PSO and ACO Algorithms Applied to Location Optimization of the WLAN Base Station

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1 PSO and ACO Algorthms Appled to Locaton Optmzaton of the WLAN Base Staton Ivan Vlovć 1, Nša Burum 1, Zvonmr Špuš 2 and Robert Nađ 2 1 Unversty of Dubrovn, Croata 2 Unversty of Zagreb, Croata E-mal: van.vlovc@undu.hr, nsa.burum@undu.hr zvonmr.spus@fer.hr, robert.nad@fer.hr Abstract - The man goal of ths wor s to show the use of evolutonary computaton technques The Partcle Swarm Optmzaton (PSO) and Ant Colony Optmzaton (ACO) n ndoor propagaton problem. These algorthms employ dfferent strateges and computatonal efforts, but also they have somethng n common. Therefore, t s approprate to compare ther performance wth the Genetc algorthm (GA). We have demonstrated ther ablty to optmze base staton locaton usng data from neural networ model of Wreless Local Area Networ (WLAN). The results show that PSO has better propertes compared to ACO algorthm. The ACO algorthm needs further wor to optmze the algorthm parameters, mprove analyss of pheromone data and reduce computaton tme. However, the ant colony based approach s utlzable for solvng such problems. 1. INTRODUCTION The feld strength predcton n ndoor envronments s a dffcult and complex tas. The methods for feld strength analyss can be emprcal, sem-determnstc and determnstc. The raytracng method provdes rather accurate propagaton model, but t s very dffcult to calculate accurate sgnal strength n every pont of nterest n ndoor envronments usng ths method. The results are hghly dependable on the accuracy of the data base and requre long computng tme. In all these models s mpossble to nclude tme varant effects, such as movement of people. The poston of reflecton and dffracton ponts depends of complete stuaton n the ndoor space and they are nfluenced by the tme varant effects [1]. An alternatve approach to feld strength predcton s based on the neural networ model [2]. We try to predct sgnal strength n ndoor wreless communcaton n gven envronment wthout any detal nowledge about buldng geometry and constructon characterstcs. The selected envronment (the ground floor of Dubrovn Unversty buldng) s rather dffcult for ray-tracng calculaton because of ts rregular shape and a lot of dfferent obects nsde (dfferent nformaton tables, boat wth sal, pots wth palms ). The relevant networ archtecture s traned usng the measured feld strength from two base statons at randomly dstrbuted locatons (Fg. 1). Such traned neural networ s used for predctng the feld strength dstrbuton as well as for predcton of the optmum base staton poston. The unconstraned optmzaton technques are selected accordng to the penalty functon approach. The Partcle Swarm Optmzaton (PSO) algorthm [3] and Ant Colony Optmzaton (ACO) [4] algorthms are compared wth results of the genetc algorthm (GA) [5]. PSO has been presented as effectve method n optmzng complex multdmensonal problems. In partcular, successful applcaton of ths method to antenna desgn has been shown [6]. Recently, the ACO has been proposed for antenna array desgn [7]. In the consdered case, we were faced wth multple local optma. The problem s overcome by fne tunng the parameters of the each optmzaton algorthm. 2. DESCRIPTION OF THE MODEL The ground floor of Dubrovn Unversty buldng s chosen for smulaton envronment. The part of the floor under consderaton s bordered by ponts ABCDEFGHI, Fg. 1, whch area s 323 m 2 and heght s 3 m. The orgn of the coordnate system s located n the left lower corner as t s shown n the Fg. 1. The locatons of base statons, used for tranng neural networ, are denoted by BS1 and BS2, and the heght of the base statons was fxed on 2.75 m above the floor. The base statons are Csco Aronet 1100 that supports g standard wth data rates up to 54 Mbps. The walls are made of the brcs wth large wndows n alumnum frames. The doors of sde rooms are made of wood, whle the celng s covered by metal plasters and the floor s made of the stone blocs. Measurements of the receved sgnal strength for the varous locatons of the recever for selected base staton postons (Fg.1) have been made n the frst step. The each WLAN access pont was operatng at the 4 th channel at GHz (100mW). The sgnal strength measurements were made by a laptop computer wth PCMCIA wreless card postoned 1.2 m above the floor.

