Memetic Algorithm-Based Multi-Objective Coverage Optimization for Wireless Sensor Networks

Transcription

1 Sesors 204, 4, ; do:0.3390/s Artcle OPEN ACCESS sesors ISSN Memetc Algorthm-Based Mult-Objectve Coverage Optmzato for Wreless Sesor Networks Zh Che,2,3, *, Shua L ad Wejg Yue 4 College of Computer, Najg Uversty of Posts ad Telecommucatos, No.9, Weyua Road, Yadog ew Dstrct, Najg 20023, Cha; E-Mal: acm@jupt.edu.c 2 Jagsu Hgh Techology Research Key Laboratory for Wreless Sesor Networks, No.66, New Mofa Road, Gulou Dstrct, Najg 20003, Cha 3 State Key Laboratory for Novel Software Techology, Najg Uversty, No.63, Xal Road, Qxa Dstrct, Najg 20023, Cha 4 Key Lab of Broadbad Wreless Commucato ad Sesor Network Techology, Mstry of Educato, No.66, New Mofa Road, Gulou Dstrct, Najg 20003, Cha; E-Mal: yuewj@jupt.edu.c * Author to whom correspodece should be addressed; E-Mal: chez@jupt.edu.c; Tel.: ; Fax: Exteral Edtor: Leohard M. Redl Receved: 9 August 204; revsed form: 8 October 204 / Accepted: 8 October 204 / Publshed: 30 October 204 Abstract: Matag effectve coverage ad extedg the etwork lfetme as much as possble has become oe of the most crtcal ssues the coverage of WSNs. I ths paper, we propose a mult-objectve coverage optmzato algorthm for WSNs, amely MOCADMA, whch models the coverage cotrol of WSNs as the mult-objectve optmzato problem. MOCADMA uses a memetc algorthm wth a dyamc local search strategy to optmze the coverage of WSNs ad acheve the objectves such as hgh etwork coverage, effectve ode utlzato ad more resdual eergy. I MOCADMA, the alteratve solutos are represeted as the chromosomes matrx form, ad the optmal solutos are selected through umerous teratos of the evoluto process, cludg selecto, crossover, mutato, local ehacemet, ad ftess evaluato. The expermet ad evaluato results show MOCADMA ca have good capabltes matag the sesg coverage, acheve hgher etwork coverage whle mprovg the

2 Sesors 204, eergy effcecy ad effectvely prologg the etwork lfetme, ad have a sgfcat mprovemet over some exstg algorthms. Keywords: sesor etworks; coverage algorthm; memetc algorthm; mult-objectve optmzato. Itroducto Wreless Sesor Networks (WSNs) are self-orgazed etworks cosstg of sesor odes wth the ablty of sesg, processg ad wreless commucatg []. Coverage cotrol s oe of the most fudametal research ssues sesor etworks, ad studes how well a sesor etwork wll motor a feld of terest wth the proper ode deploymet [2,3]. Sesor odes ofte have costraed resources ad t s sometmes dffcult to recharge ther eergy, ad thus coverage sustaablty such sesor etworks caot be guarateed. How to balace the etwork eergy cosumpto coverage cotrol s a mportat ssue, whch ca be modeled as a mult-objectve optmzato problem of prologg the etwork lfetme ad mprovg etwork coverage accordg to the characterstcs of WSNs [4]. Mult-objectve optmzato problems volve two or more coflctg objectves ad have ot oe optmal soluto but may solutos whch form the Pareto frot represetg a tradeoff of oe objectve agast the other. I most applcatos, the goal of solvg the mult-objectve optmzato problems s to compute a approxmato of the Pareto frot. Computatoal Itellgece (CI) ad evolutoary algorthms provde adaptve, flexble ad robust mechasms that exhbt tellget behavor to solve the mult-objectve optmzato problems of coverage cotrol complex ad dyamc evromets lke WSNs [5]. Habb modeled the coverage problem wth two sub-problems: floorpla ad placemet, ad used the geetc algorthm (GA) to search the optmal coverage WSNs [6]. Ozturk et al. appled artfcal bee coloy algorthm to the dyamc deploymet of the sesor etworks ad obtaed better deploymets for WSNs tha the partcle swarm optmzato algorthm [7,8]. The aforemetoed artcles emphaszed to mprove the coverage rate ad dd ot specfcally take to accout etwork lfetme ad eergy balace WSNs. Memetc algorthms are computatoal tellgece structures ad a class of stochastc global search heurstcs where evolutoary algorthms are combed wth multple ad varous local search heurstcs order to address such optmzato problems as those WSNs [9 ]. Ths paper presets a mult-objectve coverage optmzato algorthm based o memetc algorthm for WSNs, amely MOCOAMA, whch cosders the coverage degree, ode utlzato, ode resdual eergy, ad solves the -coverage mult-objectve problem for WSNs [2 5], ad fally gets the optmal deploymet of etwork coverage. The rest of the paper s orgazed to fve sectos: Secto 2 brefly troduces related work. Secto 3 dscusses the mult-objectve optmzato coverage problem of WSNs. Secto 4 presets the key schemes for the proposed coverage algorthm for WSNs. Secto 5 descrbes the mult-objectve optmzato coverage algorthm based o memetc algorthms. The smulato expermets ad evaluato are gve Secto 6. Fally, the coclusos are offered Secto 7.

