Sensors 2007, 7, 628-648 Full Paper sensors ISSN 1424-8220 2007 by MDPI www.mdp.org/sensors Dstrbuted Partcle Swarm Optmzaton and Smulated Annealng for Energy-effcent Coverage n Wreless Sensor Networks Xue Wang *, Jun-Je Ma, Sheng Wang and Dao-We B State Key Laboratory of Precson Measurement Technology and Instrument, Department of Precson Instruments, Tsnghua Unversty, Bejng 100084, P. R. Chna; E-mals: {mjj, wang_sheng00, bdw02} @mals.tsnghua.edu.cn. * Author to whom correspondence should be addressed; E-mal: wangxue@mal.tsnghua.edu.cn. Receved: 25 Aprl 2007 / Accepted: 8 May 2007 / Publshed: 10 May 2007 Abstract: The lmted energy supply of wreless sensor networks poses a great challenge for the deployment of wreless sensor nodes. In ths paper, we focus on energy-effcent coverage wth dstrbuted partcle swarm optmzaton and smulated annealng. Frst, the energy-effcent coverage problem s formulated wth sensng coverage and energy consumpton models. We consder the network composed of statonary and moble nodes. Second, coverage and energy metrcs are presented to evaluate the coverage rate and energy consumpton of a wreless sensor network, where a grd excluson algorthm extracts the coverage state and Djkstra s algorthm calculates the lowest cost path for communcaton. Then, a hybrd algorthm optmzes the energy consumpton, n whch partcle swarm optmzaton and smulated annealng are combned to fnd the optmal deployment soluton n a dstrbuted manner. Smulated annealng s performed on multple wreless sensor nodes, results of whch are employed to correct the local and global best soluton of partcle swarm optmzaton. Smulatons of wreless sensor node deployment verfy that coverage performance can be guaranteed, energy consumpton of communcaton s conserved after deployment optmzaton and the optmzaton performance s boosted by the dstrbuted algorthm. Moreover, t s demonstrated that energy effcency of wreless sensor networks s enhanced by the proposed optmzaton algorthm n target trackng applcatons. Keywords: Wreless sensor network, deployment optmzaton, energy effcency, partcle swarm optmzaton, smulated annealng.
Sensors 2007, 7 629 1. Introducton Wreless sensor networks (WSNs) can mplement varous complcated tasks n the sensng feld va a large number of smart wreless sensor nodes whch have sensng, storage, processng and communcaton capabltes. All the wreless sensor nodes work collaboratvely to leverage ther ndvdual efforts for the entre applcaton. Snce battery-powered wreless sensor nodes are greatly constraned wth regards to energy supply, energy effcency becomes a crtcal problem n WSNs. As an essental requrement, sensng coverage has been nvestgated n a few lterature reports [1,2]. The coverage problem s defned from several ponts of vew, ncludng determnstc, statstcal, worst and best case n [3]. In partcular, effcent network deployment consderng coverage as well as connectvty s dscussed n [4,5]. Target trackng s a typcal applcaton for WSNs and poses a great challenge to acheve both hgh relablty and long lfetme [6]. For WSNs whch mplement target trackng applcatons, the effcency of energy usage should be taken nto account n the deployment. Generally, wreless communcaton spends much more energy than sensng and computaton, so t should be the prmary consderaton [7]. In addton, the potental processng capablty of multple wreless sensor nodes may contrbute to better optmzaton performance [8]. Due to the above-mentoned requrements of deployment n WSNs, we propose dstrbuted partcle swarm optmzaton and smulated annealng (DPSOSA) for energy-effcent coverage. Ths method takes the energy consumpton of target trackng nto account to optmze the energy effcency of WSN coverage wth dstrbuted computng. Sensng coverage and energy consumpton models for WSNs are ntroduced frst. The purpose of optmzaton s to fnd the best deployment of moble wreless sensor nodes so that the sensng coverage requrement s satsfed and communcaton energy consumpton can be mnmzed. Then the grd excluson algorthm s exploted to calculate the coverage rate of specfc network deployment, whch has mnmzed computatonal cost and scalable granularty. We adopt Djkstra s algorthm to search the lowest cost paths for data collecton, whch wll be regarded as packet transmsson paths n target trackng applcatons. The sensng coverage rate and total energy consumpton of data collecton are defned as coverage and energy metrcs, respectvely. The DPSOSA algorthm s then employed to optmze the communcaton energy consumpton under a gven sensng coverage requrement. It s executed over a number of nodes, n whch the partcle swarm optmzaton (PSO) procedure s aded by the optmzaton results of smulated annealng (SA) for the global optmal soluton. In DPSOSA, a number of partcles are gven a better vew to search for better solutons n ther vcnty, by whch the PSO procedure can be corrected. Meanwhle, as multple partcles need to be optmzed, the optmzaton task s assgned among wreless sensor nodes to boost up the computatonal capablty. Wth smulatons of deployment optmzaton and target trackng, the energy effcency of the proposed dstrbuted optmzaton algorthm s verfed. The rest of ths paper s organzed as follows: secton 2 formulates the energy-effcent coverage problem wth statonary and moble wreless sensor nodes n WSNs, where the sensng coverage and energy consumpton models are presented. In Secton 3, two mportant metrcs, coverage and energy, are defned for network deployment evaluaton accordng to the fundamental model, where the grd excluson and Djkstra algorthm are ntroduced. Then Secton 4 presents the DPSOSA algorthm for energy-effcent coverage n WSNs. In Secton 5, we smulate the deployment optmzaton algorthm
