path algorithms based on remaining sensor energy have been shown to be effective for finding routes that maximize lifetime in sensor networks [4]. The two objectives for this problem are in conflict. Maximizing coverage will cause the network layout to be more spread out with sensors being located as far from each other as possible. This will result in a large number of relay transmissions leading to low lifetime due to the increased energy consumption. Conversely, maximizing lifetime will lead to a network layout clustered around the HECN with large overlap between sensors and low coverage. B. Particle Swarm Optimization The Particle Swarm Optimization (PSO) algorithm is a population based search technique inspired by the behavior of bird flocks and fish schools [5]. In PSO, the swarm is populated with a number of randomly initialized particles. Each particle has a position that encodes a possible solution to the optimization problem and a velocity that determines how the particles will explore the search space. Each particle maintains the position in the search space associated with the best solution it has found so far. This position, called the personal best position of the particle, is denoted as p i for the ith particle. The algorithm also stores the global best position found by any particle in the swarm, denoted as p g. The position and velocity are represented as vectors of real numbers. The position vector of each particle is updated based on that particle s velocity vector. Each particle s velocity vector is updated based on the particle s fitness. Eventually all particles move closer to an optimum in the search space. The pseudocode for the traditional PSO algorithm is presented in Algorithm 1. In Algorithm 1, P is the particle swarm, U(0, φ i ) is a vector of random numbers uniformly distributed in [0, φ i ], is component-wise multiplication, v i is the velocity vector of a particle, and x i is the position vector of a particle. Three parameters need to be defined for the PSO algorithm: φ 1 determines the maximum force with which a particle is pulled toward p i ; φ 2 determines the maximum force with which a particle is pulled toward p g ; ω is the inertia weight. The inertia weight ω is used to control the scope of the search and eliminate the need for specifying a maximum velocity. A. Existing Approaches III. RELATED WORK Optimal placement of sensor nodes is a difficult problem that has been shown to be NP-hard for most formulations [6 9]. For example, Xu et al. showed that finding the minimum number and placement of sensor nodes to meet lifetime and connectivity constraints is NP-hard [9] To address this complexity, several authors have applied heuristic search algorithms to this and other problems relevant to wireless sensor networks. Fidanova et al. [10] proposed Ant Colony Optimization (ACO) algorithm to maximize the coverage of the network and in the same time to minimize the number of nodes. It this algorithm ant bots explore and strengthen pathways (solutions) to discover the optimal one. The problem is depicted by a graph and the ants march on the graph to establish solutions. The answer is portrayed by a path through the graph. Initialization starts from random nodes and then at each step ants calculate a set of the feasible moves, select the best move based on a probabilistic heuristic function and the trails are updated. Yousefi et al. [11] suggested 2-stage algorithm that was formed on Huber M-estimator to get precise sensor location approximation. Location of sensors are estimated in the first stage by implementing convex relaxation on the Hubert cost function. In the second phase, if proportion of NLOS to LOS is small, parameters of the Huber cost function are adjusted to get a minimum of the function. In each repetition step, gradient descent is applied to find a local minimum. Authors presented strong estimation in NLOS scenarios for convex relaxation. Moreover, they proved that in 2nd step, when the cost function is minimized, a rough guess of the position is much better. Using a real set of sensor measurements is another way to calculate fitness in the algorithm. Cakier et al. [12] used particle swarm optimization and time difference of arrival to find locally optimal emitter locations. The authors proposed two advanced techniques related to arrival time that help improve positioning precision. The Cramer-Rao lower bound is used to measure approximation error. In the paper, large improvements on the positioning accuracy are attained by implementing PSO and TDOAA jointly. As a replacement to PSO, the authors suggest applying PSOA and PSOH techniques. Simulation performances demonstrate that the PSO algorithm with positioning accuracy is more effective than the classical estimators. 2