3 Sesors 204, Related Work Kostatds et al. proposed a memetc algorthm (MA)-based soluto of eergy-aware topology cotrol (ToCMA) for WSNs usg a combato of problem-specfc lght-weghted local searches ad geetc algorthms [], whch ca provde a better performace tha the classcal mmum spag tree solutos. I ToCMA, the composg ettes of a chromosome or gees are the power of sesor odes; the ftess fucto of a soluto s the sum of the power assged to each gee, ad repar ad mprovemet methods are employed to refe solutos. Feretos et al. used a memetc algorthm to dyamcally optmze the desg of WSNs ad cosdered dfferet costrats such as applcato-specfc requremets, commucato costrats ad eergy cosumpto [4]. Ther work showed that the hybrdzato of the orgal GA wth the local search operatos preseted memetc algorthms brought some mprovemet o the performace of the desg process. Jag et al. used memetc algorthms to mplemet eergy-effcet coverage cotrol cluster-based WSNs (CoCMA) [5], whch cotas a memetc algorthm-based schedule for sesor odes ad a wake-up scheme. I CoCMA, the coverage solutos are represeted by bary strgs, ad the status of a ode s represeted by a allele of a chromosome. CoCMA ca prolog the etwork lfetme whle matag coverage preservato of WSNs wth o sesg error, ad has a sgfcatly mproved performace compared wth the LEACH [6], LEACH-Coverage-U [7], etc. Tg et al. proposed a memetc algorthm to solve the set k-cover problem of WSNs, whch has the effectveess ad effcecy of extedg the etwork lfetme [8]. I MA, a chromosome represets the sequece whch all sesor odes are collected to form covers, ad the ftess value of a chromosome s the sum of coverage cotrbutos of all sesor odes ad ca ehace the dfferetato of promsg chromosomes. Arvudaamb et al. proposed a kowledge added mproved memetc algorthm (MA) for target coverage WSNs, whch s cocered wth explotg all avalable kowledge ad demostrated the effectveess extedg the lfetme of WSNs [9]. MA ecodes the caddate soluto as the chromosome represeted by a matrx whch row represets the sesor odes, ad colum represets the targets. I ths paper, our proposed MOCOAMA uses the coverage optmzato framework of CoCMA [5], MA [8] ad, MA [9], but t deals wth the coverage problem of WSNs wth the sesg error, dvdes the target area wth the vrtual cells as the bass of chromosome represetato, ad radomly ad alterately selects some local search algorthms to acheve the dyamc local search. 3. Mult-Objectve Coverage Optmzato Problem I ths paper, we assume that sesor odes are radomly ad uformly dstrbuted over the target area, wth the same physcal structure, commucato capacty, sesg rage, tal lmted eergy ad computg capacty. The sk ode or the base stato (sk) s assumed to have ulmted eergy wth plety of power supples. The sk or every sesor ode has a uque detfer, ad ca get ts ow locato formato ad commucate wth ts eghbor odes usually usg ormal power or wth each other through power cotrol.

