Ismal Abdullah,, 2017, 1:1 ScFed Journal of Telecommuncaton Research Artcle Open Access Sngle Ftness Functon to Optmze Energy usng Genetc Algorthms for Wreless Sensor Network *1 Ismal Abdullah, 2 Kald Abdlkader Marsal * Faculty of Scence and Technology, Unverst Sans Isam Malaysa Bandar Baru Nla,Neger, Semblan, Malaysa. Abstract A Sngle ftness functon s a partcular type of objectve functon that s used to summarze, as a sngle fgure of mert, how close a gven desgn soluton s to acheve the set ams. The Wreless Sensor Network (WSN) has emerged as a promsng tool for montorng the physcal world, utlzng self-organzng networks of battery-powered wreless sensors that can sense, process and communcate. A ftness functon s used n Genetc Algorthm n each teraton of the algorthm to evaluate the qualty of all the proposed solutons to your problem n the current populaton. The ftness functon evaluates how good a sngle soluton n a populaton s, e.g. f you are tryng to fnd for what x-value a functon has t's y-mnmum wth a Genetc algorthm, the ftness functon for a unt mght smply be the negatve y-value (the smaller s better for ftness functon).a reasonable soluton to a problem s to nvestgate a set of solutons, each of whch satsfes the objectves at an acceptable level wthout beng domnated by any other soluton. GA s a optmzaton tool, so generally ftness functon s a max/mn value functon consstng of all the varables. If we want to fnd the best optmal threshold value (.e. mn value of the ftness functon), we have to generate a functon wth these parameters such as Sngle-to Nose Rato (SNR), probablty of false alarm and number of samples of receved data for detecton n such a way that the value of the functon must be approachng zero. Ths functon s called ftness functon and the fnal value of ths functon after performng GA wll be the optmal outcome. The creaton of the functon s totally depends on our approach towards the soluton of the problem. In ths paper, an overvew s presented descrbng sngle ftness functon to optmze energy usng genetc algorthms n WSNs. GA are customzed to accommodate mult-objectve problems by usng specalzed ftness functons, ntroducng methods to promote soluton dversty, and other approaches. Keywords Wreless Sensor Network; Sngle Ftness Functon; Genetc Algorthm; Sngle-to Nose Rato Introducton 1- Sngle of Ftness Functon The use of genetc algorthms as the optmzaton tool of the developed system and an approprate ftness functon s developed to ncorporate many aspects of network performance. In addton, the desgn characterstcs optmzed by the genetc algorthm system nclude the status of sensor nodes (whether they are actve or nactve), network clusterng wth the choce of approprate clusterheads and fnally the choce between two sgnal ranges for the smple sensor nodes. The showed that optmal sensor network desgns constructed by the genetc algorthm system satsfy all applcaton-specfc requrements, fulfll the exstent connectvty constrants and ncorporate energy-conservaton characterstcs. Energy management s optmzed to guarantee maxmum lfe span of the *Correspondng author: Ismal Abdullah, Faculty of Scence and Technology, Unverst Sans Isam Malaysa. E-mal: sbah@usm.edu.my Receved September 11, 2017; Accepted October 12, 2017; Publshed October 25, 2017 Ctaton: Ismal Abdullah (2017) Sngle Ftness Functon to Optmze Energy usng Genetc Algorthms for Wreless Sensor Network. SF J Telecommun c1:1. Copyrght: 2017 Ismal Abdullah. Ths s an open-access artcle dstrbuted under the terms of the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal author and source are credted. page 1 of 8
