Particle Swarm Optimization-Based Consensus Achievement of a Decentralized Sensor Network

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1 , pp Particle Swarm Optimization-Based Consensus Achievement of a Decentralized Sensor Network Hyunseok Kim 1, Jinsul Kim 2 and Seongju Chang 1*, 1 Department of Civil and Environmental Engineering, Korea Advanced Institue of Science and Technology, Daejeon , Korea, 2 School of Electronics and Computer Engineering, Chonnam National University, Gwangju , Korea, hertzkim@kaist.ac.kr; jsworld@jnu.ac.kr; schang@kaist.ac.kr *Corresponding author Abstract. This paper explores the possibility of enhancing the decision-making capability of a decentralized sensor network by establishing cooperative behavior among sensor agents. For that purpose, it was necessary to devise a robust consensus mechanism that distributes sensing information through local fusing with neighbors rather than through a centralized control. This paper proposed a novel particle swarm optimization framework to achieve robust consensus of decentralized sensors; the new framework showed an 16.5% improvement in consensus achievement as compared to the classic majority rule method. Noteworthy enhancements in consensus achievement are also pertinent to the comparable situation of decentralized-sensor network. Keywords: Consensus achievement, decentralized sensor networks and particle swarm optimization 1 Introduction The distributed deployment of multiple sensors is designed to establish cooperative behavior between sensors, thus providing sufficient local information with different focuses and from different viewpoints relative to a given environment. In such a deployment, peer-to-peer communications between adjacent sensors are enabled to avoid the communication bottlenecks possible in a centralized network [1]. In a decentralized sensor network, sensing information of neighbors is fused locally rather than via central control as enabled by a distribution of intelligent agents with some degree of decision-making autonomy. A major research objective is to establish cooperative behavior between sensors with no external supervision. Where each sensing mechanism among multiple sensor agents concurrently perceives environmental changes, each can derive an opinion in accordance with the sensing results. Furthermore, these opinions are shared with neighbors and spread. As the technology has developed to date, when a conflict of nominal opinion arises and central coordinator cannot intervene, the central coordinator is unable to execute any service for the user. To address that failure, this paper proposes a scheme for consensus achievement of decentralized sensors (CADS) based on the particle swarm ISSN: ASTL Copyright 2013 SERSC

2 optimization (PSO) framework for decision-making among decentralized multiple sensor agents. 2 Proposed PSO CADS Mechanism The proposed CADS is based on the two main concepts of PSO: to match nearestneighbor velocity (acceleration) and to weigh acceleration using a random term (craziness) [2][3]. Under the former concept, individual opinion moves toward a matching nearest-neighbor consensus. Under the latter concept, swarm opinion converges from alternatives, accelerating toward a better decision. As the model iterates, individual opinions conspire to achieve optimal consensus. First, each agent requests neighbors opinions via a static or dynamic adjacent link, and the individual opinions thus gathered are coordinated. Second, swarm particles are initiated according to these opinions and statistical mode values are extracted as alternative decisions. Third, swarm particles move toward a consensus position. Fourth, all particles converge at an optimum consensus. Finally, the above consensus process iterates until it meets the stop conditions. To detail this process concretely, let the opinion of node i be x i, 1 i n, and the length of vector x i and v i equal the dimensionality of the opinion. The swarm size can be determined as the number of nodes multiplied by the number of alternatives. The terms c 1 and c 2 are cognitive and social constants, respectively, changing the velocity of particles toward the previous best position and the global best position. The velocity of the i-th particle at iteration n is followed to (1) and its next position is determined by (2), where uniform random numbers rand 1 and rand 2 are stochastic variables, called craziness, to avoid the unfortunate state of all particles quickly settling into a unanimous, unchanging direction [4]-[7]. ω v i [n 1] v i [n] = χ + c 1 rand 1 p ibest [n 1] x i [n 1] (1) + c 2 rand 2 (g best [n 1] x i [n 1]) x i [n] = x i [n 1] + v i [n] (2) This paper defines the cost function, cost_pbest() for moving toward consensus as (3), and derives the previous best position, p ibest, through the cost function for its own previous best positions. The cost function, cost_gbest(), for ascertaining the best decision is (4), and the global best position, g best, is determined by the cost function. Finally, a consensus is derived by (5). cost gbest(xi ) (perf, decision) = ( min{e[(x i M) 2 ]}, cost_pbest(x i ) X x i 2 (3) arg min m M {E[(x i M) 2 ]}) (4) consensus = cost_gbest(g best [n]){decision} (5) Copyright 2013 SERSC 163