2 Up Up Up y I H G MAIN ENTRANCE BS2 F GROUND FLOOR HALL E BS1 C D A Recepton des Student admnstraton Student admnstraton B x Fg. 1. Plan of the unversty buldng, ground floor wth tranng BS The measurements were performed for 233 recevng locatons that were 1 m apart from each other. Three measurements were made for each locaton and mean value was used as the feld strength at the consdered locatons. These values were used n the tranng and testng of the neural networ. The traned neural networ model that s used n the optmzaton procedure s the same as n [8]. The nputs to the model are coordnates of the recevng locaton, whle the output s the feld strength at that pont. 3. BASE STATION OPTIMIZATION In order to fnd the optmal locaton of a sngle transmtter for a gven dstrbuton of recevng ponts, we need to develop a numercal representaton for the qualty of sgnal coverage over the gven space as a functon of the transmtter locaton. To obtan such functon we need to dvde gven space nto grd of possble recever and transmtter locatons. The densty of the grd s determned by the desred accuracy. The traned neural networ s used to determne the sgnal level at arbtrary pont wherever the base staton s located. Accordng to such approach cost functon s presented as sum of all weghted relatve sgnal level predctons (n dbm) along wth a penalty value that represents a volaton of a maxmum tolerated path loss threshold at recever locaton, whch n our case was the recever threshold (- 72dBm for 54 Mbps). The cost functon, then, can be expressed as N M = ) w( S )), (1) f S = 1 = 1 where N and M are the number of possble locatons of base statons and recevng ponts respectvely. S s relatve sgnal level (n dbm) receved from base staton at locaton wth coordnates (x,), whle w s relevant prorty weght ascrbed to the th recever locaton, and t maes constrant n the cost functon. Ths constrant requres that the qualty of sgnal coverage at each recever locaton over a gven space must be above a gven threshold value (-72 dbm). In our case the value of weght w s obtaned as S ) > 60dBm w = 60 S ) 72dBm S ) < 72dBm w = 1 w = 10 w = 100 (2) The cost functon as a functon of two varables (x, y), that represent locaton of base staton, s calculated accordng the equatons (1) and (2) where the needed sgnal levels are obtaned from neural networ traned model. The coverage s not a dfferentable functon of the base staton locatons, so small changes n the base staton locaton can cause great changes n receved sgnal strength, whch s caused by completely dfferent pattern of reflected, transmtted and dffracted rays. We may expect a lot of such rapd changes n real ndoor envronment. The mentoned arguments mae such cost functon extremely lmted n accuracy when t s evaluated at lmted number of grd ponts. As n our method the cost functon s calculated from neural networ propagaton model, there are no lmts n the number of grd ponts.

