Ope Archive TOULOUSE Archive Ouverte (OATAO) OATAO is a ope access repository that collec the work of Toulouse researchers ad makes it freely available over the web where possible. This is a author-deposited versio published i : http://oatao.uiv-toulouse.fr/ Epri ID : 15237 The cotributio was preseted at ISNCC 2015: http://www.iscc-cof.org/ To cite this versio : Masri, Sami ad Thaljaoui, Adel ad Nasri, Nejah ad Val, Thierry A geetic algorithm-based approach to optimize the coverage ad the localizatio i the wireless audiosesors etworks. (2015) I: IEEE Iteratioal Symposium o Networks, Computers ad Commuicatios (ISNCC 2015), 13 May 2015-15 May 2015 (Hammamet, Tuisia). Ay correspodece cocerig this service should be set to the repository admiistrator: staff-oatao@listes-diff.ip-toulouse.fr
A geetic algorithm-based approach to optimize the coverage ad the localizatio i the wireless audiosesors etworks Sami MNASRI Uiversity of Toulouse UT2J, CNRS-IRIT-IRT Toulouse, Frace Sami.Masri@fsgf.ru.t Adel THALJAOUI Uiversity of Toulouse UT2J, CNRS-IRIT-IRT Toulouse, Frace Adel.Thaljaoui@irit.fr Nejah NASRI Uiversity of Sfax ENIS,,LETI Sfax, Tuisia ejah.asri@isecs.ru.t Thierry VAL Uiversity of Toulouse UT2J, CNRS-IRIT-IRT Toulouse, Frace val@irit.fr Abstract Coverage is oe of the most importat performace metrics for sesor etworks that reflec how well a sesor field is moitored. I this paper, we are iterested i studyig the positioig ad placemet of sesor odes i a WSN i order to maximize the coverage area ad to optimize the audio localizatio i wireless sesor etworks. First, we itroduce the problem of deploymet. The we propose a mathematical formulatio ad a geetic based approach to solve this problem. Fially, we preset the resul of experimetatios. This paper prese a geetic algorithm which aims at searchig for a optimal or ear optimal solutio to the coverage holes problem. Compared with radom deploymet as well as existig methods, our geetic algorithm shows sigificat performace improvemet i terms of quality. Keywords Target Coverage, Audio Localizatio, Mobile Node, Deploymet; Geetic Algorithm; NSGAII I. INTRODUCTION Coverage area ca be defied, accordig to [1], as: "the area i which a sesor ca perform i sesig, moitorig, surveillace ad detectio tasks with a reasoable accuracy (i.e., the sesor readig have at least a threshold level of sesig detectio probabilities withi the area). The target coverage (called also poit coverage) iterest i cotrollig a target i the field of iterest that ca be statioary or mobile. The k-coverage problem requires preservig at least k sesor odes cotrollig ay target to cosider it covered. The works of [2] preset ad discuss the types of coverage problems. The localizatio of the sesors is the most sigificat factor related to the cover etwork. Also, localizatio is a importat issue whe there is a ucertaity of the exact positio of some odes. Ideed, i wireless sesor etworks, the locatio iformatio is crucial especially whe a uusual evet occurs. I this case, sesor ode that detected that evet eeds to locate it ad the report this positio to the base statio. The use of acoustic iformatio captured by sesor odes is oe of the axes that ca brig more possibilities i term of localizatio. I our work, time differece of arrival (TDoA) usig correlatio techique was used for estimatig the delay betwee two sigals captured by two differet microphoes placed o oe ode. The directio of arrival of the soud source ca be obtaied usig this delay ad the soud source is positioed by adoptig the geometric locatio method. For most deploymet formulatios, the problem of optimal placemet of the sesor odes is prove NP-hard [3]. Cosequetly, for large scale istaces, this problem caot be solved by determiistic methods such as the circle packig algorithm. We defie the problem formally ad we propose a efficiet geetic algorithm to resolve the problem of the coverage holes after the iitial radom deploymet. For a give umber of sesors, the proposed algorithm attemp to maximize the sesor field coverage usig a set of operators. I our works, we are iterestig i usig WSN i smart buildigs applicatios. Despite the differet challeges i WSNs, research works have oly focused o post-deploymet problems such as: sesors localizatio, MAC efficiecy or routig optimizatio, etc. Our works aim to esure the deploymet of the odes while maximizig the coverage ad optimizig the audio localizatio usig a efficiet geetic algorithm. Our proposed model is differet from the existig models sice it itegrates sesor ode deploymet, ad audio localizatio approach i a sigle model. The rest of the paper is orgaized as follows: I Sectio II a mathematical modelig is proposed. I Sectio III, the geetic algorithm based approach is explaied. I Sectio IV, the target localizatio issues are discussed. I Sectio V, umerical resul are preseted ad discussed ad fially, Sectio VI cocludes this paper. II. RELATED WORKS Differet research works deals about the deploymet problem i order to maximize the coverage i WSN. The works of [4] ad [5] iteres i studyig the sesor deploymet problems. Also, i [6], the coverage problem is studied i the domai of the robot exploratio. This work cosiders each robot as a sesor ode ad the used algorithm