Sensors 2007, 7 630 for target trackng applcaton and analyze energy-effcency of WSNs. We conclude the paper n Secton 6. 2. Prelmnares We assume a WSN composed of two types of wreless sensor nodes: statonary and moble nodes. In the sensng feld, the statonary nodes are deployed randomly, whle the moble ones can adjust ther postons adaptvely aganst the envronment. Wth the moble nodes located at ther proper postons, WSN can mplement target trackng applcatons. As shown n Fgure 1, wreless sensor nodes whch are close to the moble target trajectory may acqure data. A snk node s located n the centre of sensng feld, to whch the observatons wll be forwarded hop by hop [9,10]. It s assumed that the postons of nodes can be obtaned by global postonng system (GPS) [11]. In ths secton, we wll descrbe the sensng coverage model for relablty detecton. Consderng the energy effcency problem, energy consumpton model of communcaton wll be dscussed. Fgure 1. In the target trackng applcaton of WSNs, the moble target moves through the sensng feld and wreless sensor nodes around t wll report ther data to the snk node n a mult-hop manner. 2.1. Sensng coverage model Each wreless sensor node ntegrates three radar sensors wth the same sensng radus R, orented at 120 ntervals. Azmuth coverage of radar sensor s 60 ~ +60 [12]. For each wreless sensor node, t s assumed that the strength of receved detecton sgnal vares exponentally wth the dstance from the target. If the coordnates of wreless sensor node and a target are (x,y ) and (x target,y target ), respectvely, the receved sgnal strength reflected off the target s: d, G target = G0e β (1)
Sensors 2007, 7 631 where G 0 s a constant whch denotes the strength of emsson sgnal, β s the attenuaton constant. And d target, s the Eucldean dstance between the target and sensor: 2 2 dtarget, = ( xtarget x ) + ( ytarget y ) (2) Accordng to the senstvty and relablty of sensor, we can defne a threshold of receved sgnal strength G th, and calculate the detecton relablty as: 0 G < G r = r0 G G th th (3) where r 0 s the relablty of sensor when the receved sgnal strength exceeds G th, 0 <r 0 <1. Thus, wreless sensor node can physcally cover a plate area wth radus R a, where the centre locates at (x,y ). The sensng radus R a can be calculated as: 1 G = ln th Ra β G 0 (4) Consderng the nherent redundancy of WSNs, we dscuss the k-coverage problem, that s, certan area s covered by k or more wreless sensor nodes at the same nstant. In ths case, synthess detecton relablty of the area s at least: k = 1 R = 1 (1 r ) (5) Therefore, we can acqure hgh synthess detecton relablty even though the detecton relablty of ndvdual wreless sensor node s lmted. 2.2. Energy consumpton model Durng target trackng, wreless sensor nodes have the functons of data acquston, processng and reportng. The related sensng, computaton and communcaton operatons wll lead to energy depleton. Out of all the energy consumpton sources n WSNs, wreless communcaton s the largest porton. Thereby, t s the man one taken nto account here. As rado sgnal attenuaton n the ar s related wth the propagaton dstance, we adopt the free space propagaton model [13], whch s expressed as: L p λ s = 4 π d, j where L p s the path loss, λ s s the wavelength of sgnal, and d,j s the propagaton dstance. If rado sgnal propagates between wreless sensor node and j, whch are located at (x,y ) and (x j,y j ), the correspondng propagaton dstance can be calculated as: ( ) ( ) 2 2 2 d, j = x x j + y y j (7) Accordngly, a model of wreless communcaton s assumed to analyze energy consumpton of communcaton. Here, the power consumpton of data transmsson between wreless sensor node and j s calculated as [14]: (6)
Sensors 2007, 7 632 α α (8) Ψ = r + d r 2 1 d 2, j d where r d denotes the data rate, α 1 denotes the electroncs energy expended n transmttng one bt of data, α 2 >0 s a constant related to the rado energy. Gven the transmsson tasks through the network, the energy consumpton feature of WSNs can be obtaned. 3. Evaluaton Metrcs of Energy-effcent Coverage To acheve relable detecton and energy conservaton n target trackng applcaton, WSNs should apply an energy-effcent coverage scheme. Coverage and energy performance s concerned n potental moble node deployment. For specfed detecton relablty, sensng area needs to be covered by certan number of wreless sensor nodes. The area whch can satsfy ths relablty requrement n the whole sensng feld can reflect the coverage performance. On the other hand, data packet transmsson from wreless sensor nodes to the snk node results n energy consumpton. An energy-effcent communcaton framework can be establshed by the lowest cost paths. Ths framework ndcates the lowest energy consumpton level whch can be provded by dfferent deployment of WSNs. It s assumed that there are n statonary nodes and m moble nodes n a L x L square sensng feld. The coordnates of snk node are (L/2, L/2). In a possble network deployment, the coordnates of all wreless sensor nodes (x,y ) (=1,2,..,n+m) can be obtaned, where the ndces of the statonary and moble nodes are (=1,2,..,n) and (=n+1,n+2,..,n+m), respectvely. Accordngly, coverage and energy metrcs and related algorthms wll be presented to evaluate the network deployment n ths secton. 