4 Sesors 204, A target feld D s a two-dmesoal plae dvded to M N vrtual cells. The pots of terest are dstrbuted D ad there exsts at most oe pot of terest oe vrtual cell. A set of sesor odes T are deployed over D where T = { t, t2,..., t }, t = ( x,y,r), s the umber of sesor odes, [, ], ( x,y ) s the coordate of the sesor ode t, ad r s the maxmum deal sesg radus of The coverage feld of t s a crcle area wth ( x,y ) as the ceter ad r as the radus. The Eucldea dstace betwee t ad the pot of terest c whose coordate s ( x,y) D s: 2 2 dt (, c) = ( x x) + ( y y) () If the set of vrtual cells sesed by the sesor ode t s s, the coverage area of all sesor odes s: = (2) = S(T) γ s where γ s the decso varable to be determed by the coverage algorthm, γ = f t s the state of actvato, ad γ = 0 f t s the state of actvato. The probablty of sesg the pot of terest c by the sesor ode t D s: t. 0 r d( t, c) d(t, d) r re λ r d(t, d) pt (,c) e r re d( t, c) r = < < r re d( t, c) (3) where r e s the sesg error value of the sesor odes, r has the same value for all sesor etworks assumed ths paper ad λ s the sesg atteuato coeffcet. As log as the pot of terest c s effectvely sesed by a sesor ode, t ca be sad that c s covered by the etwork. If a set of pots of terest (.e., c, c 2,..., c k, k M N ) at the same tme s sesed by t, we get: k s = k( ( p( t, c ))) (4) j j = We defe sesg coverage degree or coverage degree as the percetage of the feld area covered by sesor odes the motored feld, whch reflects the actual etwork sesg ablty of motorg a gve feld of terest or the pots of terest. Accordg to Equato (2), the coverage degree of sesor etworks deployed D s: γ s ST ( ) (T) = = M N M N = ϖ (5) Accordg to Equato (4), we ca get: ϖ (T) γ s γ k( ( p( t, cj))) = j = M N M N = k (6) If k = M N, we ca get: M N (7) ϖ(t) γ ( ( pt (, c))) j = j =

5 Sesors 204, We defe the objectve optmzato model of the etwork coverage as: m γ = max ϖ (T) (8) I WSNs, due to the lmted eergy of sesor odes, reducg the eergy cosumpto of some odes ad balacg the eergy cosumpto of the etre etwork ca effectvely save the lmted eergy of the etwork ad exted the etwork lfetme. Uder the premse of guarateeg some certa coverage degree, we may reduce the umber of sesor odes workg ad deactvate the redudat odes to reduce the eergy cosumpto as much as possble to crease the etwork lfetme. We defe ode utlzato as the rato of the umber of cells havg actve sesor odes to the total cell umber the target area gve by: T UT ( ) = (9) M N where T s the umber of cells havg actve sesor odes ad sesor odes are deployed the target feld D whch s dvded to M N vrtual cells. To exted the lfetme of sesor etworks, we also cosder the resdual eergy of WSNs the target feld D. If E s the resdual eergy of the sesor ode t, the eergy dstrbuto of the etwork s expressed as: ET ( ) = = 2 2 (E E ) (E E ) = = = = 2 2 ( E ) ( E ) = = where ET ( ) reflects the degree of eergy dfferece the etwork; f ts value s smaller, the eergy dfferece betwee sesor odes may be smaller, ad the resdual eergy of the sesor odes may be hgher. To crease the etwork lfetme, we may ot oly use as few odes as possble to reduce eergy cosumpto, but also make sure to select the odes wth balaced eergy cosumpto ad a hgher resdual eergy. Therefore, we defe the objectve optmzato model of the eergy cosumpto as: m α UT ( ) + β ET ( ) max ϖ (T) () where α s the ode utlzato weghtg coeffcet, β s the eergy balace weghtg coeffcet ad α + β =. Accordg to Equatos (8) ad (), MOCOAMA, we pay atteto to Pareto optmal solutos of the mult-objectve coverage optmzato problem of WSNs formulated as: mγ = max ϖ (T) m α UT ( ) + β ET ( ) st.. γ = 0or, [,] (0) (2)