network wthout lack of the network characterstcs that are requred by the specfc applcaton. Furthermore, sngle ftness functon weghtng the meanng a functons that can solve problem. In the case under examnatonof the ftness functon s a weghtng functon that measures the qualty and the performance of a specfc sensor network desgn. Ths functon s maxmzed by the Genetc Algorthm (GA) system n the process of evolutonary optmzaton. Bascally, a ftness functon must nclude and correctly represent all or at least the most mportant parameters that affect the performance of the (WSN) desgn. Havng descrbed these parameters the next ssue s the decson on the mportance of each parameter on the fnal qualty and performance measure of the network desgn. The fnal form of the weghtng lnear ftness functon f of a specfc WSN desgn s gven bythe followng equaton: f = 1( α1. MRD + α2. SDE + α3. SCE + α4. SORE + α5. OE + α6. CE + α7. BCP) The sgnfcance of each parameter s defned by settng approprate weghtng coeffcents α = 1, 2... 7 n the ftness functon that wll be maxmzed by the GA. The values of these coeffcents are determned based on experence about the mportance of each parameter. Frst, weghtng coeffcents that resulted, n average the same mportance of each parameter are determned frst column of ths table and after some rudmental expermentaton, the fnal values that best represented the ntuton about relevant mportance of each parameter are set as the second column of Table1. As can be seen n Table1, the fnal weghts are such that network connectvty parameters weghts ( α 3,α 4 )are treated as constrants, n the sense that all sensors should be n range wth a cluster head and no cluster head should be connected to more than the predefned maxmum number of sensors. There s no need for an ncrease of the SDE weght value. Table1: Weghtng Coeffcents of GA Ftness Functon Weghtng coeffcent Equal mportance values Fnal values α 1 10 2 10 2 α 2 10 4 10 4 α 3 2 10 6 α 4 10 3 10 5 α 5 10 10 α 6 5*10-3 10-2 (1) 2- Problem Statement The proposal an algorthm to dynamcally desgn WSN topologes by optmzng energy-related parameters that affect the battery consumpton of the sensors and thus, the lfe span of the network. It became a bg challenge of optmzaton of energy of sensor nodes. At the same tme, the proposal an algorthm tres to meet some embedded connectvty constrants and optmze some physcal parameters of the WSN mplemented by the nature of the specfc applcaton. The multple objectves of the optmzaton problem are blended nto a sngle objectve functon, the parameters of whch are combned to formulate a ftness functon that gves a qualty measure of WSN topology and t can s optmzed by the proposed algorthm. In that case, we try to fnger out t of best way of optmzaton sensor nodes of wreless. There dentfy three sets of parameters whch domnate the desgn and the performance of a WSN for precson agrculture. The frst set s the applcaton specfc parameters whch nclude two parameters regardng the deployment of sensors for the specfc case consdered here. These are the hghest possble unformty of sensng ponts and some desred spatal densty of measurng ponts. The second set s the connectvty parameters whch nclude an upper bound on the number of sensors that each cluster head sensor can communcate wth, and the fact that all sensors must have at least one cluster head wthn ther sgnal range. Fnally, the thrd set refers to the energy-related parameters whch nclude the operatonal energy consumpton dependng on the types of actve sensors, the communcaton energy consumpton dependng on the dstances between sensors that communcate wth ther correspondng cluster head, and fnally the battery energy consumpton. The optmzaton problem s defned by the mnmzaton of the energy-related Parameters (say, objectves ( J, J and J ) and the maxmzaton of 1 2 3 sensng Ponts unformty (objectves J 4 ) subject to the connectvty constrants (say, C constrants and 1 C ) 2 and the spatal densty requrement (constrant C ),(see 3 Table 1for the exact correspondences). Thus, the objectves are: mn J ; = 1, 2,3and max J 4 Subject to C ; = 1, 2, 3 In order to combne all objectves nto a sngle page 2 of 8
