Optimal Sensor Deployment in Non-Convex Region using Discrete Particle Swarm Optimization Algorithm

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1 01 IEEE Conference on Control, Systems and Industral Informatcs (ICCSII) Bandung, Indonesa, September 3-6, 01 Optmal Sensor Deployment n on-convex Regon usng Dscrete Partcle Swarm Optmzaton Algorthm Agung S. Majd and Endra Joelanto Instrumentaton and Control Research Group Faculty of Industral Technolog Bandung Insttute of Technology Bandung, Indonesa agung.majd@bmkg.go.d, ejoel@tf.tb.ac.d Abstract The rapd development of Wreless Sensor etwork (WS) has ncreased ts applcaton n the mltar ndustr medcal, and envronment. Coverage mprovement s one of the man ssue n WS deployment. Maxmum erage ensures a better utlty of the WS. Ths paper consders the use of Dscrete Partcle Swarm Optmzaton (Dscrete PSO) algorthm to deal wth optmal deployment problem n non-convex regon. Smulaton results show that the Dscrete PSO algorthm leads to performance mprovement compared wth random sensor deployment. Keywords- Wreless Sensor etwork, erage optmzaton; dscrete PSO; non-convex regon, grd I. ITRODUCTIO Wreless Sensor etworks (WS) are a group of low cost, low power, and multfunctonal sensor nodes that work together to sense the envronment and to communcate wrelessly over a short dstance [1]. A rado s attached to each sensor n WS for wreless communcaton whch connects the sensors to a base staton (e.g a laptop, a handheld devce, or an access pont to a fxed nfrastructure) for further data processng. Recentl Wreless Sensor etworks (WS) have become one of the most attractve research area because of promsng mplementaton n many practcal applcatons for ether mltary or cvl purposes. In mltar a WS s used to detect and to dentfy unwanted nstruson n target trackng and survellance. In natural dsaster mtgaton, sensor nodes are able to sense and to measure the envronment condtons n order to forecast dsasters and to gve early warnngs before the occurrences. Ad hoc sensor deployment along the unreachable volcanc area can detect the sesmc actvty and send nformaton to a montorng base. One of major ssues n WS deployment s area erage, snce t must be ensured that each pont n the regon of nterest (ROI) s ered by the sensors. Ths problem leads to consequences that the sensor nodes need to be placed not to close each other n order to fully utlze the sensng capablty of the WS and also must not be placed too far each other n order to mnmze the erage holes. Ths paper consders area erage problem n a non convex regon as the ROI s sometmes lmted by obstacles exstence, admnstratve boundares, or geographcal condtons. Dscrete Partcle Swarm Optmzaton (Dscrete PSO) algorthm s appled wth the use of grd system to dscretze the ROI. Ths approach s a modfcaton of the orgnal PSO [] whch uses contnuous search space, due to nexpensve computatonal cost. The paper s organzed as follows: Secton II presents the related work n the context of Area Coverage. Secton III contans problem formulaton. Secton IV gves a short descrpton of orgnal PSO algorthm, whle secton V presents DPSO algorthm. Secton VI presents smulaton results. The paper s concluded wth Secton VII. II. RELATED WORKS Coverage problem s a major ssue n WS deployment. Ths ssue deals wth the ablty of WS to er a certan area or event [4]. umerous formulatons of erage ssues have been proposed n lterature among whch the followng three methods are most dscussed [4]: Area Coverage: the man objectve s to montor the whole ROI of WS. Pont Coverage: the objectve s to er a set of statonary or movng ponts n ROI. Barrer Coverage: the goal s to mnmze the probablty of undetected ntruson through the WS. Ths paper s focused on the Area Coverage problem. In the Area Coverage problem, the objectve s to fnd the maxmal number of ers whch consst of a set of nodes that s able to completely er the ROI [4]. Chakrabarty et al. [] proposed a dvde-and-conquer strategy to solve the k-erage problem of a number of n- ponts as a lnear programmng problem. The objectve of the problem s to fnd the best soluton n grd ponts such that each pont s ered by at mnmum k nodes. The proposed method was able to decrease the cost of sensors for maxmum erage. Haymar et al. [3] developed moblty control of /1/$ IEEE 109