6 Sesors 204, Mult-Objectve Coverage Optmzato Desgs A memetc algorthm uses the oto of meme(s) as uts of formato ecoded computatoal represetatos [20], whch s a combato of global search ad local search, ad the objects of geetc mapulato are ot ay dvduals the populato space, but some locally-optmal represetatves elected by local search ad from the local area. Usg the heret parallelsm of memetc algorthm, we ca greatly accelerate the rate of covergece of the mult-objectve coverage optmzato algorthm for WSNs. 4.. Ecodg Rule Ecodg s a mappg from the problem space to the soluto space, but memetc algorthm caot drectly process the soluto data of the soluto space, so before searchg, the varables of the soluto space must be mapped to the data structures of evolutoary space, amely chromosomes. I MOCOAMA, whe the sk dvdes the target area to M N cells, each chromosome represets a deploymet soluto of WSNs wth the form of a M N matrx gve Equato (3): x, x,2 x, N x2, x 2,2 x2, N ℵ= (3) x M, x M,2 x M, N I each chromosome ℵ, allele X, j deotes oe of the sesor odes coverg the vrtual cell of (, j) where X, j [0, ] ; f X, j= 0, the vrtual cell of (, j) s ot covered by ay sesor ode. The sesor odes oe cell have oe of three states: sleepg state, detectg state ad workg state; the workg state s the state of actvato, ad other two states are the states of actvato. Sesor odes coverg oe cell update ther remag eergy real tme, ad the sk chooses oe sesor ode as the workg ode whch has shorter dstace from the ceter of the vrtual cell or has more resdual eergy ad has a prorty rght to beg the workg ode. After collectg the formato o locatos ad resdual eergy of all odes coverg each cell, the sk computes the probablty of beg a workg ode for each sesor ode. The ode wth greater probablty wll be elected as the workg ode coverg oe cell, or a ode wll be radomly selected as the workg ode from those odes wth the same probablty, ad other odes wll tur to beg the sleepg state from the detectg state. I order to balace the eergy cosumpto of each ode, re-electo of the workg ode coverg oe cell wll be requested uder the cotrol of the sk whe the remag eergy of the workg ode s less tha the average eergy of sesor odes coverg oe cell. I MOCOAMA, oly oe of the sesor odes s elected ts vrtual cell; oe vrtual cell s covered at least oe sesor ode at the dfferet tme uless t caot be covered by ay sesor ode. Therefore, from each chromosome, gve the WSNs of T = { t, t2,..., t }, we ca get some sets of sesor odes workg state ad oe set of sesor odes ca be descrbed as: = M, j= N { X, j} γ t (4) =, j= = Ψ= = where γ = f the sesor ode s workg state ad γ = 0 f otherwse.

7 Sesors 204, Accordg to Equatos (3) ad (4), we ca get oe of the decso solutos of deployg WSNs gve by: Γ= γ (5) = 4.2. Ftess Fucto I MOCOAMA, the ftess of each chromosome may be evaluated accordg to the values of the multple optmzato sub-goals. We apply Pareto rakg [2] as the ftess value evaluato scheme searchg for a set of Pareto-optmal solutos of mult-objectve coverage optmzato for WSNs. The allocato order of each o-domated dvdual curret populato s ; the allocato order of ay other dvdual s the umber of domat dvduals plus ; the formula s as follows: R( ℵ ) = { ℵj ℵj P, ℵj ℵ, ℵ P} (6) where ℵ s ay dvdual of the populato P, meas the domace relatoshp betwee two dvduals, R( ℵ ) meas the umber of dvduals whch domate ℵ populato P. The allocato order of ℵ s R( ℵ ) +. If the dvdual ℵ s closer to the optmal soluto, the order umber of ℵ s smaller. Whe ℵ s a o-domated soluto, the order umber of ℵ s. Accordg to Equatos (2) ad (6), the ftess fucto MOCOAMA s: 2 ( R( ℵ ) + ) γ = f( ℵ ) = ( δ ( α U( T) + β E( T)) δ ϖ (T)) (7) 4.3. Local Search Strategy The local search strategy of memetc algorthms s a process of screeg the excellet dvduals the local area. The combato of global search algorthms ad local search algorthms ofte shows good covergece ad strog global search capablty solvg the mult-objectve optmzato problem, but there are o uform stadards ad gudes the choce of local search strateges, as well as the posto, mld ad frequecy, so we eed to dscover the local search strategy whch s sutable for the uresolved problem. Sytheszg the advatages of a varety of local search algorthms ca make the process of the local search coverge faster ad have hgher soluto qualty by desgg specfc local search access polces. I order to acheve dyamc local search, we propose some self-adapto schedulg rules of the local algorthm. I every terato of MOCOAMA, some algorthms from the pool of local search algorthms are radomly ad alterately selected to make local search ad get dverse solutos. The the sk searches m searched earest pots from the tal pot of the local search ad the stuato of soluto ftess mprovemet correspodg to the local search algorthms used the m pots s evaluated. The oe of the local search algorthms havg the most obvous mprovemet o ftess s evetually used the mult-objectve optmzato. The proposed rules lear from the search hstory formato to regulate the local search strategy wth adaptve, self-learg features. The pool of local search algorthms s a collecto of may local search algorthms, cludg the tabu search algorthm [22], hll clmbg search algorthm [23] ad adaptve drectoal local search strategy [24]. Tabu search s a optmzato algorthm for smulatg huma tellgece, whch