3.1. Coverage metrcs Typcally, certan detecton relablty R req s requred for specfc target trackng applcaton. Based on Equaton (5), the requred number of wreless sensor nodes, whch can detect the target wth relablty r 0 at the same tme, can be calculated as: req req k = log (1 R ) (9) 1 r0 The area whch s covered by k req or more wreless sensor nodes s regarded as the relable detecton area. To provde ntegrated and contnuous detecton of targets n the sensng feld, the relable detecton area should be as large as possble. Therefore, we defne the proporton of relable detecton area n the whole sensng feld as the coverage metrc. As dscussed n Secton 2.1, each wreless sensor node covers a plate area wth radus R a. Due to the rregular network deployment, the coverage state problem s too complcated for geometrc analyss. Thus, we explot a numercal method, the grd excluson algorthm, to extract the coverage state nformaton. The pseudo-code for grd excluson algorthm s outlned n Algorthm 1. Algorthm 1 1. Intalzaton
Sensors 2007, 7 633 Dvde the square sensng feld nto lxl unform grds. Each grd s a (L/l)x(L/l) square area. Smplfy the grds nto ponts, then each grd can be denoted by ts centre pont. The coordnates of ponts are: Intalze the coverage state matrx {cov(,j)}: g g g g {( x, y ) x, y = L / 2 l,3 L / 2 l, L,(2l 1) L / 2 l } (10) cov(, j) = 0, j = 1,2, L, l (11) Set the number of relable detecton pont num = 0 and set the number of unrelable detecton ponts n r =0. 2. Coverage state for statonary nodes on the whole sensng feld Check the detecton relablty pont by pont. For x g = L/2l,3L/2l,,(2l-1)L/2l For y g = L/2l,3L/2l,,(2l-1)L/2l Ths pont s related to the element cov( g,j g ) of the coverage state matrx: g g g g = x l / L + 1/ 2, j = y l / L + 1/ 2 (12) Check whether statonary node covers ths pont. For = 1, 2,, n Calculate the dstance between statonary node and the pont: Update the coverage state matrx as: g g 2 g 2 d = ( x x ) + ( y y ) (13) If cov( g,j g ) > k req g g g g g cov(, j ) + 1 d < Ra cov(, j ) = g g g cov(, j ) d Ra Update the number of relable detecton pont: (14) Else Record the unrelable detecton pont: num = num +1 (15) g g g g nr = nr + 1, ( xn, yn ) = ( x, y ), ( n, jn ) = (, j ) (16) r r r r The coverage state matrx of statonary nodes s obtaned. 3. Coverage state for moble nodes on the unrelable detecton area
Sensors 2007, 7 634 Check the detecton relablty excludng the relable detecton pont. For j= 1, 2,, n r Check whether moble node covers ths pont. For =n+1, n+2,, n+m Calculate the dstance d g between (x j,y j ) and (x,y ). Update the coverage state matrx adoptng Equaton (14). If cov( j,j j ) > k req Update the number of relable detecton ponts as Equaton (15). Fnally, the coverage metrc C can be calculated as: num C = (17) l l Instead of calculatng the coverage state of all wreless sensor nodes at one tme, the coverage state matrx of statonary nodes s frst extracted n the grd excluson algorthm. Excludng the relable area, the coverage state of moble nodes s then calculated on the remanng area. In ths way, only Step 3 of the algorthm needs to be mplemented repeatedly when a dfferent deployment of moble nodes s evaluated, thereby computatonal costs could be reduced. Moreover, only the recorded nformaton of unrelable detecton area s necessary for multple wreless sensor nodes n dstrbuted optmzaton algorthms, such as DPSOSA, to be covered n Secton 4, so that the dstrbuted optmzaton structure can be smplfed and ts communcaton costs wll be low. Notce that granularty of computaton s scalable by easly adjustng the dvson parameter l. The tradeoff can be made between computatonal cost and coverage evaluaton 3.2. Energy metrcs Durng target trackng n WSNs, wreless sensor nodes spend sgnfcant energy reportng ther observatons. Wth the model presented n Secton 2.2, we analyze the energy consumpton of wreless communcaton. Accordng to Equaton (8), the wreless sensor nodes whch are far away from the snk node would spend too much energy when ther data packets are transmtted drectly. These nodes may fnd a number of other nodes for data forwardng and such a mult-hop manner wll potentally conserve energy. Thus, the lowest cost path to snk node should be found for each wreless sensor node. Here, Djkstra s algorthm s ntroduced to solve ths lowest path problem, whch can accomplsh breadth-frst path search between one sngle destnaton vertex and all the other vertexes on the connected graph [15,16]. Snce any vertex that has shorter path to the destnaton vertex s traversed, the optmal soluton can always be found.