2 sensors usng Partcle Swarm Optmzaton (PSO) that s able to gve relablty of k-erage, suffcent sensng on target area, and fault tolerant capablty. There were two types of the k-erage approxmaton algorthm: centralzed algorthm and dstrbuted algorthm Dfferent strateges to solve the area erage problem have also been proposed n varous lterature whch can be grouped nto three categores: force based, grd based, dan computatonal geometry based [5]. Force based methods use attracton and repulson forces to determne the optmal poston of the sensors whle grd based methods utlze grd ponts to acheve the same objectve. In computatonal geometry approach, Vorono dagram and Delaunay trangulaton are usually used n WS erage optmzaton algorthm. Azz et al. [13] proposed an off-lne PSO-Vorono algorthm to mnmze the area of erage holes. Overall, ths algorthm acheves almost deal erage but gnores the tme complexty n determnng the Vorono polygons. All lteratures related to grd base system [7, 8, 9, 10, 11, 1] use convex polygon to defne ROI. In ths paper, t s proposed an algorthm to solve the WS deployment problem by usng a Dscrete Partcle Swarm Optmzaton (Dscrete PSO) on a grdded non-convex regon. The proposed algorthm ntroduces a regroupng mechansm to prevent partcles spreadng out from the search space. III. PROBLEM FORMULATIO A. Coverage Problem Let the sze of the target area s A total, and the sze of the montorng area s A area. Under the grdded system, they represent the number of grd ponts of target area and the number of grd pont of montorng area. ow suppose the set of k grd ponts nsde a polygon s denoted by G={g 1, g,..., g k }, the sensor set s S={n 1, n,...,n ), and the sensng radus set s R={R 1, R,..., R ), where R s the sensng radus of node n [14]. The erage model of the node n s assumed as a crcle centered at ts coordnates (x,y ) wth radus r, as shown n Fg.1. A random varable c s used to descrbe the event that the sensor n ers a pxel (x,y). The probablty of event c s denoted as c ) whch equals to the erage probablty P (x,n ). Ths may result n a twovalue functons [14]: c ) = P 1 ( x, n ) = 0 f ( x x ) else + ( y y ) r If a random event c s ndependent to the others, c and c j are unrelated for, j [1,] and j. The followng two relatonshps can then be concluded [14]: P c ') = 1 c ) = 1 P ( x, n ) () P ( ( c j j j (1) c ) = 1 c ' c ') = 1 c '). c ') (3) where c s the complement of c, denotng that sensor node n fals to er pont (x,y). The pxel (x,y) s consdered to be ered by the sensor set f any sensor node n the set ers t. The probablty of the event that the pxel (x,y) s ered by the sensor set can be expressed as the unon of c [14]: P ( x, y, S ) = P ( = 1 = 1 = 1 c ) = 1 (1 P P ( = 1 c ( x, y, n It s also defned the erage rate of the sensor set, R, as the proporton of the montorng area A area to the total area A total [14] gven by the followng rato: R k ') )) (4) = A / A = P ( x, c ) k (5) area total / = 1 In a grd system, t means the proporton of grd ponts of the montorng area to the total grd ponts under the total area. The objectve functon of area erage optmzaton problem becomes to maxmze the erage rate R as follows: max R (6) B. Dscretzaton of ROI In ths paper, t s assumed that the ROI s planar and nonconvex polygon. In order to approxmate the ROI, the area nsde the polygon s dvded by a grd of magnary lnes to a net of equally szed cells, see Fg.. Fgure 1. Sngle sensor node erage llustraton Fgure. Dscretzaton of ROI by equally szed cells 110

3 The grd ponts nsde the polygon denote the potental locaton of sensor deployment and the place where the erage probablty s calculated. IV. PSO ALGORITHM Partcle Swarm Optmzaton (PSO) algorthm s a stochastc based optmzaton method whch s orgnally proposed by Kennedy and Eberhart [4] n The algorthm s nspred by socal behavour of anmals movng n large groups brds flock or school of fsh. PSO has been succesfully appled n varous engneerng problems, to llustrate [15][16]. The PSO algorthm uses partcles a group of potental solutons to explore the search space. The swarm s usually referred as a set of all partcles. In evolutonary termnolog the partcle would be then equvalent to the ndvdual, whle the swarm s equvalent to the populaton. When flyng through the search space, each partcle s characterzed by ts poston and velocty. The poston of partcles represents the potental soluton found by that partcles. The velocty s descrbed as the dfference between the current and prevous poston. The number of partcles s usually specfed n advanced, and s not changed durng the search. Intal populaton, poston, and