8 Sesors 204, mmcs the huma memory fucto, saves the searched optmal soluto to the tabu table the process of solvg, ad marks the solutos to avod repeatg the same search order to ga a broad search rage [22]. The hll-clmbg algorthm s a heurstc search algorthm based o greedy search strategy, whch selects a radom soluto as the curret soluto the soluto space ad compares wth the solutos the eghborhood scope oe by oe utl you fd a local optmal soluto [23]. The adaptve drectoal local search strategy dyamcally adjusts the eghborhood radus ad/or local search probablty, depedg o the relatve local ad global effectveess of evolutoary operators ad the local search operator [24]. 5. Memetc Algorthm Based Mult-Objectve Coverage Optmzato I ths paper, MOCADMA uses the dyamc local search strategy ad a local algorthm schedulg mechasm to adapt to the selecto of local search algorthms; ad creases the optmal storage strategy to accelerate the covergece speed of the algorthm. The pseudo code of MOCADMA s descrbed as follows: Pseudo code of MOCADMA Gve formato : the target feld D, the pots of terest { c, c2,..., ck }, the sk ode( Sk), the set of sesor odes T = { t, t2,..., t}, the caddate populato ( CP), the optmal populato ( P) the caddate populato sze ( pts), the optmal populato sze ( pos), the crossover probablty ( pcross), the mutato probablty ( pmutato) maxmum teratos ( m), parameters used the ftess fucto step(a) : Deployg T over D for to do Sk ( locato, r, re, resdual _ eergy) edfor step( B): D M N vrtual cells step( C) : for todo for j to k do Calculate p( t, c j) edfor edfor for todo calculate s edfor repeat for to M do for j tondo X, j t= RouletteWheelSelect( T,, j) edfor edfor = M, j= N ℵ EcodeChromosome( Matrx=, j= ( X, j)) f ( ℵ CP) the CP ℵ edf utl the umber of dvdualscp reaches pts

9 Sesors 204, for to pts do Calculate f ( ℵ ) edfor repeat Select the Pareto optmal dvdual CP ad add t to P utl the umber of dvduals P reaches pos repeat step( D) : for to NumofCrossover do ChromoA Select( P) ChromoB Select( P) OP OP + Crossover( A, B, pcross) edfor step( E): for to NumofMutato do ChromoA Select( OP) OP OP + Mutate( A, pmutato) edfor step( F): // radomly ad alterately s elect somelocal search algorthms to makelocal search P SelectTabuSearch( P OP) // example P2 HllClmbgSearch( P OP) // example2 P3 AdaptveDrectoalSearch( P OP) // example3 CP Evaluate( P, P2, P3) // select the optmal caddate soluto stepg ( ): repeat Select the Pareto optmal dvdual CP ad add t to P utl the umber of dvduals P reaches pos utl the umber of teratos reaches m step( H ): Get curret optmal deploymet soluto from P step( I ): Executecurret optmal deploymet soluto over T MOCADMA cludes terated evolutoary operatos of memetc algorthm ad dyamc local search strategy, whch s descrbed detal as follows: (A). The Sk Collects the Iformato of Sesor Nodes After tal uform deploymet, every sesor ode s the detectg state ad seds ts locato formato (#locato), maxmum deal sesg radus (#r), sesg error value (#re) ad eergy formato (#resdual_eergy) to the sk by floodg commucato. (B). The Sk Dvdes the Network The sk dvdes the motored target feld to M N vrtual cells (or uts) accordg to the locatos of the sesor odes; each sesor ode belogs to oly oe cell but ca cover umerous cells; oe cell may have may sesor odes. (C). The Sk Geerates the Ital Populato, Calculates the Ftess Values ad Saves the Optmal Solutos The sk calculates the probablty of sesg pots of terest by sesor odes accordg to Equato (3) ad the umbers of vrtual cells sesed by sesor odes accordg to Equato (4) usg the formato (#locato, #r, #re) of every sesor ode, repeatedly selects oe ode every cell as the workg ode by roulette wheel selecto that takes the umber of the sesed vrtual cells as the