objectve functon (weghted Sum approach),the optmzaton parameters are formed n such a way that all of them are mnmzed. Thus, objectve J 4 s expressed ' by ts dual objectve, say J 4, whch has to be mnmzed. Further, the penalzaton of the constrants C1, C2 And C 3 allows ther transformaton nto objectves J5, J 6, and J respectvely, whch have to be mnmzed? Thus, 7 a sngle objectve functon that blends all (obvously conflctng) objectves s of the form 7 f mn ' wj+ w4 J = 1 4 Ths form of objectve functon s sutable for the formulaton of a numerc evaluaton functon [1] (namely a ftness functon n the termnology of GAs), whch gves a qualty measure to each possble soluton of the optmzaton problem. Table 2: Correspondences between Objectve and Optmzaton Parameters Objectve Optmzaton parameters Parameters symbols n GA methodology (2) Subject to the connectvty constrants j 1 Operatonal energy OE c 1 j 2 Communcaton CE c 2 energy j 3 Battery capacty BCP c 3 penalty j 4 Unformty of _ measurements j 5 mean relatve MRD devaton of measurements ponts j 6 Sensor-per-CH error SCE j 7 Sensors out of range SORE j 8 Spatal densty error SDE What follows descrbes the mathematcal representaton of the optmzaton Parameters n ther mnmzaton are the followng 1-The applcaton-specfc parameters: The man goal of a WSN used n precson agrculture s to take unform measurements over the entre area of nterest, so that an overall and unform pcture of the condtons of the area s realzed. Ths has been acheved usng the followng two parameters: Frst of all the measure of unformty of measurements. The metrc of the unformty of measurement ponts that was used here was the Mean Relatve Devaton (MRD). The entre area of nterest was dvded nto several overlappng sub-areas. Sub-areas are defned by four factors: two that defne ther sze (length and wdth) and two that defne ther overlappng rato (ratos n the two drectons). All these factors are expressed n terms of the unt length of each drecton. The larger the overlappng rato s, the hgher precson s acheved n the evaluaton of unformty, but also, the slower the algorthm becomes. In order to defne MRD, the noton of spatal densty ( ρ ) of measurements was used. More specfcally,, the spatal densty of measurements n sub-area was defned as the number of measurements over the area of the th sub-area, =1,2,.,N, where N s the number of overlappng sunarea nto whch the entre area, say S, was dvded. In addton,, the spatal densty of the entre area of nterest, was defned as the total number of measurements of the network over the total area of nterest. Thus,MRD was defned as the relatve measure of the devaton of the spatal densty of measurements n each sub-area from the total spatal densty of measurements n the entre area N 1 ρs ρs MRD = =. (3) N. ρ S Low values of MRD mean hgh unformty of measurement ponts. Acceptable values for our applcaton example are of MRD below 0.15. The second of applcaton-specfc parameter of the ftness functon was the Spatal Densty Error (SDE) that was used to penalze network desgns that dd not meet the mnmum requred spatal densty of measurement ponts that would suffce adequate montorng of the measured varables (e.g., ar or sol temperature, ar or page 3 of 8
sol relatve humdty, solar radaton, etc.) n the area of nterest. The desred spatal densty ρ d was set equal to 0.2 measurement ponts per square length unt and the SDE factor was evaluated by ρd ρs f ρs ρd ρ d SDE = 0 otherwse 2-Connectvty parameters: A crucal ssue n WSNs s the assurance that network connectvty exsts and all necessary constrants are satsfed. Here, these necessary characterstcs of the sensor network were taken nto account by the ncluson of the followng parameters n the ftness functon: (a) A Sensors-per-Cluster-head Error (SCE) parameter to ensure that each cluster-head dd not have more than a maxmum predefned number of sensors n regular operatng modes n ts cluster. Ths number s defned by the physcal communcaton capabltes of the sensors as well as ther data management capabltes n terms of quantty of data that can be processed by a cluster-head sensor. It was assumed to be equal to 15 for the applcaton consdered here. Ifnfull s the number of cluster-heads (or clusters) that have more than 15 actve sensors n ther clusters and n s the number of sensors n the th of those clusters, then: SCE nfull 1 n = nfull = 0 fnfull 0, otherwse b) A Sensors-Out-of-Range Error (SORE) parameter to ensure that each sensor can communcate wth ts cluster-head. Ths of course depends on the sgnal range capablty of the sensor. It s assumed that HSR-sensors cover a crcular area wth radus equal to 10 length unts, whle LSR-sensors cover a crcular area wth radus equal to 5 length unts. If nout s the number of actve sensors that cannot communcate wth ther cluster-head and ns (4) (5) the