Sensors 2007, 7 635 For any gven WSN deployment, the snk node s regarded as the destnaton vertex and denoted by u 0, whle wreless sensor nodes are taken as all the other vertexes and denoted by U = { u1, u2, L, u n + m }. The edge weght between vertex u and u j s defned accordng to Equatons (7) and (8): ω = α + α d j = n + m j (18) 2, j 1 2, j, 0,1,2, L,, Then the pseudo-code for the lowest cost path search s outlned n Algorthm 2. Algorthm 2 1. Intalzaton Adopt varable D to represents estmate of the lowest cost from u to u 0. It converges to the real value after teratons. Intalze the connected graph as: D = 0, D = ω = 1,2, L, n (19) 0,0 The set of vertexes whch have found the lowest cost paths s denoted by Q, set Q=Ø. 2. Iteraton Whle Q U Fnd the next vertex wth the lowest cost path to u 0. For any vertex u Q If D satsfes: D = mn n+ m D (20) k = 1 The lowest cost path from vertex u to u 0 s found. Update Q: k Q = QU{ u } (21) Record the vertex u, set 0 =. For any vertex Update D j : u j Q D = mn{ D, ω + D } (22) j j j, 0 0 After teraton, D denotes transmsson energy consumpton per bt from vertex u to u 0 adoptng the lowest cost path, where = 1, 2,, n+m. Thus, the lowest cost paths from all wreless sensor nodes to snk node are avalable, whch form an energy-effcent communcaton framework. Ths framework reflects the lowest energy consumpton
Sensors 2007, 7 636 level whch can be provde by the gven network deployment. Snce each wreless sensor node has the opportunty to detect a target and report ts data, we can evaluate the energy consumpton by the total cost of all the reportng paths. Therefore, the energy metrc E of network deployment s calculated as: n + m E D (23) Generally, dfferent deployment of moble nodes corresponds to dfferent energy metrc values. The proposed coverage and energy metrc wll be used to evaluate dfferent network deployment n the optmzaton algorthm. = = 1 4. Dstrbuted Optmzaton Algorthm for Energy-effcent Coverage When WSNs are ntally organzed, proper deployment of moble nodes s desrable to acheve energy-effcent coverage. Also, the envronment may cause changes n WSNs, such as the appearance of node falures. Therefore, poston adjustng of moble nodes s necessary for resource re-allocaton. Wth the proposed coverage and energy metrcs, deployment optmzaton should be mplemented to provde adaptablty for WSNs n these cases. Then, the optmzaton results are broadcasted over the network so that WSNs can be self-organzed. Followng the prevous assumpton, there are n statonary nodes and m moble nodes avalable n the deployment problem. The coordnates of moble nodes are taken as non-ntegral nput vectors for optmzaton. As descrbed n Secton 3.1, certan coverage rato C 0, namely the optmzed coverage metrc, s demanded under the detecton relablty requrement. Thus, the objectve of optmzaton s to decrease the energy consumpton level of WSNs n target trackng applcatons under the condton that the requred coverage metrc s satsfed. Kennedy et al. developed partcle swarm optmzaton n 1995 based on the analogy of swarms of brds and fsh schools. PSO s an effcent optmzaton tool for solvng combnatoral optmzaton and dynamc optmzaton problems n mult-dmensonal space, whch mplements fast convergence and good robustness [17]. Here, t s consdered as a deployment optmzaton algorthm n WSNs. Lke other evolutonary algorthms, PSO uses a ftness functon as crteron to evolve the behavor of the soluton populaton. In the algorthm, potental solutons, namely partcles, fly through the search space. Each partcle keeps track of the best poston t has acheved so far, whch represents a partcle experment. Another knd of experment s the best poston whch has been acheved by the companon of partcle so far. The partcle velocty s constantly adjusted accordng to the two knds of experences. PSO has a strong ablty for fndng the most optmal result. However, t has a dsadvantage n local mnma. Thus, smulated annealng [18] whch has a strong ablty for fndng the local optmal result s ntroduced to avod the problem of local mnma. SA manly conssts of the repeatng of two steps: a generaton mechansm and an acceptance crteron. It starts off at an ntal random state wth a hgh temperature, and then a sequence of teratons s generated. A perturbaton mechansm transforms the current state nto a next state selected from the neghborhood of the current state. If ths neghborng state has better ftness, the neghborng state s accepted as the current state. If ths neghborng state has worse ftness, the neghborng state s accepted wth a certan probablty determned by the