10 Sesors 204, weght of every ode, ad geerates the deploymet solutos whch form the tal caddate populato CP of chromosomes. The the sk gets the decso varables of sesor odes from the chromosomes ad calculates the ftess value of dvdual chromosome ℵ the tal populato accordg to Equato (7) usg the formato (#resdual_eergy) of sesor odes, selects the chromosomes wth hgher ftess value as the local Pareto-optmal solutos, ad the saves these solutos the curret optmal populato P. For the local optmal soluto, f the populato P does ot cota ℵ ad ℵ s ot domated by the exsted solutos P, the sk adds ℵ to P. At the same tme, the Eucldea dstace of the local best dvdual ℵ to other dvduals the exteral populato space s calculated, ad the closer dvdual s substtuted for ℵ. (D). Crossover The sk takes mult-pot crossover through exchagg the statuses of odes dfferet local optmal chromosomes represeted as the matrces. Two dvdual chromosomes the curret optmal populato P are radomly ad cotuously selected ad exchage oe radom row wth the gve crossover probablty; f ths recombato geerates two ew dvduals, they wll be added to the offsprg populato OP. (E). Mutato To mata the dversty of solutos, the sk geerates a varety of solutos through radomly chagg the status of the odes the vrtual cells. The mutato operator s appled to all dvdual chromosomes OP, ad every allele oe chromosome s modfed wth the gve mutato probablty; f ths recombato geerates a ew dvdual, t wll be added to OP. (F). Dyamc Local Search Some algorthm from the pool of local search algorthms, cludg the tabu search algorthm [22], hll clmbg search algorthm [23] ad adaptve drectoal local search strategy [24] s radomly ad alterately selected to make local search P OP, ad every local search algorthm geerates ts local populato; the the sk compares the average ftess values of the same umber of sample dvduals aroud the tal pot of the local search those local populatos, gets the local search algorthm that has the hghest average ftess value, ad selects ts local populato as the curret caddate populato CP. (G). The Sk Calculates the Ftess Values ad Saves the Optmal Solutos The sk calculates the ftess value of dvdual chromosome ℵ the curret caddate populato CP, selects the local Pareto-optmal solutos, ad the saves these solutos P. (H). The Sk Determes the Curret Optmal Deploymet Soluto Whe the umber of teratos has reached the predetermed maxmum threshold, the sk fshes determg the curret optmal deploymet soluto havg the hghest ftess value; otherwse, MOCADMA cotues to ru from (D).

11 Sesors 204, (I).The Sk Broadcasts the Deploymet Soluto The sk broadcasts the optmal etwork deploymet soluto to each sesor ode, ad forms each ode ts cell resposble as the workg ode or the o-workg ode. The workg odes are the workg state coverg the target area wth the optmal deploymet soluto, ad the o-workg odes are alterate the sleepg or detectg state a perod of tme. The sk motors the etwork ad evaluates the eergy cosumg of every sesor ode. Whe the ext roud threshold tme that may be decded by the routg protocol has arrved, or the remag eergy of oe workg ode s less tha the average eergy oe cell, aother ew roud comes ad MOCADMA cotues to ru from (D). 6. Expermets ad Evaluato We use Matlab to perform the smulato expermets of MOCADMA whch the sk s placed at the ceter of the target area. I fact, the sk may be deployed at ay place the area, but the eergy cosumpto wll be dstrbuted over the feld evely f the posto of the sk approxmates the geometrc ceter of the target area [5]. A eergy cosumpto model [5,6,25] s used the smulato expermets. I the eergy cosumpto mode, the trasmsso eergy E TX for trasmttg K bts of formato betwee two sesor odes s calculated by Equato (8); the cosumed eergy E RX for recevg K bts of formato by oe sesor ode s calculated by Equato (9); whe the clustered routg algorthm s appled to the WSNs, the eergy cosumpto of oe cluster head [6] s calculated by Equato (20): E K E K 2 TX = elec + ε fs d (8) E K E RX = elec (9) 4 ( ECH = ) K Eelec + K Eelec + K EDA + ε amp K dtosk (20) C C where s the umber of sesor odes, C s the umber of clusters, d tosk s the dstace betwee the cluster head ad the sk, Eelec s the eergy cosumed by the electrocs the trasmtter or recever, ε fs s the eergy cosumpto of the sgal power amplfer per square meter, E DA s the eergy cosumpto of processg oe-ut bt data, ad ε amp s the eergy cosumpto of trasmttg oe-ut bt data to the sk ode. To evaluate the performaces of MOCADMA, smulato results are compared to those of CoCMA [5], MA [8] ad MA [9] usg the same parameters show Table, ad all the results are from the expermets repeated 30 tmes. For MOCADMA, the M N vrtual cells dvdg the target area at the tal stage brdge the problem space of WSNs ad the soluto space of chromosomes. I the smulato expermets, we cosder 400 sesor odes wth o sesg error ( r = e 0 ) ad 64 pots of terest radomly ad uformly deployed a 00 m 00 m target area. Fgure shows the average sesg coverage degree (SCD) versus dfferet dvdg of vrtual cells ad dcates that the average SCD has the maxmum value at N = 6 whe M = 6, N = 8 whe M = 8, N = 2 whe M = 2, ad N = 3 whe