total number of actve sensors n the network,then: nout SORE =. n 3- Energy-related parameters: Energy consumpton n a wreless sensor network, as explaned earler, s a crucal factor that affects the performance, relablty and lfe span of the network. In the optmzaton process durng the evolutonary desgn of the sensor network, three dfferent energy-related parameters were taken nto account: (a)- Operatonal Energy (OE) consumpton parameter, whch refers to the energy that a sensor consumes durng some specfc tme of operaton. It bascally depends on the operaton mode of the sensor, that s, whether t operates as a CH, a HSR or a LSR sensor, or whether t s nactve. The correspondng relevance factors for the energy consumpton of the three actve operatng modes of the sensors are taken proportonal to 20:2:1, respectvely and zero for nactve. Therefore, meanng s that the energy consumpton of a sensor operatng n CH mode s 10 tmes more than that of a sensor operatng n HSR mode and 20 tmes more than that of a sensor operatng n LSR mode. These relevant factors were used to smplfy the analyss and dd not necessarly represent accurately the real energy relatons between the avalable operaton modes of the sensors. Ther exact values depend on electromechancal characterstcs of the sensors and were not further consderedn the analyss presented here. The OEconsumpton parameter was then gven by: nch nhs nls OE = 20. + 2. + (6) n n n Where, nch, nhs and nls are the number of CH, HSR and LSR sensors n the network, respectvely.(b)- Communcaton Energy (CE), whch refers to the energy consumpton due to communcaton between sensors n regular operatngmodes and cluster heads. It manly depends on the dstances between these sensors and ther correspondng cluster head, as defned n[2]. It s depcted by n c CE =. k µ d j (7) = 1 j = 1 Where c s the number of clusters n the network, n s the number of sensors n the th cluster, d j s page 4 of 8
the Eucldean dstance from sensor j to ts cluster-head (of cluster ) and µ and k are constants, characterstc of the topology and applcaton ste of the WSN. For the specfc precson agrculture applcaton for open feld montorng, the values of µ = 1 And k= 3 were chosen. (c)- Battery lfe. An mportant ssue n WSNs s self-preservaton of the network tself, that s, the maxmzaton of the lfe span of the sensors. Each sensor consumes energy from some battery source n order to perform ts vtal operatons, lke sensng, communcaton, data aggregaton f the sensor s a clusterhead. Battery capacty of each sensor of the network was taken nto account n the desgn optmzaton process by the ntroducton of a Battery Capacty Penalty (BCP) parameter. Snce the operaton mode of each sensor s known, ts Battery Capacty (BC) can be evaluated at each tme. Thus, when the desgn optmzaton algorthm s appled at a specfc tme t (measurng cycle), the BCP parameter s gven by: [ t] ngrd [ t] 1 BCP = PF., t 1,2,... 1 [ t] = = BC Note that BC s updated accordng to the operaton mode (CH, HSR or LSR) of each sensor, durng the prevous measurng cyclet-1 of the network: (9) [ t] [ t 1] [ t 1] BC BC = BRR In the above: 1-BCP [t] s the Battery Capacty Penalty of the WSN at measurng cycle t. It s used to penalze the use of sensors wth low-battery capactes, gvng at the same tme larger penalty values to operatng modes that consume more energy (especally CH mode). 2-ngrd s the total number of avalable sensor nodes. [ t] 3-PF s the Penalty Factor assgned to sensor. The values t takes are gven accordng to the operaton mode of sensor. The values used here are proportonal to the (8) relevant battery consumptons of the sensor modes, namely, 20:2:1 for actve sensor modes (CH, HSR and LSR, respectvely) and 0 for nactve. They provde dfferent penaltes accordng to the specfc modes of the sensors n the WSN of the followng measurng cycle. However, as t s explaned n the next secton, further exploraton of the optmal relevance values needs to be performed. 