deploy odes oe by oe icremetally. Hece, the proposed algorithm is computatioally expesive, whe we icrease the umber of odes. Some recet researches proposed geetic algorithms to resolve the deploymet problem i WSNs. As example, the works of [7] propose a multi-objective paradigm to solve the deploymet ad power assigmet problem. This evolutioary algorithm is based o the MOEA/D (Multi Objective Evolutioary Algorithm/Decompositio). They gave a compariso betwee the MOEA/D algorithm ad the NSGAII algorithm. The former is batter is some istaces while the latter is better i some other istaces. III. MATHEMATICAL MODEL We preset the followig model to resolve our problem. The objective is to provide a deploymet scheme while optimizig the target coverage of the localizatio. To best locate, we aim to optimize the placemet of odes with the most possible uiform distributio of odes (achors ad mobile odes) aroud the target to locate. Amog the cosidered costrai, the o-aligmet of odes ad a wellstudied distaces betwee them. The set of targe to detect; the locatio of potetial sites to istall the sesors; the trasmissio power, the cost ad the miimum umber of received sigals to detect a target are cosidered kow i our model. A. Assumptios We set the followig assumptios: Each achor ode is composed of two sesors ( a bar cotaiig two microphoes), istalled i such a maer that the bars of the differet adjacet achors are ot aliged (Fig.1). Optimizig the localizatio cosiderig that the target to be located must be withi the audio rage of at least two achors odes. There are two cases: either usig two achors, either usig three achors. Whe usig two achors, it is better to have a right agle betwee the two bars of microphoes. Whe usig three achors, it is better that the mobile ode is i the rage of three achors. Thus, each achor must be orieted at 60 degrees with respect to each other. B. Notatio The followig otatio is used i this paper. It is composed of se, decisio variables ad parameters. Se T: set of targe to detect i the field, tk is a target. N: the set of differet types of sesor odes, N = Na Nb. Na, the set of differet types of statioary odes Nb the set of differet types of mobile odes S: set of potetial sites to istall the sesor odes S = Sa Sb Sa the set of potetial sites to istall the statioary sesor odes, a is a site of a statioary ode. Sb the set of potetial sites to istall the mobile sesor odes, m is a site of a mobile ode. (a site may ot be i both se, that is, Sa Sb ) Decisio Variables Ws be a 0-1 variable such that W s = 1 if ad oly if a ode of type N is istalled at site s S X, a 0-1 variable such that X = 1 if the ode of type N istalled at site s S receives a sigal from a target at the positio t T with a power greater tha or equal to the miimum required power by the ode to detect it. Sg ss ' is also a 0-1 variable such that Sg ss ' = 1 if ad oly if the ode istalled at site s S receives a sigal from aother ode istalled at site s' S with a power greater tha or equal to the miimum required. ' ' Sg, be a 0-1 variable such that Sg = 1 if ad oly if the ode of type N istalled at site s S receives a sigal from aother ode of type ' N istalled at site s' S with a power greater tha or equal to the miimum required power. Ms is the miimum umber of hops betwee a statioary ode istalled at site s S to ay mobile ode. Parameters be the sigal atteuatio ratio from the target t T to site s S, ss ' the atteuatio ratio betwee the sites s S ad s' S, P t is the trasmissio power of a target at the positio t T (i wat). p is the trasmissio power of a ode of type N (i wat). P mi is the miimum power of a received sigal by a ode of type N to detect it (i.e. the sesibility). mi the miimum umber of odes receivig a sigal from a target to localize it (i our case, mi {2,3}), hp max, the maximum umber of hops betwee a achor ode ad a mobile ode, c s the cost of a ode of type N ad istallig it at site s S. 1 2 m m Ag ij agle betwee two microphoes m1 ad m2 of two differet ad adjacet odes i ad j.