3 Zhang et al. [13] presented a thorough analysis of the LEACH protocol, its benefits, and its downsides. The authors used a genetic algorithm and simulated annealing as part of a clustering routing protocol for energy balance of wireless sensor networks. In this algorithm, if the average energy of the cluster is smaller than the energy of the node in the cluster, then it becomes the candidate cluster head. The candidate cluster head can become the cluster head based on the distance to the cluster center. The author s experiments demonstrate that the algorithm is effective at load balancing and extending the lifecycle of wireless sensor networks One of the most crucial issues related to wireless sensor networks is energy efficiency, because sensor nodes are powered by batteries with limited energy. Marcelloni et al. [14] explored how evolutionary algorithms can be used to create energyaware compressors and address sensor localization. The authors tested three different datasets composed by real WSNs. Experimental results show that the evolutionary algorithms outperform most methods suggested in recent literature. Jalsan et al. [15] suggest a method to approximate node energy consumption for WSNs in layout optimization. The authors took into consideration radio propagation with the free-space path loss and the fading effects. The network is simulated with a balanced simulation granularity to obtain low complexity while maintaining good approximation accuracy. The experiments compared the proposed method with energy models suggested in related work and demonstrated an improvement in approximation accuracy. Jourdan and Weck [2] describe a genetic algorithm for the placement of sensors in WSNs. The algorithm uses Pareto dominance to evaluate solution quality. The authors found that the algorithm produced two different types of layouts: a huband-spoke layout and a closely packed layout Pradhan et al. [1] proposed a Multi-Objective Particle Swarm Optimization algorithm for finding sensor network layouts that maximize coverage and lifetime. The authors used a traditional single-swarm PSO approached with a fitness function based on Pareto dominance. While the authors experiments did evaluate the coverage and lifetime of the learned layouts, they did not compare the algorithm to existing population based approaches. B. Multi-population Algorithms Several authors have proposed multi-population search algorithms. The most common multi-population search techniques are genetic algorithms (GA) in which the members of each sub-population encode full solutions to the optimization problem [16 19]. In these algorithms, several subpopulations or islands, are maintained by the genetic algorithm, and members of the populations are exchanged through a process called migration. These methods have been shown to obtain better quality solutions than traditional GAs when applied to the problems of neural network parameter learning, the traveling salesman problem, and several deceptive problems proposed by Goldberg et al. [17, 20]. Because the islands ensure some independence between the populations, each island can explore a different section of the search space while sharing information with other islands through migration. This improves genetic diversity and solution quality [19]. Bergh and Engelbrecht developed several multi-population PSO methods for training multi-layer feed-forward neural networks [21]. These algorithms differ from the island models described above in that each individual in a sub-population maintains a partial solution to a larger problem. These methods include NSPLIT in which there is a single particle swarm for each neuron in the network and LSPLIT in which there is a swarm assigned to each layer of the network. Bergh and Engelbrecht argue that splitting the swarms in this way results in a finer-grained credit assignment, reduces the chance of neglecting a potentially good solution for a specific component of the solution vector. The results obtained by the authors indicate that the distributed algorithms outperform traditional PSO methods. Recently a new distributed approach to improve the performance of the PSO algorithm has been explored where multiple swarms are assigned to overlapping subproblems. This approach is called Overlapping Swarm Intelligence (OSI) [22 24]. In OSI each swarm searches for a partial solution to the problem, and solutions found by the different swarms are combined to form a complete solution once convergence has been reached. Where overlap occurs, communication and competition take place to determine the combined solution to the full problem. Haberman and Sheppard first proposed OSI as a method to develop an energy-efficient routing protocol for sensor networks that ensures reliable path selection while minimizing the energy consumption during message transmission [22]. In this approach a swarm is associated with each node in the sensor network and each swarm consists of a particle for its corresponding node and the particles for all of the nodes immediate neighbors. Thus, the swarms for a given node overlaps with its neighboring swarms. This algorithm was shown to be able to extend the life of the sensor networks and to perform significantly better than current energy-aware routing protocols. Ganesan Pillai extended the OSI method to learn the weights of deep artificial neural networks [23]. This algorithm separates the structure of the network into paths where each path begins at an input node and ends at an output node. Each of these paths is associated with a swarm that learns the weights for that path of the network. A common vector of weights is maintained across all swarms to describe a global view of the network. This vector is created by combining the weights of the best particles in each of the swarms. This method was shown to outperform the back-propagation algorithm, the traditional PSO algorithm, and both NSPLIT and LSPLIT on deep networks. A distributed version of this approach was developed subsequently by [24]. Fortier and Sheppard developed a method for abductive inference in Bayesian Networks based on OSI [25]. In this approach, multiple swarms are used to find the most probable state assignments for a Bayesian network given the evidence. 3