Sensors 2007, 7 637 acceptance crteron [19]. After suffcent tmes of acceptance, the temperature s decreased. Ths process s repeated untl the fnal temperature s reached. We propose dstrbuted partcle swarm optmzaton and smulated annealng here. SA s appled on the global best poston of PSO. Then the vcnty of the global best poston s searched to obtan a local optmal result. Thereby, the procedure of PSO s corrected by the result. In the same way, the best poston acheved by ndvdual partcle can be corrected by SA. Snce SA mantans only one soluton, ths extended optmzaton tasks can be assgned smply to a number of wreless sensor nodes utlzng the dstrbuted computng capacty of WSNs. The pseudo-code for DPSOSA s outlned n Algorthm 3. Algorthm 3 The snk node performs man part of the algorthm. 1. Intalzaton The populaton of partcles s set as pop. For = 1, 2,, pop For partcle, X represents the current poston, where the elements present the coordnates of all moble nodes: X = ( x, y, x, y, L, x, y ) = { x j = 1,2, L,2 m} (24) n+ 1 n+ 1 n+ 2 n+ 2 n+ m n+ m j V represents the current velocty t has acheved so far: P represents the best poston t has acheved so far: Intalze X as a random poston X (1) n the search space. Intalze V as a random velocty V (1). Set the ntal P as: V = { v j = 1,2, L,2 m } (25) j P = { p j = 1, 2, L, 2 m } (26) j P (1) = X (1) (27) Accordng to the purpose of energy-effcent coverage n WSN, the mnmzaton objectve functon f(x) s defned for the poston X of any gven partcle as: ρe C C < C f ( X ) = ρe 1 C C 0 0 0 (28) where E and C are the metrcs defned n Secton 3.1 and 3.2 respectvely. E 0 s a constant whch denotes the upper bound of energy metrc, whle C 0 s the demanded coverage rato. ρ s a constant for balancng the two metrcs.
Sensors 2007, 7 638 2. PSO teratons For t = 1, 2,, PSO_ITER The global best poston of partcle s calculated as: For = 1, 2,, pop The velocty of partcle s updated as: P ( t) = mn{ f [ P ( t)], f [ P ( t)], L, f [ P ( t)]} = { p j = 1,2, L,2 m} (29) g g 1 2 pop j v ( t + 1) = η( t) v ( t) + c r [ p ( t) x ( t)] + c r [ p ( t) x ( t)] (30) 1 2 g j j 1 j j j 2 j j j Γ 1 ={r 1 j} and Γ 2 ={r 2 j} are two separate random sequences, where j = 1, 2,, 2m, c 1 and c 2 are acceleraton constants, representng the weght of acceleraton terms that pull each partcle toward the local best poston and global best poston and η(t) s the nerta weght for balancng the global and local search ablty. It s defned as: The poston of partcle s updated as: The best poston of partcle s calculated as: t PSO _ ITER η ( t) = 0.9 0.5 (31) x ( t + 1) = x ( t) + v ( t + 1) (32) j j j P ( t) f [ X ( t + 1)] f [ P ( t)] P ( t + 1) = X ( t + 1) f [ X ( t + 1)] < f [ P ( t)] (33) The snk node sorts P (t+1) by ther ftness. Select the best SA_NUM postons {P s = 1, 2,, SA- NUM}, whch are to be optmzed wth SA. The optmzaton of global best poston wll be performed by the snk node, whle SA_NUM 1 wreless sensor nodes are randomly selected to optmze the other postons. The snk node transmts each partcle to the related node. Then snk node and these nodes perform parallel SA optmzaton. For = 1, 2,, SA-NUM Perform SA teratons takng the ntal state as: s A = P = { a j = 1,2, L,2 m } (34) Set an ntal temperature T. For k = 1, 2,, SA-ITER The coolng condton s that the best state remans unchanged for K tmes. Whle the coolng condton s not satsfed Use a perturbaton mechansm to generate a new state A : j A = A + rand _ norm (35)