: legth of the RoI (Regio of iterest). m: width of the RoI r: radius of a sesor (all the sesor odes have the same sesig rage). bna: umber of statioary odes bnm: umber of mobile odes eeded to add. bt: umber of targe Sg ij : power of the sigal trasmitted betwee two odes i ad j. d ij : distace betwee two odes i ad j, d m1m2 : a costat represetig the distace betwee two sesors (microphoes) of the same ode. d max : a costat represetig the maximum distace betwee two odes i ad j (or a ode i ad a target j) so that they ca be detectable. C. Objective fuctio To model the problem of target coverage cosiderig the localizatio, we cosider the followig objective fuctio. Coverage: Let F1 be the fitess of a mobile ode i (mi) which calculates the coverage as a fuctio of the targe it covered, we obtai the followig fuctio F1 for the coverage F1= Maximize ( F( ) m ) mnm Localizatio: each target must be moitored by at least mi odes (mobile or achor), thus: x mit T, we obtai the followig ss fuctio F2 for the localizatio: ( x ) ) F2= Maximize ( mi tt ss kowig that (x) + = max(0,x) Thus, the fitess fuctio is give by: F = F1 + F2 =Maximize ( x ) F( ) mi (3) m tt ss N D. Costrai F is subject to: x mit T ss Sg Ag k t s (5) m1m 2 1 / mi, m1m2 (6) Sg 1 Ag 0. k, t s N bna m r (7).( / 2 2 ) mi d. Sg. g( Sg ), R (8) ( Sg 1) ( d d ) (9) max x Ws (10) ss N P Sg P Sg (11) ' ' ' mi N ' N ' N N Sg Sg (12) N ' N ' Pt Pmi Ws, t T, ss (13) N The objective fuctio (3) of the problem aims to optimize the target coverage ad the localizatio. Costrait (4) impose that the umber of odes receivig a sigal from the target i must be greater tha or equal to the miimum ecessary to localize it. Costrait (5) force the agles of arrival betwee sesors (microphoes) to be 90 i the case of 2-coverage ( mi =2) ad to be 60 i the case of 3-coverage ( mi =3). Costrait (6) cocers the o-liearity of the adjacet odes i order to optimize the localizatio. Costrait (7) imposes the umber of the achors deployed iitially. Costrait (8) lik the distace ad the power trasmissio of the sigal betwee two odes. g is a fuctio, is real coefficiet. Costrait (9), imply that if there is a sigal Sg betwee two odes, the distace betwee these two odes (d ij ) should ot exceed a fixed maximum distace (d max ). Costrait (10), impose that a target caot be detected by a umber of odes that exceeds the umber of istalled odes i the differet sites. Costrait (11) impose that if the ode s is detected by the ode s, the the power trasmissio resultig from s towards s must be higher tha the miimum ecessary power trasmissio so that s is detectable by s. Costrait (12) cocers the power trasmissio emitted by the ode s ad received by the ode s, for differet types of odes. Costrait (13) idicate that the ode istalled at site s must receive a sigal from a target at positio t with a power greater tha or equal to the miimum required to detect it. IV. TARGET LOCALIZATION Let's cosider a mobile source emittig a soud s(t) ad a ode equipped with two microphoes. Each oe of the two microphoes is receivig a sigal (s_1 (t) for the first ad s_2 (t) for the secod). Due the distace betwee the two microphoes, a differece of time betwee the observatios of the soud sigal will be oted at each microphoe, referred to as Time differece of Arrival. TDoA (Fig.1) is computed usig the spatial positios of the target ad microphoes.