velocty are chosen randomly from a predetermned range of values. Let x d (t) and v d (t) denote the poston and velocty of the - th partcle n d-th dmenson at t-th teraton. Each partcle has capablty to memorze the best poston acheved so far defned as the personal best poston, p best. The swarm as a whole also memorzes the best poston ever acheved by any of ts partcle, known as the global best poston by p gbest. Based on the prevouse defntons, the partcles manpulaton can be stated as follows: v t + 1) = w* v ( t) + c * rand( ) * ( p x ) + (7) d ( d 1 best d values. Ths paper proposes a modfcaton of the orgnal PSO whch s sutable for such a search space, where each sensor node acts as the partcles of the swarm. The use of dscrete search space wll reduce the computatonal complexty snce not all of ponts nsde the polygon need to be evaluated. Assume that the contnuos search space s mapped nto some rectangular subspace of Ζ n, where Ζ s the set of ntegers, and n s the dmenson of the search space. The partcle velocty s calculated usng the same formula as n (7), but t s dscretzed afterword by roundng off to the near nteger υ ( t + 1) = round( v ( t + 1)) (9) d A new constant m s ntroduced as multpler of the partcle velocty when calculate the partcle poston as follows χ ( t + 1) = x ( t) + ( υ ( t 1)* m) (10) d d d + The value of m defnes the step sze of partcles movement, n ths paper, t uses value of 10. Fg.3 denotes the flowchart of the proposed algorthm. d c * rand( ) * ( p gbest x d and the next poston s obtaned by xd ( t + 1) = xd ( t) + vd ( t + 1) (8) In equaton (7), w s an nerta factor whch s ntroduced by Sh and Eberhart n [17] and s used to control the stablty of the algorthm. From varous studes, t has been found that the nerta value should not be greater than one, and that t should be lnearly decreased, commonly from 0.9 to 0.4, durng the optmzaton process. The varable c 1 s a cogntve factor that affects the partcles movement regardless to the result obtaned by ts neghbour. The varable c s a socal factor that determnes the relatonshp among partcles. Large socal factor means that the partcles tend to move together to explore good solutons found by a swarm as a whole. In ths paper, a predefned number of teratons s used as stoppng crtera of optmzaton process. ) V. DISCRETE PSO ALGORITHM The orgnal PSO algorthm n prevous secton s not well suted for a dscrete search space, that s f the poston of each partcle and of potental soluton s lmted to a dscrete set of Fgure 3. The Dscrete PSO flowchart 111

4 In order to prevent the partcles move away from the search space, a clampng mechansm s ntroduced by brngng the partcles back to the random unered grd ponts n ROI. Ths clampng mechansm s dfferent from that s mostly dscussed n lterature for square or convex polygon ROI n whch t uses maxmum and mnmum axes value of search space. VI. RESULT The Dscrete PSO ntalzes wth a set of randomly deployed sensors n a predefned polygon. The parameters are set as follow: w = (lnearly decreasng) [17], c 1 =4, c =, maxmum teraton= 400. A. Optmzaton vs. Random Deployment Ths test uses 10 sensor nodes wth sensng range 0.5 unts and ntal erage value 67,34%, as shown n Fg. 4. After optmzaton process usng Dscrete PSO, the erage rate reaches 89,68%. The fnal formaton of WS s shown n Fg.5. Fgure 5. Performance of Dscrete PSO compared to random deployment B. Impact of Intal Poston on Coverage Rate Experment s then conducted to evaluate the performance of the Dscrete PSO for two dfferent ntal postons; outsde and nsde ROI. Fg. 6 and Fg. 7 show the ntal and fnal poston of the sensors. It can be concluded that the ntal sensors deployment does not have sgnfcant mpact on the fnal erage value. Poston and randomness of ntal deployment only affect the optmzaton rate. The largest optmzaton rate s acheved when ntal deployment s outsde ROI as llustrated by an experment result n Fg. 6 wth optmzaton rate 90,83% whle n Fg. 7 only about 30%. Fgure 4. Randomly deployed WS (erage rate 67,34 %) (a) (b) Fgure sensor nodes are deployed randomly outsde ROI: (a) ntal, erage rate 0%; (b) fnal, erage rate 90,83% Fgure 5. WS deployment after optmzaton (erage rate 89,68 %) Results from several runs usng aforementoned parameters show that overall the Dscrete PSO outperforms random deployment approach, see Fg.5. The Dscrete PSO ncreases the erage rate of WS deployment about 7% n average. (a) (b) Fgure sensor nodes are deployed randomly nsde ROI: (a) ntal, erage rate 61,46%; (b) fnal, erage rate 91,55% 11