3 3.1 Partcle Swarm Optmzaton Algorthm The PSO, although orgnally nvented for research on smulatng the movement of the swarm n 2-dmensonal space, can be appled as an optmzaton method n n-dmensonal space [6]. The partcles are defned wth ts own poston x, velocty v, and personal best result so far (pbest). The ey element of the entre optmzaton s the changng of partcle's velocty [3]. For the +1 partcle movement, the -th coordnate component of velocty -th partcle, we can wrte for the partcle velocty v + 1 ( pbest x ) = c0v + c1rand1 c rand ( gbest x ) (3) where = 1,2,.m, where m s the sze of the swarm; = 1,2,.n, where n s dmenson of the space; c 0, c 1, and c 2 are postve constants that scale the old velocty and ncrease new velocty toward pbest (local best result) or gbest (global best result), respectvely. rand 1 and rand 2 represent random numbers that are unformly dstrbuted n the nterval [0,1]. The parameter c 0 s called "nertal weght" and t determnes f the partcle wll stay on ts current traectory or f t wll be strongly pulled toward pbest or gbest. Its value s between 0 and 1. The new partcle locaton s gven by = x + tv x. (4) The new velocty s appled after some tme-step t, whch s usually one. In other words, partcles exchange nformaton about results they obtaned, so they now the best of all results so far. Accordng to ths nformaton they accelerate n the drecton of the global best result (gbest) and at the same tme toward ts own best result (pbest), so ther traectory s alterng between these two goals dependng whch drecton prevals. A proper selecton of parameter values s very mportant to obtan qualtatve result. Varous authors have proposed dfferent nertal weghts and other constants. After runnng PSO algorthm wth dfferent parameters we got the best result when nertal weght c 0 was changed lnearly from 0.9 to 0.2 durng the run of algorthm. In ths way, partcles n the begnnng are less pulled toward pbest and gbest, but after a number of teratons they are more rapdly pulled toward these values. Hgher value of c 0 means faster move toward gbest, faster convergence, but less accuracy. For the constants c 1 and c 2, value of 2 s used, snce n our case where very lttle change n coordnates may result n great change n cost functon value, the tme step needs to be chosen carefully. Consderng dfferent values for c 0, c 1, c 2, we have selected 0.4 for the tme step value. We have carefully selected populaton sze among large populatons wth a lot cost functon evaluatons and longer computaton tme, and smaller populatons that gve the result much faster. It was determned by many parametrc studes [6] that relatvely small populatons can suffcently explore the space under consderaton, so populaton of 30 partcles s used n our algorthm. Among the suggested boundary condtons, ntroduced by varous authors, we have selected socalled "reflectng walls" to avod movng the partcle out from the gven space [6]. 3.2 Ant Colony Optmzaton Algorthm The ACO algorthm s orgnated from ant behavor n the food searchng. When an ant travels through paths, from nest to food locaton, t drops pheromone. Accordng to the pheromone concentraton the other ants choose approprate path. The paths wth the greatest pheromone concentraton are the shortest ways to the food. The optmzaton algorthm can be developed from such ant behavor. The frst ACO algorthm was the Ant System [4], and after then, other mplementatons of the algorthm have been developed [7]. Our approach requres some modfcatons of the algorthm proposed for Travelng Salesman problem soluton [9]. In our case the pheromone matrx s generated wth matrx elements that represent a locaton for ant movement, and n the same tme t s possble recever locaton. The ant populaton s randomly generated (30 ants) and each ant s assocated to one matrx locaton (node). Each ant can move to any of ts eght adacent locatons (matrx elements). The next nod (locaton) s selected accordng to the probablty wth whch ant wll choose to go from current locaton to next locaton p = α [ ][ η ] α [ l ] [ ηl ] l N β β, (5) where t s the pheromone content of the path from locaton to locaton, N s the neghborhood locatons for ant when t s at locaton. The neghborhood ncludes only locatons that have not been vsted by ant. η s the desrablty of locaton, and t depends of optmzaton goal so t can be our cost functon. The nfluence of the pheromone concentraton to the probablty value s presented by the constant α, whle constant β do the same for the desrablty. These constants are determned emprcally and our values are α=1,