Fig. 1. Time Differece of Arrival (TDoA) Acoustic localizatio is doe followig two major steps; The first step cosis o estimatig the time differece of arrival (TDoA) of the sigals captured by two separated microphoes of oe ode. The, the directio of arrival of the soud with respect to this ode is computed usig trigoometry specificatios. The secod step cosis o localizig the acoustic source usig at least two odes. The process cosis o mergig the resul obtaied with each ode i term of directio of arrival ad the use a specific geometric positioig method i order to compute the geometric coordiates of the acoustic source i a 2D space. V. A GENETIC ALGORITHM FOR THE DEPLOYMENT CONSIDERING THE TARGET LOCALIZATION I this sectio, we preset the suggested approach. We preset the assumptios of the etwork, the coverage model, ad we discuss the approach based o the geetic algorithm. A. Network Assumptios We assume that the sesor odes are radomly deployed ad the umber of sesor odes iitially deployed is equal to the required umber to achieve mi-coverage (mi {2,3}) as if these odes were determiistically deployed. We also assumed that mobile odes are used to repair the coverage holes after the iitial deploymet of the statioary odes. B. Coverage Model We assume that each sesor ode has a sesig radius r which covers a circular area. We also assume that a target tk ca be detected by the sesor Si if tk is withi the sesig rage of Si. We also assumed that d is the distace betwee the target object beig sesed tk ad the sesor ode Si. The coverage fuctio Coverage(S) is equal to 1 if the target object ca be sesed ad covered; otherwise it is equal to 0. This biary model of sesor detectio ca represeted as follows: Coverage (S) = 1, d (S i, t k ) r 0, d (S i, t k ) r C. The Proposed Geetic Algorithm (NSGAII) We aim at maximizig the coverage rate by reducig the holes, ad maximizig the localizatio.. Assumig that Si is the statioary sesor odes deployed radomly over the regio of iterest, r is the sesig rage of the sesors. The proposed geetic algorithm star with a iitial radom populatio (the distributio of the iitial odes). The, the objective fuctio evaluates i each iteratio the costrai satisfactio rate. The ew solutio (populatio) is improved after each iteratio of the algorithm. This improvemet is carried out through the operators (crossover ad mutatio). A stoppig criterio is used to stop the executio of the algorithm. The geetic algorithm is ru by the base statio after gatherig the positios of the statioary odes i order to determie the umber ad positios of the mobile odes as follow: Represetig a chromosome I the proposed geetic algorithm a chromosome represe a solutio that idicates the positio (locatio) of a potetial mobile ode i the regio of iterest (RoI). This positio is modeled as a (X, Y) poit. The differet ges of the chromosome represet a biary digit that resembles the value of the positio o the X ad Y axises. For example, to represet a mobile ode mapped to the locatio (50, 65), the correspodig chromosome is show i Fig.2. The Choice of the size of the chromosome populatio is based o two factors: the area of the RoI ad the iitial cofiguratio of the etwork. For istace, if the radius of each ode is 48m ad the area of the sesig field is 70 m * 80 m, the umber of deployed statioary odes will be (i.e.; (70*80)/(.482) 117), the the algorithm will start with populatio of 117 radomly geerated chromosomes to esure the full coverage. The value 117 is selected based o the assumptio that 117 sesor odes would cover the etire field as if they were determiistically deployed. If we aim to esure a k-coverage (each target must be covered by at least k sesor odes), we have to start with 117 * k chromosomes as a iitial populatio. Fig. 2. Chromosome represetig the sesor positio (50, 65) Evaluatio After the iitializatio, each chromosome fitess (i.e.; the goodess of the solutio) is evaluated usig the fitess fuctio. The fitess or the formulatio of the objective depeds o characteristics of the problem. The fitess fuctio is used to choose the best fittest