4 Each node in the network is associated with a swarm that learns the state assignments for its Markov blanket. Swarms periodically communicate and compete for inclusion in the final set of most probable state assignments. IV. APPROACH In traditional single-population search algorithms unfavorable entries in the solution vector may become established in the population following an early association with an instance of a highly fit entries in the solution vector. This phenomenon is called hitchhiking and can be addressed using cooperative multi-population approaches, such as the one proposed here. By splitting up the population and assigning each subpopulation to a portion of the solution vector we can obtain finer-grained credit assignment, and reduce the chance of associating an unfavorable component of the solution vector with a potentially good solution. We propose SSplit, a cooperative swarm algorithm for optimizing sensor network layouts. Our approach optimizes over several populations simultaneously and the solution vector is split across the different populations. Because there is no overlap between the space covered by different subpopulations, a solution to the global problem can be obtained by combining representatives from each sub-population. In our approach, a swarm is associated with each sensor node in the network. Each node s corresponding swarm will learn the x and y positions for that sensor in the network layout. The algorithm maintains a list of elite layouts that have not been dominated by any of the examined layouts. Because the lifetime and coverage can only be computed using a full layout of all the sensors, one of these elite layouts is chosen as the global network layout L, represented as a vector of real numbers encoding the position of each sensor: L = [x 1 y 1... x n y n ] The global layout is chosen as the elite layout that maximizes the average between the normalized coverage and lifetime. The list of elite layouts is updated each time a new network layout is evaluated. In this way we ensure that the list of elite layouts represents the Pareto front of the explored region of the search space. Each particle s position is defined by a two-dimensional vector of real numbers x i R 2 where 0 x M for each x x i. The position and velocity for each particle are initialized randomly and are updated as described in Algorithm 1. Each particle contains a coverage, lifetime, and fitness score. To evaluate the fitness of a particle p, the corresponding sensor position stored in the particle is substituted into the global layout L. If any nodes in the new layout are not connected to the HECN, then each unconnected sensor is moved to the closest point that would result in full connectivity. The coverage and lifetime for the layout L are then computed and assigned to the particle as p.c and p.l respectively. The fitness of a particle is based on Pareto dominance, and is inversely proportional to the number of particles that dominate it. The number of particles in swarm s that dominate a particle p is computed from its lifetime and coverage as: s d(p) = [p i.c > p.c p.l < p i.l] (3) i=1 From this value a particle s fitness is computed as follows: f(p) = d(p) Using this fitness function, we ensure that the fitness of a particle increases as fewer particles within its swarm dominate it. V. EXPERIMENTAL DESIGN To measure the efficiency and usefulness of our algorithm, we have compared our approach to the Multi-Objective Particle Swarm Optimization (PSO) algorithm proposed in [1], the Multi-Objective Genetic Algorithm (GA) discussed in [2], and Ant Colony Optimization (ACO) algorithm proposed in [10]. We will compare these methods in terms of mean coverage and lifetime averaged over several runs. For our algorithm, four particles were assigned to each subswarm. For the other population based approaches, the total number of individuals was four times the number of sensors, to ensure a fair comparison between the algorithms. For both swarm-based algorithms φ 1 and φ 2 were set to , while w was set to Eberhart and Shi empirically determined that these are good parameter choices for w, φ 1, and φ 2 [26]. For the experiments we set the number of sensors to 25, 50 and 75 to best simulate a live sensor network. For each network size, we varied the Rs R c ratio between the following 1 values: 2, 2 2, and 2 1. For each combination of network size and radius ration we ran each algorithm 10 times. Overall, each algorithm was run 30 times for each sensor network size. We have compared the average coverage and lifetime of the algorithms over these 10 runs. A paired student t-test with a confidence interval of 95% was used to evaluate the statistical significance of our results. We are making the assumption that all sensors have the same battery life and is the only source of energy. There is also the assumption