12 Sesors 204, M = 4 f M N.. As Fgure 2 shows, we ca get the best dvdg of vrtual cells havg maxmum average SCD Table. Parameters used smulatos Parameter Value Network sze: 400 Number of pots of terest 64 Crossover probablty: pcross 0.6 Mutato probablty: pmutato 0. Maxmum teratos 8000 Commucato radus 20 m~80 m Packet legth: K 300 bt Number of clusters: C 40 Node tal eergy: E 0 0 J Maxmum deal sesg radus: r 5 m Sesg error value: r e m λ E elec 50 J/bt ε 00 pj/bt/m 2 fs E DA 5 J/bt ε pj/bt/m 4 amp δ δ 2 Fgure. Average SCD versus dfferet dvdg of vrtual cells. Average Sesg Coverage Degree (%) N M=6 M=8 M=0 M=2 M=4 I the ftess fucto of MOCADMA, α ad β ( β = α ) are the ode utlzato weghtg coeffcet ad the eergy balace weghtg coeffcet, respectvely. I the ext smulato expermets, we assume that N = 8, M = 8, or N = 0, M = 0, or N = 3, M = 4. Fgures 3 ad 4 depct

13 Sesors 204, the etwork lfetme (rouds) versus dfferet values of α whe r = e 0 ad r = e, respectvely, ad we ca see that the etwork has a maxmum lfetme (rouds) whe α 0.4 ( β 0.6 ). Fgure 2. The best dvdg of vrtual cells havg maxmum average SCD. M N Fgure 3. Network lfetme versus dfferet values of α wth r 0 e =. Network Lfetme (rouds) α r e = M=8,N=8 M=0,N=0 M=4,N=3 I a hostle evromet, the sesg error ofte exsts the applcatos of WSNs, so we cosder t ( r e ) computg the probablty of sesg the pot of terest by oe sesor ode evetually used the ftess fucto of MOCADMA. Fgure 5 shows the average SCD versus dfferet values of r e ad dcates that the average SCD decreases wth the crease of r e. It s clearly see that the more ucertaty from the sesg error causes more dffcultes for etwork coverage. 0

14 Sesors 204, Fgure 4. Network lfetme versus dfferet values of α wth r e =. Network Lfetme (rouds) r = e M=8,N=8 M=0,N=0 M=4,N= Fgure 5. Average SCD versus dfferet values of r e. α Average Sesg Coverage Degree (%) M=8,N=8 M=0,N=0 M=4,N= r e Fgure 6 presets the average SCD versus etwork sze wth the fxed umber of pots of terest where α = 0.4, r e = 0. As Fgure 6 shows, whe 64 pots of terest radomly ad uformly are deployed the 00 m 00 m target area, ad the umber of deployed sesor odes vares from 50 to 400, the average SCD creases wth the crease of etwork sze ( ).

15 Sesors 204, Fgure 6. Average SCD versus etwork sze wth the fxed umber of pots of terest. 80 Average Sesg Coverage Degree (%) M=8,N=8 M=0,N=0 M=4,N= I the ext smulatos, we verfy the feasblty of MOCADMA WSNs ad cosder 400 sesor odes ad 64 pots of terest radomly ad uformly deployed the 00 m 00 m target area. To evaluate the performace of the MOCADMA, a LEACH-based clustered routg protocol [26] s appled to the WSNs, ad CoCMA [5], MA [8] ad MA [9] are re-mplemeted. I addto, the desg of CoCMA, MA ad MA dd t allow the sesg error, so we oly cosder the WSNs wth o sesg error ( r = e 0) the smulato expermets. Fgure 7 depcts the SCD versus etwork lfetme rouds ( α = 0.4 MOCADMA). We ote that all the algorthms have good capabltes matag the sesg coverage, but MOCADMA has mataed the sesg coverage degree at 00% utl the 3800th addtoal roud whch s a sgfcat mprovemet over other algorthms. As Fgure 7 shows, the etwork lfetme s prologed to 7000 more rouds by the MOCADMA, whch lasts about 800 rouds loger compared to CoCMA ad MA. Fgure 7. SCD versus etwork lfetme rouds. Sesg Coverage Degree (%) MOCADMA MA CoCMA MA Network Lfetme (rouds)