Sensors 2007, 7 639 where rand_norm s a normally dstrbuted random number, = {δ j j = 1, 2,, 2m} and = { δ j j = 1,2, L,2 m} and δ j s defned wth a random nteger j 0 n [1, 2m]: The decrease of ftness s: 1 j = j δ 0 j = 0 j j (36) 0 df = f ( A ) f ( A ) (37) Check whether the new state should be accepted accordng to Metropols crtera. If df < 0 Accept the new state: A = A. Else f e df/(γt) > rand, where γ s Boltzmann constant and rand s a random number n [0,1] Accept the new state: A = A. Else The new state A cannot be accepted. Cool down wth a parameter λ: T = λ T (38) If any result s better the ntal state, the wreless sensor node sends t back to the snk node, where the former poston wll be replaced. Fnally, the global best poston presents the optmzed deployment of WSN. In PSOSA, the snk node performs PSO_ITER teratons of PSO, where the nerta weght η(t) lnearly decreases through the course of the run. A large nerta weght facltates a global search whle a small nerta weght facltates a local search. Accordngly, the optmzaton process can converge to the neghborhood of the global optmal soluton smoothly at the prophase and converge to the global optmal soluton quckly at the anaphase. SA_NUM local best postons are optmzed by SA on the snk node and SA_NUM 1 other wreless sensor nodes. After SA_ITER teratons of SA, the optmzed results are utlzed to correct the former postons. In ths way, the algorthms have good potental to obtan the optmal deployment of WSNs. 5. Smulaton Experments In ths secton, we wll analyze the effcency of DPSOSA algorthm wth smulaton experments. The smulaton envronment wll be specfed. Then the smulaton and comparson of algorthms wll be gven. Fnally, the network smulatons wll be present for target trackng applcaton.
Sensors 2007, 7 640 5.1. Smulaton envronment The fundamental parameters of WSN are presented n Table 1. The statonary nodes are placed randomly n the square sensng feld as shown n Fgure 2(a). Wth the specfed sensng radus of wreless sensor node, we can calculate the ntal coverage state of statonary nodes accordng to Secton 3.1. Fgure 2(b) shows the ntal coverage state, and the area wth darker grey levels means that there s coverage by more nodes. Table 1. Fundamental parameters of WSN. Parameter Value Sensng feld dmenson LxL 240m 240m Statonary node number n 108 Moble node number m 20 Snk node coordnates (120,120) Sensng radus R a 30m Sensor relablty r 0 0.6 In the energy consumpton model, we set α 1 = 50nJ/bt and α 2 = 100pJ/bt/m 2. When we calculate the coverage metrc, the sensng feld s dvded nto 100 x 100 unform grds. Accordngly, the ntal coverage metrc of k-coverage area s presented n Table 2, where k changes from 1 to 6. As more coverng nodes are requred to satsfy the relablty, the ntal coverage metrc turns lower rapdly. Based on Equaton (5), Fgure 3 llustrates the detecton relablty wth dfferent coverng node number. The detecton relablty grows exponentally and exceeds 0.99 when the coverng node number s 6. Fgure 2. Intal deployment and coverage state of WSN: (a) Placement of snk node and statonary nodes; (b) Coverage state of statonary nodes n the sensng feld. (a)
Sensors 2007, 7 641 (b) In the DPSOSA algorthm, the partcle number pop s set as 30, the acceleraton constants c 1 =c 2 =1, and the PSO teraton number PSO_ITER s specfed as 40. Durng each SA optmzaton, we set ntal temperature T as 0.0001 accordng to the ftness functon. Parameter K s 4 n the coolng condton, whle the coolng parameter λ s 0.6. Besdes, Boltzmann constant γ = 1, and the PSO teraton number SA_ITER s specfed as 5. Table 2. The ntal coverage metrc of k-coverage area. k 1 2 3 4 5 6 Coverage metrc (%) 98.00 91.45 83.17 70.80 54.03 37.25 Fgure 3. Detecton relablty as a functon of coverng node number. Target trackng applcaton of the optmzed WSN wll be smulated on a modelng platform, Opnet Modeler, whch s developed for communcaton network and dstrbuton system. It s assumed that the samplng perod of WSN s 0.5 s. Wthout loss of generalty, a moble target moves randomly n the sensng area for 120 s. Wreless channel model s bpsk, the free space propagaton model s utlzed and data rate s 1 Mbps.