chromosomes to reproduce the ext geerated solutios by the algorithm. The fitess fuctio calculates the maximum umber of the covered targe by each mobile ode. The overlappig redudacy is preveted by the fitess fuctio amog the coverage regios of the deployed mobile odes. The fitess fuctio is give by: F = Maximize ( Reproductio ( x mi ) + F( m ) tt ss N ) (14) Reproductio is composed of four steps: selectio, crossover, mutatio, ad acceptig the solutio. The fitess is used as a measure to rak the chromosomes ad to perform paret selectio accordig to the ratio participated by each chromosome i the fitess fuctio i order to reproduce ew solutios. However, less fitess members will have also a chace to be selected. Differet mechaisms are used to implemet the selectio step such as the rollet wheel method. The selectio will be performed o two chromosomes to reproduce two ew chromosomes each time. After selectig the chromosomes, a crossover operatio is performed betwee a
pair of paret chromosomes by selectig a radom poit i chromosomes ad exchagig gees after this poit. We choose two radom crossig poi. The child iheri eleme positioed betwee the two crossover poi of the first paret. These eleme occupy the same positios, ad appear i the same order i the child. The selectio ad crossover operatios may lead to a set of idetical chromosomes ad the algorithm stops creatig ew idividuals. This may prevet the average fitess improvemet ad thus trappig ito a local optimum. To avoid this problem, a mutatio operatio is applied where a gee is selected radomly ad i value is chaged. Mutatio performs a larger exploratio of the search space, to avoid the premature covergece or the disappearace of the diversity while brigig iovatio to the populatio. The mutatio is carried out by reversig the positio of two gees. Ofte, each gee is represeted by a bit; the mutatio is doe by flippig a bit radomly i the chromosome. After crossover ad mutatio, two ew chromosomes are reproduced. Fially, if they are better tha their pare, they will be accepted as a ew populatio. Stoppig Criterio The stoppig criterio is either reachig a maximum umber of iteratios; either reachig a predefied localizatio rate (if a rate of k-coverage is esured, k= mi ). Also, we ca use a maximum executio time of the algorithm as a stoppig criterio. VI. EXPERIMENTAL RESULTS I this sectio, we evaluate the performace of the proposed geetic algorithm i terms of the amout of coverage (coverage rate), the degree of coverage (k-coverage), the umber of iteratios, ad the pareto frot. We use the followig parameters for the geetic algorithm: Area of Simulatio ( x m) = 200x300. Maximum umber of geeratio = 350. Size of populatio (umber of mobile odes) = m/ 2r2. Number of iitial statioary odes= m/ 2r2. Probability of mutatio = 0.1. Probability of crossover = 0.8. Number of costrai = 10. The followig figures (Fig.3, Fig.4 ad Fig.5) show the differece, i terms of coverage rate betwee the iitial radom coverage ad the coverage rate esured by our algorithm. Fig. 4. Deploymet after executig the GA for the 2-coverage case Fig. 5. Deploymet after executig the GA for the 3 coverage case The followig Fig.6 represe the coverage rate (axis y) whe icreasig the umber of iteratios (axis x). This figure shows that the coverage rate improves whe icreasig the umber of iteratios util reachig the demaded degree of coverage. 2,5 2 1,5 1 0,5 0 Number of iteratios vs Coverage rate 0 100 200 300 400 Fig. 6. Number of iteratios vs the coverage rate for the 2 coverage case Actually, our aim is to better locate a acoustic source (target) usig geetic algorithm. I fact, as discussed i [8], audio localizatio performace depeds o distace betwee odes ad the target. I order to perform audio experimetatios, we cosidered a array of two pairs of microphoes (as two odes), two computers, oe Smartphoe emittig a cotiuous soud. Every ode is hooked to a computer. We place the Smartphoe i a already kow positio. We the compute for ode the agle of arrival of the soud emitted by the Smartphoe (as the target). The obtaied values of the two agles are automatically stored i order to be used to determie the geographic positio of the soud source (Fig.7). Fig. 3. Iitial Radom Deploymet