4 β=10. The ants depost pheromone on the locatons they vsted accordng to the relaton new current = +, (6) where t s the amount of pheromone that ant exudes to the locaton when t s gong from locaton to locaton. Ths addtonal amount of pheromone s defned by 1 =, (7) f where f s the cost functon of the locaton (because the goal of the algorthm s to fnd the mnmum of the cost functon). The pheromone evaporates durng tme and dmnshes f there are no new addtons. The pheromone evaporaton s appled to all locatons as follows new = ( 1 ρ), 0 < ρ 1. (8) The value of ρ s selected emprcally, what s n our case ρ = EXPERIMENTAL RESULTS The developed algorthms (PSO, ACO) are used to optmze base staton locaton for the case from chapter 2, and these results are compared wth results obtaned by genetc algorthm. The sutable computer programs are developed and run for deferent optmzaton parameters. The convergence of PSO algorthm s llustrated n Fg. 2. The best cost functon values are plotted for every teraton. The PSO algorthm converges very fast, n less then 80 teratons. The convergence n the case of ACO algorthm wasn't so fast; t needs more then 300 teratons. In other words ACO algorthm needs more computer tme to converge for ths type of optmzaton problem. The Fg. 3 shows ths result for ACO algorthm. The genetc algorthm s used as reference and Fg. 4 shows cost functon convergence versus the number of generatons. The algorthm s run wth populaton of 30 ndvduals, crossover rate of 0.8 and mutaton rate of Very fast convergence wth short computaton tme s characterstc of ths algorthm. The complete results are summarzed n the Table 1. The colon Result shows optmzed locatons of base staton (coordnates), whle colon f ncludes the values of cost functon at optmum locatons. CPU tme s gven n seconds. All three methods gve smlar results. It can be emphaszed that PSO shows better performance than two others, whch s manfestng n shorter CPU tme, and the lowest value of cost functon. Note that all three methods satsfy the coverage requrements (.e. that feld strength s larger than -72dBm). Obectve functon (gbestf) Iteratons Fg. 2 PSO convergence of the cost functon versus the number of teratons Max desrablty 1.05 x Iteratons Fg. 3. ACO convergence of cost functon value versus the number of teratons 5. CONCLUSION In ths paper the optmzaton of the base staton locaton s studed based on the neural networ, as propagaton model, and two optmzaton algorthms PSO and ACO were used for determnng the base staton locaton. The PSO have already been used n the optmzaton of varous electromagnetc problems whle ACO algorthm hasn't been used n the propagaton problem yet. The best performance we got wth the PSO algorthm, where results show the lowest cost functon and consumng tme. The comparson wth genetc algorthm shows equalty. The ACO algorthm doesn't converges so fast and ts result s lttle worse then of other two algorthms. It must be

5 emphaszed that the accuracy of fnal results depends on accuracy of the feld strength estmaton obtaned by descrbed neural model Cost functon Generatons Fg. 4. Convergence of genetc algorthm versus the number of generatons Table 1. Optmzaton results obtaned by three methods PSO ACO GA Result f CPU tme Result f CPU tme Result f CPU tme (5.52, 8.2) (5.2, 8.8) (5.62, 8.32) REFERENCES [1] T.S. Rappaport, Wreless Communcatons - Prncples and Practce, Prentce Hall, USA, 2002 [2] G. Wolfle, F. M. Landstorfer, "Feld Strength Predcton wth Neural Networs for Indoor Moble Communcaton, 47 th IEEE Internatonal Conference on Vehcular Technology, pp May [3] R.C.Eberhart, Y. Sh, "Partcle swarm optmzaton: developments, applcatons, and resources", Proc Congr. Evolutonary Computaton, vol. 1, [4] M. Dorgo, V. Manezzo, and A. Colorn, "Ant system: Optmzaton by a colony of cooperatng agents", IEEE Trans. on System, MAN, and Cybernetcs-Part B, vol. 26, pp , February [5] Goldberg, D. E. Genetc Algorthms n Search, Optmzaton, and Machne Learnng, Readng MA, Addson-Wesley, [6] J. Robnson, and Y. Rahmat-Sam, "Partcle Swarm Optmzaton n Electromagnetcs", IEEE Trans. on Antennas and Propagaton, vol. 52, No. 2, February [7] E. Rao-Iglesas, O. Quevedo-Teruel, "Lnear Array Synthess usng an Ant Colony Optmzaton based Algorthm", IEEE Trans. on Antennas and Propagaton, vol. xx [8] I. Vlovc, N. Burum and Z. Spus, "Indoor Feld Strength Predcton Based on Neural Networ Model and Partcle Swarm Optmzaton", Proc. of 23 rd Internatonal Revew of Progress n Appled Computatonal Electromagnetcs, Verona, [9] Camela-Mhaela Pntea, D. Dumtrescu, "Improvng ant systems usng a local updatng rule", Proc. of the 7 th Internatonal Symposum on Symbolc and Numerc Algorthms for Scentfc Computng, 2005.