3 (a) (b) (c) (d) Fig. 1. (a) A predefined network with 46 nodes and 347 links. (b) Its initial opinions. The proposed PSO-based CADS can make a decision through only local interactions: (c) Final iteration. (d) Performance graph. 3 Simulation Outcomes This paper used the number of statistical modes as alternative decisions. For example, given a predefined network of 46 nodes and 347 links, as shown in Fig. 2(a), and given the opinion of dataset x, the mode of the dataset is not unique and may be said to be bimodal, as illustrated in Fig. 2(b). In this case, the number of statistical modes is two and the mode values are 22 and 36: Thus, M = (22, 36) T. The previous consensus algorithm, the standard average consensus algorithm [8][9], derives a value near the mean value from the dataset. In this paper, the results of the two CADS simulations among multiple agents use no global knowledge or centralized communication, but rely solely on local interaction with neighbors. The majority rule based on statistical modes cannot advance the process, given a conflict of opinions. On the other hand, it also shows that the proposed PSO-based CADS can make a decision only through local interactions absent a conflict of opinions, as shown in Figs. 3. Table I shows the parameters of PSO-based consensus achievement. Additional experiments applied two approaches for simulating experimental network topologies for 46 agents randomly generated 1000 times. Fig. 4(a) and 4(b) shows the histogram for the number of links and the number of alternatives, respectively. Fig. 4(c) and 4(d) shows that traditional majority rule using the statistical mode achieved consensus in 748 of the 1000 independent trials, while the 164 Copyright 2013 SERSC

4 (a) (b) (c) (d) Fig. 2. The information for randomly generated networks in 1000 independent trials. (a) The histogram of the number of links. (b) The histogram of the number of alternatives (= the number of statistic mode values). (c) The result of majority rule approach. (d) The result of the proposed PSO-based CADS approach. proposed PSO-based CADS approach achieved consensus in 872 of 1000 independent trials. Table 1. Parameters for PSO-based consensus achievement Parameters Value Swarm size (Z k ) Size(input_data) Number of Alternatives Initial global best position 0 Initial particle position input_data Minimum position (min_pos) ( -max(input_data) + 3 min(input_data) ) / 2 Maximum position (max_pos) ( 3 max(input_data) - min(input_data) ) / 2 Minimum norm of velocity (max_pos - min_pos) / 100 Inertial constant (ω) 1 Cognitive constant (c 1 ) 2.05 Social constant (c 2 ) 2.05 Use constriction factor TRUE Clip the particle position TRUE Maximum initial velocity 1 Maximum iteration 10 Copyright 2013 SERSC 165

5 4 Conclusion This paper has explored a possible new way to enhance the decision-making capability of a decentralized sensor system through a consensus mechanism that distributes sensing information through local fusing with neighbors rather than through centralized control. For that purpose, this paper has proposed a novel PSO framework to achieve robust consensus of decentralized sensors. The new framework shows a 16.5% improvement in consensus achievement as compared to the classic majority rule method. Therefore, an SAS using the proposed framework is expected to offer little or no delay in executing user service requests. The method will help establish cooperative behavior between agents with no external supervision and may be expected to occasion remarkable enhancements in consensus achievement that are also pertinent to the comparable situation of decentralized-sensor systems. Acknowledgments. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology(NRF-2013R1A1A ) References 1. Xiong, Ning, and Per Svensson. "Multi-sensor management for information fusion: issues and approaches." Information fusion 3, no. 2 (2002): J. Kennedy and R. Eberhart, Particle Swarm Optimzation, Neural Networks, 1995, Proceedings., IEEE International Conference on, vol. 4, no., pp , Nov/Dec Hyunseok Kim and Seongju Chang, "High-Resolution Touch Floor System Using Parti-cle Swarm Optimization Neural Network," Sensors Journal, IEEE, vol.13, no.6, pp , June R. C. Eberhart and Y. Shi, "Guest editorial special issue on particle swarm optimization," Evolutionary Computation, IEEE Transactions on, vol. 8, pp , Y. Shi and R. Eberhart, Parameter selection in particle swarm optimization, In Evolutionary Programming VI, pp , Y. Shi, "Particle swarm optimization: developments, applications and resources," Evolutionary Computation. Proceedings of the 2001 Congress on, vol.1, no., pp vol. 1, M. Clerc, "The swarm and the queen: towards a deterministic and adaptive particle swarm optimization," Evolutionary Computation, CEC 99. Proceedings of the 1999 Congress on, vol.3, no., pp.3 vol., R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems," Proceedings of the IEEE, vol. 95, pp , W. Ren, R. W. Beard, and E. M. Atkins, "Information consensus in multivehicle cooperative control," Control Systems, IEEE, vol. 27, pp , Copyright 2013 SERSC