Sensors 2007, 7 642 5.2. Smulatons of deployment optmzaton Wth the stated smulaton envronment, the DPSOSA algorthm can be adopted to acheve energyeffcent coverage. Frst, we should defne the coverage requrement, whch s gven by two parameters, detecton relablty R req and coverage rato C 0. Consderng the ntal coverage state, we dscuss two knd of coverage requrement to analyze the performance of algorthm aganst dfferent condtons: (1) R req = 0.8, C 0 = 95%; (2) R req = 0.9, C 0 = 95%. The requred coverng node numbers k req are 2 and 3 respectvely. Accordng to Table 2, the latter coverage requrement s much strcter than the former one. Second, the constant E 0 whch denotes the upper bound of energy metrc should be specfed for the ftness calculaton. Here, we search the lowest cost paths of the staton nodes wthout any moble node. Assume the related path cost s {D s = 1, 2,, n}, then E 0 s defned as: 0 n s n = 1 = 1 s E = max( D ) m + D (39) In ths case, E 0 s 7.26 x 10 5 J/bt, and ρ s set as 10 5. Then, we mplement DPSOSA to optmze the deployment of WSN wth a dfferent computng node number SA_NUM, whch vares from 1 to 9. Specally, the algorthm s accomplshed by the snk node when SA_NUM s set as 1. Snce each wreless sensor node has lttle nformaton to exchange wth the snk node and the computng node number s lmted durng DPSOSA, ts communcaton cost can be gnored. As shown n Fgure 4, the optmzaton results of DPSOSA are obtaned under the two knds of coverage requrement. We can fnd that all the optmzed coverage metrcs exceed 95%, whle the energy metrc trends to be lower as the computng node number becomes larger. Hence, the performance of DPSOSA benefts from the computaton capacty of multple wreless sensor nodes. Fgure 4. Optmzaton results of DPSOSA utlzng dfferent computng node numbers under two knds of coverage requrement: (a) R req = 0.8, C 0 = 95%; (b) R req = 0.9, C 0 = 95%. (a)
Sensors 2007, 7 643 (b) Fgure 5. Convergence curves of the metrcs under two knds of coverage requrement durng DPSOSA: (a) Coverage metrc; (b) Energy metrc. (a) (b)
Sensors 2007, 7 644 To obtan deal optmzaton results, the computng node number s fxed as 9 n the followng dscusson. Then, Fgure 5 shows the convergence curves of the metrcs under the two knds of coverage requrement. Rather than the coverage requrement that R req = 0.8 and C 0 = 95%, t s more dffcult to acheve the coverage requrement that R req = 0.9 and C 0 = 95%. Therefore, the former coverage requrement s satsfed at the begnnng, whle the latter one s satsfed after 8 teratons n the optmzaton procedure, whch s shown n Fgure 5(a). In Fgure 5(b), the algorthm can make more effort to acheve mproved energy metrc wth the former coverage accordngly. Meanwhle, the former coverage requrement provdes more adjustablty for moble node deployment to acheve lower energy metrc. Fgure 6. Convergence curves of the metrcs durng DPSOSA and PSO under the coverage requrement that R req = 0.9 and C 0 = 95%: (a) Coverage metrc; (b) Energy metrc. (a) (b) Furthermore, we wll compare the performance of DPSOSA and general PSO algorthms. Here, only the coverage requrement that R req = 0.9 and C 0 = 95% s consdered. The same scenaro and ftness functon s employed n PSO. In Fgure 6, the convergence curves of coverage and energy
Sensors 2007, 7 645 metrcs are presented durng DPSOSA and PSO. From Fgure 6(a), we can fnd that PSO spends much more teratons than DPSOSA to satsfy the coverage requrement though t has a better ntal coverage of moble nodes. And the energy metrc s sgnfcantly mproved by DPSOSA compared to the optmzaton result of PSO as shown n Fgure 6(b). Accordng to the optmzaton results of PSO and DPSOSA, we can obtan optmzed deployment and communcaton paths of WSN as shown n Fgure 7. The coverage rato of the WSN n Fgure 7(a) and (b) s 95.13% and 95.31%, respectvely. It can be seen that the data paths obtaned by DPSOSA tend to provde more potental for mult-hop communcaton nstead of usng longer dstance data transmsson, although both algorthms attempt to acheve energy effcency. As a result, the energy metrcs obtaned by PSO and DPSOSA are 5.83 x 10 5 J/bt and 5.57 x 10 5 J/bt, respectvely. Fgure 7. Optmzed WSN deployment and communcaton paths adoptng two algorthms: (a) PSO; (b) DPSOSA. (a) (b)