5 It also shows an opportunty to ncrease moblty of a moble WS, snce t can be ntally deployed remotely from the ROI whch could be a dangerous or unreachable regon for human. C. Impact of Sensor Range on Coverage Rate Evaluaton on the mpact of sensor node range to the erage rate of ROI s carred out by varyng the radus of the sensor nodes crcles usng several values: 0.3, 0.5, and 0.8 unts. Fgure 8. Impact of sensor node range on erage rate Fg. 8 shows that the larger the radus of the sensor nodes, the larger the erage rate s acheved by both random and optmzed sensor deployment. Resylts show the proposed optmzaton algorthm s stll superor to random sensor deployment. VII. COCLUSIO AD FUTURE WORK Ths paper presented a novel combnatoral optmzer, called Dscrete PSO, whch s appled to solve erage problem of WS deployment n a non-convex regon. The smulaton results showed the capablty of the proposed algorthm to ncrease the erage rate of a randomly deployed WS. In the future research, t would be nterestng to nvestgate the behavour of the algorthm appled to a multrange WS nvolvng real terran analyss. It s also of nterest to combne wth another type of swarmng algorthm n order to solve erage problems wth weghted grd ponts. Fourth Internatonal Conference on etworked Computng and Advanced Informaton Management, 008 IEEE,vol 1,pp [4] J. Kennedy and R. Eberhart, Partcle swarm optmzaton, n Proceedngs of the IEEE Internatonal Conference on eural etworks, vol. 4, 7 ov. 1 Dec. 1995, pp [5] M. Esnaashar, and M.R. Meybod, A learnng automata based schedulng soluton to the dynamc pont erage problem n wreless sensor networks, n: Computer etworks journal (Elsever), 010 [6] J. Ja, J. Chena, G. Changa, Y. Wena, and J. Songa, Mult-objectve optmzaton for erage control n wreless sensor network wth adjustable sensng radus, n: Elsever, Computers and Mathematcs wth Applcatons 57, 009, pp [7]. Azlna, A. Azz, K. Azz et al. Coverage Strateges for Wreless Sensor etworks, n: World Academy of Scence, Engneerng and Technology 50, 009, pp [8] Shen, X., Chen, J., Wang, Zh. And Sun, Y. Grd Scan: A Smple and Effectve Approach for Coverage Issue n Wreless Sensor etworks. IEEE Internatonal Communcatons Conference, June 006 Volume: 8, pp.: [9] Howard, A., Matarc, M.J, and Sukhatme. Moble Sensor etwork Deployment usng Potental Felds: A Dstrbuted, Scalable Soluton to the Area Coverage Problem, [10] Xu, K., Takahara, G. and Hassanen, H. On the Robustness of Grd- Based Deployment n Wreless Sensor etworks IWCMC 06 pp.: (006) [11] Ba, X. Kumar, S., Xuan, D.,.Yun, Z. and La, T.H Deployng Wreless Sensors to Acheve Both Coverage and Connectvty In Proceedngs of the Seventh Internatonal Symposum on Moble Ad Hoc etworkng and Computng (ACM MobHoc), Florence, Ital 006 [1] Bagon, E.S. and Sasak, G. Wreless Sensor Placement for Relable and Effcent Data Collecton [13]. A. B. A. Azz, A. W. Mohemmed, and B. S. D. Sagar, Partcle swarm optmzaton and Vorono dagram for wreless sensor networks erage optmzaton, n Proceedngs of the Internatonal Conference on Intellgent and Advanced Systems (ICIAS), 007, pp [14] J. Ja, J. Chena, G. Changa, Y. Wena, and J. Songa, Mult-objectve optmzaton for erage control n wreless sensor network wth adjustable sensng radus, n: Elsever, Computers and Mathematcs wth Applcatons 57, 009, pp [15] Q. He, L. Wang, An Effectve Co-Evolutonary Partcle Swarm Optmzaton for Constraned Engneerng Desgn Problems, Engneerng Applcatons of Artfcal Intellgence, 0 (007) [16] G. G. Dmopoulos, Mxed-Varable Engneerng Optmzaton Based on Evolutonary and Socal Metaphores, Computer Methods n Appled Mechancs and Engneerng 196 (007) [17] Y. Sh, R.C. Eberhart, Emprcal study of partcle swarm optmzaton, n: Proc. IEEE Int. Congr. Evolutonary Computaton, vol 3, pp , 1999 REFERECES [1] Ghosh, A. and Das, S.K, Coverage and Connectvty Issues n Wreless Sensor etworks n Shore R., Ananda, A.L, Chan, M.C. and Oo, W.T Moble, Wreless, and Sensor etworks: Technolog Applcatons and Future Drectons, John Wley & Sons, Inc (006). Trans. Roy. Soc. London, vol. A47, pp , Aprl [] Chakrabart K., Iyengar, S.S., Q, H. and Cho, E. Grd Coverage for Survellance and Target Locaton n Dstrbuted Sensor etworks IEEE Transactons on Computers Vol 51, o. 1 pp.: (00) [3] Haymar.K Cho.Y, Park, Self-Organzed Moblty n anosensor etwork Based on Partcle Swarm Optmzaton and Coverage Crtera. 113