4-BC [ t] [ t 1] and BC are the Battery Capactes of sensor at measurng cycles t and t-1, respectvely, takng values between 0 and 1, wth 1 correspondng to full battery capacty and 0 to no capacty at all. [ ] t 1 5- BRR s the Battery Reducton Rate that depends on the operaton mode of sensor durng the measurng cycle t-1 and reduces ts current battery capacty accordngly, usng the percentage of the relevance factors for the energy consumpton of the operatng modes of the sensor as follows: 0.2 for CH, 0.02 for HSR 0.01 for LSR operaton modes and 0 for nactve sensors. 3-The methodology and formulaton of GAs for some specfc applcaton ncorporates three basc steps the problem representaton, the encodng mechansm of the problem s phenotypes nto genotypes that GAs manpulate and evolve, the formulaton of the sngle of ftness functon that gves to each ndvdual possble network desgn a measure of performance, and fnally the choce of the genetc operators and the selecton mechansm used. These steps are of major mportance, as they drastcally affect the performance of the fnal results and they are descrbed n detal n the followng Sectons 3.1 3.2, respectvely. Of the next part 3.4presents the algorthm that s dynamcally appled to acheve adaptve desgn of the WSN towards contnuous energy conservaton. 3.1 Wsn Representaton The varables that are ncluded n the WSN representaton are those that gve all the requred nformaton so that the performance of a specfc network desgn can be evaluated. These varables are the placement of the actve sensors of the network, the operaton mode of each actve sensor, that s, whether t s a cluster head or a regular sensor, and n the case of a regular sensor, the range of ts sgnal (hgh or low). Each ndvdual n a GA populaton specfes the composton and arrangement of sensors encoded as a vector of genes. Fgure 1 shows an example ndvdual whch represents a grd of sensors wth page 5 of 8
r rows and c columns. For a sensor placed at each of the r. c grd postons, there are four possbltes represented by a two-bt encodng scheme: beng an nactve sensor (00), beng an actve sensor operatng n a low-sgnal range (10), beng an actve sensor operatng n a hghsgnal range (01) and beng an actve cluster-head sensor (11). The grd junctons are encoded row by row n the bt strng, as shown n Fgure 1. Each poston needs two bts for the encodng, thus, the length of an ndvdual (GA strng) s 2rc. In the specfc desgn problem analyzed here, the szes of r andcare both equal to 30, thus the length of the ndvduals are equal to 1800. Fgure1: Bnary Representaton on the Locaton and State of Sensors n a Randomly Generated (WSN) on the Left. Representaton of the Frst Row s shown best ndvdual at each generaton of the algorthm always survved to the next generaton. 3.3. Dynamc Optmal Desgn Algorthm Havng completed the development of a representaton scheme and formng the ftness functon, the dynamc genetc algorthm for optmal adaptve desgn of the WSN could be developed. The algorthm conssted of two parts: the Optmal Desgn Algorthm (ODA), whch s appled to a set of sensors wth specfc battery capactesfgure 2, and the Dynamc Optmal Desgn Algorthm (DODA), whch updates the battery capactes of the sensors and reapples the optmal desgn algorthm accordngly Fgure 3. Both algorthms as well as all smulatons presented n the followng sectons were mplemented n (Matlab). Some of the ssues that have to be clarfed follows. 1. Optmal Wsn Desgn Algorthm: A-The sze of the populaton s a parameter of exploraton that s further dscussed n the next secton. B- In the assgnment of a ftness value to each ndvdual, specfc weghtng coeffcents are used n [10], Table 2. 3.2. Genetc Operators and Selecton Mechansm The types of crossover and mutaton are of major mportance to the performance of the GA optmzaton. Two types of the classcal crossover operator defned n [3] were tested, the one-pont and the two-pont crossover. The mutaton type that was used was the classcal one for bnary representaton, that s, the swappng of the bts of each strng (0 becomes 1 and vce versa) wth some specfc low probablty. Crossover s also appled wth somespecfc probablty. Both these probabltes are tuned after proper expermentaton, as explaned n. The adopted selecton mechansm was the roulette wheel selecton scheme. The probablty of selectng some ndvdual to become a parent for the producton of the next generaton was proportonal to ts ftness value. In addton, n order to assure that the best ndvdual of each generaton was not destroyed by the crossover and mutaton operators durng the evoluton process, eltsm was ncluded n the algorthm, meanng that the current C- The probablty of selecton of parent ndvduals s proportonal to ther ftness value. Set populaton sze M; Set max # of generatons G; The genetc operators of crossover and mutaton are appled wth specfc probabltes, as t s explaned n the next secton. 