16 Sesors 204, Fgure 8 dsplays the percetage of ode death versus etwork lfetme rouds ( α = 0.4 MOCADMA). The MOCADMA, CoCMA, MA, ad MA lose ther 50% of odes at the 556th, 542d, 4889th, ad 403rd roud, respectvely. The smulato result demostrates that the proposed MOCADMA sgfcatly prologs the lfetme of the etwork compared to other three methods. The proposed MOCADMA dvdes the WSNs at the early stage ad helps form the clusters earler tha other three methods that save much eergy, get the mult-objectve Pareto-optmal solutos of etwork coverage by the ftess fucto preseted Equato (7) that has a quck-covergece characterstc, so the loger etwork lfetme ca be obtaed. The smulato results show that MOCADMA ca acheve hgher etwork coverage whle mprovg the eergy effcecy ad effectvely prologg the etwork lfetme. Fgure 8. Percetage of ode death versus etwork lfetme rouds. Percetage of ode death (%) MOCADMA MA CoCMA MA Network Lfetme (rouds) Fgure 9. Performaces of the dyamc local search strategy the dfferet cases. Sesg Coverage Degree (%) Normal tabu hll clmbg adaptve drectoal Network Lfetme (rouds)

17 Sesors 204, Fally, we aalyze the dyamc local search strategy of MOCOAMA through the smulato expermets wth the same codtos as the prevous expermets. I the ormal case, there are tabu search algorthm, hll clmbg search algorthm ad adaptve drectoal local search strategy the pool of local search algorthms, but whe oly oe of those algorthms s the pool, MOCOAMA would have a dfferet performace. Fgure 9 shows the performaces of the dyamc local search strategy the dfferet pools, ad the ormal case of MOCOAMA has a better SCD tha other cases. The better performace the ormal case may be due to the fact that MOCOAMA ca dyamcally use the advatages of the multple local search algorthms. 7. Coclusos Ths paper presets a mult-objectve coverage optmzato algorthm for WSNs, called MOCOAMA, whch uses a memetc algorthm ad gets the Pareto optmal solutos of the coverage problem. MOCOAMA maps the alteratve solutos to the chromosomes represeted as the matrces ad uses a ftess fucto over sesg coverage degree, etwork coverage, eergy cosumpto ad Pareto rakg. We also troduce the dyamc local search strategy ad a local algorthm schedulg mechasm to mprovg some or all chromosomes oe populato. The smulato results show that MOCOAMA ca solve the -coverage mult-objectve problems for WSNs, get optmal etwork coverage, effectvely extedg the etwork lfetme, ad have a sgfcat mprovemet over some related algorthms eve whe the sesg error exsts the etwork. I real applcatos, MOCOAMA depeds o the sk whch s assumed to have ulmted eergy ad fshes most of the problem-solvg work accordg to the data set from the sesor odes, so how to reduce the depedece o the sk desgg memetc algorthm-based coverage algorthm shall be a challegg research task the future. Ackowledgmets The authors would lke to thak the revewers for ther very valuable commets ad suggestos, whch have helped to mprove the mauscrpt. Ths work was supported by the Natoal Natural Scece Foudato of Cha (Grat No ), the Basc Research Program of Jagsu Provce (Natural Scece Foudato) (Grat No.BK20756, BK203382), the th Sx Talet Peaks Program of Jagsu Provce (XXRJ-009), Cha Postdoctoral Scece Foudato (GratNo.202M525, 203M53393), Jagsu Plaed Projects for Postdoctoral Research Fuds (Grat No.0006B, 0202C), Scetfc Research Foudato of Najg Uversty of Posts ad Telecommucatos (Grat No.NY2335, NY2352) ad the Project Fuded by the Prorty Academc Program Developmet of Jagsu Hgher Educato Isttutos (Grat No.yx00200). Author Cotrbutos Zh Che maly desged the proposed algorthm ad revsed all the mauscrpt; Shua L tally aalyzed the mult-objectve coverage optmzato problem, co-desged the framework of the proposed algorthm ad wrote the tal mauscrpt uder the supervso of Zh Che; Wejg Yue carred out all the expermets ad performace evaluato o the proposed algorthm.

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