that for every transmission, one unit of energy is used. The HECN battery life is assumed to be infinite and is placed in the middle of our testing area. The testing area is considered to be flat and without obstacles. VI. EXPERIMENTAL RESULTS Tables I and II show the mean coverage and lifetime for all algorithms averaged over 10 runs for each configuration. Bold values indicate that the corresponding algorithms significantly outperformed the other algorithms based on the paired student t-test. Table I shows that SSplit significantly outperforms the other algorithms in terms of coverage for most configurations and, for all configurations, SSplit outperformed the traditional single swarm PSO algorithm. Table II shows that SSplit significantly outperforms the other algorithms in terms of (4) 4

5 lifetime for four of the nine configurations. For the other configurations SSplit tied with either PSO or the GA. SSplit is the only algorithm that performed the best in terms of both coverage and lifetime for eight of the nine configurations. We believe that this advantage is due to the distribution of swarms over the sensors. By assigning a swarm to each individual sensor, SSplit reduces the possibility of neglecting a potentially good sensor position for a specific component of a complete sensor layout. This finer grained credit assignment allows SSplit to avoid the hitchhiking phenomena that traditional single-population search algorithms suffer from. TABLE I COMPARISON OF AVERAGE COVERAGE BETWEEN ALGORITHMS Number of Sensors Rs / Rc GA ACO PSO SSplit 1/ / / / / / / / / TABLE II COMPARISON OF AVERAGE LIFETIME BETWEEN ALGORITHMS Number of Sensors Rs / Rc GA ACO PSO SSplit 1/ / / / / / / / / VII. CONCLUSION AND FUTURE WORK We have proposed a new Cooperative Particle Swarm Optimization algorithm for learning WSN layouts that maximize coverage and lifetime. Our hypothesis was that the multiswarm approach proposed here will mitigate the hitchhiking phenomenon and outperform traditional single-population search techniques. We have compared our approach to several existing algorithms to validate this hypothesis. Our experiments indicate that our algorithm surpasses existing single-population search techniques in terms of either lifetime or coverage on nearly all of the configurations. These results support our hypothesis that splitting the swarms over the sensors provides a finer grained credit assignment thereby improving performance. For the future work we will improve SSplit by including obstructions. We will simulate non-flat terrains by using nonuniform densities of points to approximate coverage. Varied densities will simulate the change in height, where low densities are areas of poor sensing (such as the top of hills). Moreover, we will add communication blocking objects by marking areas off as obstructions and disallowing communication across these objects. This will force the algorithm to compensate by avoiding the blocking object and will increase the complexity of the fitness function. Additionally, will take into consideration lifetime variance in a sensor and we will explore discrepancies in a drop locations. In our approach we have made several unrealistic assumptions when computing lifetime. Currently we assume that no energy is used for idle or receiving states and the energy consumption is not based on estimates of network flow. For future work we will explore more realistic energy consumption and network traffic models when estimating lifetime. REFERENCES [1] P. M. Pradhan, V. Baghel, G. Panda, and M. Bernard, Energy efficient layout for a wireless sensor network using multi-objective particle swarm optimization, in Advance Computing Conference, IACC IEEE International. IEEE, 2009, pp [2] D. Jourdan and O. L. de Weck, Layout optimization for a wireless sensor network using a multi-objective genetic algorithm, in Vehicular Technology Conference, VTC 2004-Spring IEEE 59th, vol. 5. IEEE, 2004, pp [3] K. Chaudhuri and D. Dasgupta, Multi-objective evolutionary algorithms to solve coverage and lifetime optimization problem in wireless sensor networks, in Swarm, Evolutionary, and Memetic Computing. Springer, 2010, pp [4] J.-H. Chang and L. Tassiulas, Maximum lifetime routing in wireless sensor networks, IEEE/ACM Transactions on Networking (TON), vol. 12, no. 4, pp , [5] R. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, in Proceedings of the Sixth International Symposium on Micro Machine and Human Science. IEEE, 1995, pp [6] X. Cheng, D.-Z. Du, L. Wang, and B. Xu, Relay sensor placement in wireless sensor networks, Wireless Networks, vol. 14, no. 3, pp , [7] A. Efrat, S. Har-Peled, and J. S. Mitchell, Approximation algorithms for two optimal location problems in sensor networks, in Broadband networks, BroadNets nd international conference on. IEEE, 2005, pp [8] S. Poduri, S. Pattem, B. Krishnamachari, and G. S. Sukhatme, Sensor network configuration and the curse of dimensionality, in Proc. Third Workshop on Embedded Networked Sensors (EmNets 2006), Cambridge, MA, USA, [9] K. Xu, Q. Wang, H. Hassanein, and G. Takahara, Optimal wireless sensor networks (wsns) deployment: minimum cost with lifetime constraint, in Wireless And Mobile Computing, Networking And Communications, 5

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