Pareto Frot 1,1 0,9 0,7 17,8 18 18,2 18,4 18,6 18,8 19 Fig. 9. The Pareto Frot of the geetic algorithm Fig. 7. Scree shot of the developed applicatio for step 2 As we ca see i Table I ad Fig.8, the error betwee the estimated positios ad the real oes ca be explaied by the assumptios we had made. Real agles ( ) 12 34 theo theo TABLE I. Real positios (m) X Y theo theo EXPERIMENTAL RESULTS Estimated agles ( ) 12 34 esti esti Estimated positios (m) X Y esti esti 90 45 1 1.3 94.15 39.03 0.946 1.25 90 135 1 2.3 95.9 135.048 0.831 2.132 90 90 1 1.8 84.078 89.554 1.13 1.79 45 45 1.4 0.9 44.61 41.77 1.35 0.84 45 90 2.3 1.8 53.28 87.38 1.92 1.735 Fig. 8. Acoustic source estimated positios vs theoretical positios For a multi-objective problem, there is o sigle solutio. The goal of the multi-objective geetic algorithm is to fid a set of solutios i that rage (ideally with a good spread). The set of solutios is also kow as a Pareto frot. All solutios o the Pareto frot are optimal. I the case of bi-objective problems, iformig the decisio maker cocerig the Pareto frot is usually carried out by i visualizatio. The Fig.9 shows the pareto frot of the geetic algorithm. I Fig.9, the x axis represe the values of the first objective fuctio F1 while the axis y represe the values of the secod objective fuctio F2. VII. CONCLUSION I this paper we are iterested i deployig a wireless audio-sesor etwork to optimize coverage ad audio localizatio. We provided a geetic algorithm for a optimized placemet of audio-sesor odes. The aim is to purpose a optimal solutio for odes deploymet guarateeig the followig objectives: maximizig the coverage area, maximizig the precisio audio localizatio at the level of the detectio sigal. The proposed geetic algorithm show sigificat performace improvemet i quality compared to the radom deploymet ad the existig methods. As a prospect of our study, we aim to optimize the proposed algorithm i odrer to esure the redeploymet problem while optimizig differet objectives other tha the coverage ad the localizatio, such as the lifetime ad the etwork coectivity. Also, we aim to to test our cotributios by simulatio ad i reality o a set of testbeds of the OpeWiNo emulator, deployed to the IUT of blagac i Toulouse. REFERENCES [1] Mauli, P., Chadrasekara, R. ad Vekatesa, S., "Eergy Efficiet Sesor, Relay ad Base Statio Placeme for Coverage, Coectivity ad Routig," IEEE Iteratioal Performace, Computig ad Commuicatios Coferece, pp. 581-586, 2005. [2] Masri S., Nasri N., Val T. A Overview of the deploymet paradigms i the Wireless Sesor Networks.Iteratioal Coferece o Performace Evaluatio ad Modelig i Wired ad Wireless Networks (PEMWN 2014), Tuisia 04-07 th November 2014. [3] S. Meguerdichia, S. Slijepcevic, V. Karaya ad M. Potkojak, Coverage problems i wireless ad-hoc sesor etworks, Proc. IEEE Ifocom, vol. 3, pp. 1380-1387, 2001. [4] H. Qi, S. S. Iyegar, ad K. Chakrabarty, Multi-resolutio data itegratio usig mobile age i distributed sesor etworks, IEEE Trasactios o System, Ma ad Cyberetics (Part C), vol. 31, pp. 383-391, August 2001. [5] R. R. Brooks ad S. S. Iyegar, Multi-Sesor Fusio: Fudametals ad Applicatios with Software, Pretice Hall, Upper Saddle River, NJ, 1997. [6] A. Howard, M. J. Matari c ad G. S. Sukhatme, Mobile Sesor Network Deploymet Usig Potetial Field: a distributed scalable solutio to the area coverage problem, to appear i Proc. Iteratioal Coferece o Distributed Autoomous Robotic Systems, Jue 2002. [7] A. Kostatiidis, K. Yag, Q. Zhag, ad D. Zeialipour-Yazti, A multi-objective evolutioary algorithm for the deploymet ad power assigmet problem i wireless sesor etworks, Computer Networks 54(6): 960-976, 2010. [8] Thaljaoui A., Val T., Bruli D. ad Nasri N., "Real Time Acoustic Localizatio of Elderly Persos i a Smart Home," The Iteratioal Coferece o Performace Evaluatio ad Modelig i Wired ad Wireless Networks (PEMWN2014), 04-07 th November, Sousse, Tuisia 2014.