Sensors 2007, 7 646 Fnally, scenaros of WSN are set up accordng to Fgure 7(a) and (b) for target trackng smulatons. Besdes, we dscuss a coverage-only deployment, whch s optmzed by DPSOSA takng only coverage metrc nto account. In each sensng perod, the closest wreless sensor node to the moble target s chosen va negotaton. It then acqures nformaton and sends a 2KB data packet to the snk node along the optmzed path. The total energy consumpton over tme s extracted from the smulatons, as shown n Fgure 8. We fnd that the WSN optmzed by DPSOSA has a lower energy consumpton than the one optmzed by PSO. Moreover, target trackng s a long term task, so more energy could be saved durng the lfetme of WSNs. Compared to the coverage-only deployment, DPSOSA acheves an energy conservaton of 4.68%. Fgure 8. Energy consumpton comparson of WSNs optmzed by PSO and DPSOSA n target trackng applcaton From the experments, the effcency of multple computng nodes s verfed and t s shown that DPSOSA can appled under dfferent coverage requrements. Then, the mproved energy effcency of DPSOSA s demonstrated by algorthm smulatons and target trackng applcaton compared wth general PSO. 6. Conclusons Focusng on the energy-effcent coverage problem of WSNs, ths paper has proposed dstrbuted partcle swarm optmzaton and smulated annealng to optmze the network deployment. In a network composed of statonary and moble wreless sensor nodes, the proper placement of moble nodes s dscussed, consderng sensng coverage and energy consumpton. Then, the coverage metrc s defned utlzng a grd excluson algorthm, whle the energy metrc s calculated by Djkstra s algorthm, whch provdes the optmal communcaton paths for data reportng. Partcle swarm optmzaton and smulated annealng are combned to fnd the global optmal soluton, where the ftness functon s desgned to mnmze the energy metrc guaranteeng specfed coverage rato. Besdes, computaton capablty of multple wreless sensor nodes s adopted to enhance the optmzaton capacty. Expermental results represent that sgnfcant energy conservaton can be
Sensors 2007, 7 647 acheved by the proposed optmzaton algorthm compared to general PSO, and energy effcency of WSN s boosted up n target trackng applcaton. Ths paper presents an evaluaton method for energyeffcency of coverage problem n WSNs. The applcaton-orented property s realzed by target trackng. Stll, further nvestgaton should be made on adaptve routng schemes and scalable network topologc. Acknowledgements Ths paper s supported by the Natonal Grand Fundamental Research 973 Program of Chna under Grant No.2006CB303000 and the Natonal Natural Scence Foundaton of Chna (No.60673176; No.60373014; No.50175056). References and Notes 1. Huang, C.F.; Tseng Y.C. A survey of solutons to the coverage problems n wreless sensor networks. Journal of Internet Technology 2005, 6, 1-8. 2. Dhllon, S.S.; Chakrabarty, K. Sensor placement for effectve coverage and survellance n dstrbuted sensor networks. IEEE Wreless Communcatons and Networkng Record 2003, 1609-1614. 3. Meguerdchan, S.; Koushanfar, F. Coverage problems n wreless ad-hoc sensor networks. Proceedngs of the IEEE INFOCOM 2001, 1380-1387. 4. Wang, X.; Xng, G. Integrated coverage and connectvty confguraton n wreless sensor networks. Proceedngs of ACM Internatonal Conference on Embedded Networked Sensor Systems 2003, 28-39. 5. Ba, X.; Kumar, S. Deployng wreless sensors to acheve both coverage and connectvty. Proceedngs of ACM MobHoc 06 2006, 131-142. 6. Wang, X.; Ma, J.; Wang, S.; B, D. Predcton-based dynamc energy management n wreless sensor networks. Sensors 2007, 7, 251-266. 7. Wang, X.; Wang, S. Collaboratve sgnal processng for target trackng n dstrbuted wreless sensor networks. Journal of Parallel and Dstrbuted Computng 2007, 67, 501-515. 8. Wang, X.; Wang, S.; Ma, J. An mproved co-evolutonary partcle swarm optmzaton for wreless sensor networks wth dynamc deployment. Sensors 2007, 7, 354-370. 9. Hu, F.; Cao, X.; May, C. Optmzed schedulng for data aggregaton n wreless sensor networks. Proceedngs of IEEE Internatonal Conference on Networkng, Sensng and Control 2005, 2, 557-561. 10. Wang, X.; Wang, S.; Ma, J. An mproved partcle flter for target trackng n sensor system. Sensors 2007, 7, 144-156. 11. Sadler, B.M. Local and broadcast clock synchronzaton n a sensor node. IEEE Sgnal Processng Letters 2006, 13, 9-12.
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