2. Dynamc Optmal Desgn Algorthm: a-the measurng cycle s defned as the perod of tme durng whch a clusterhead sensor consumes 20% of ts full battery capacty. b- The steps of battery capactes update and reapplcaton of the optmal WSN desgn algorthm are performed durng data collecton of the measurng cycle. Ths s because battery capactes at the end of the cycle can be evaluated based on the developed model, wthout havng to wat untl the actual end of the measurng cycle. Thus, at the end of each measurng cycle, the next optmal page 6 of 8
WSN desgn has already been formed and t s then used for the next data measurng cycle. c- The lfe span of the network, whch s referred to as WSN s alve n the pseudocode, defnes the applcaton tme of the dynamc algorthm. The network,.e. the set of sensors n the feld, s consdered to be alve f the set of sensors wth battery capactes above zero s such that some operatonal WSN can be desgned and appled to the next measurng cycle. The numbers of teratons performed by the algorthm n a sngle measurng cycle are n the order of G M 2, where G s the number of generatons of the GA, l s the bt-strng length and M s the populaton sze. If n s the total number of avalable sensors n the WSN desgn, then obvously the computatonal complexty of the algorthm s O(n), as only the l parameter depends on n ( = 2 n ). The provde energy promsng on sensor cost,ths s a measure of the energy requred cost n detectng a vector and generatng a packet.meanwhle, ths s the energy cost expended n sendng a packet by transmt cost. A very hgh value leads to a rapd depleton of a node s energy durng transmsson, whch nvarably leads to wearng out after sendng only a few packets. Settng ths value very low on the other hand mples that the nodes may be able to send several hundred of packets. However, t should be noted that transmt cost s scaled based on the dstance between the nodes. Therefore, energy s often rapdly depleted snce more dstant nodes can only be reached by a more powerful broadcast. In addton, ths s the energy cost n recevng a packet. Once, t takes the value of the transmt cost once the transmt cost s set n receve cost. There s no need to partcularly scale t. so that an ntegrated optmal WSN was desgned. From the development of network characterstcs durng the optmzaton process, whch can conclude that t s preferable to operate a relatvely the hgh number of sensors node and sensors wth consequently larger energy consumpton for communcaton purposes. In addton, (GA) generated desgns compared favourably to random desgns of sensors. Totally of sensng ponts of optmal desgns s satsfactory, whle connectvty constrants are met and operatonal and communcaton energy consumpton s mnmzed. That also showed that the dynamc applcaton of the algorthm n (WSN) desgn can lead to the extenson of the network s lfe SPAN, whle keepng the applcaton-specfc propertes of the network close to optmal values. For future research, wll deal wth the development of theoptmal ofroutng n sensor nodes by dynamcally selected cluster-head sensors, through some mult-hop communcaton protocol wll be death wth. Fgure 2: Pseudo Code of the Optmal WSN Desgn Algorthm (ODA) Conclusons The algorthm for the optmal desgn and dynamc of networkn applcaton (WSNs), based on the evolutonary optmzaton propertes of genetc algorthms as presented. A fxed sensor n wreless network of dfferent operatng modes s consdered on a grd deployment wth the (GA) system decded whch sensors should be actve, whch ones should operate as cluster heads and whether each of the remanng actve normal nodes should have hgh or low-sgnal range of savng. The durng optmzaton, parameters of network connectvty, energy conservaton as well as applcaton requrements are taken nto account page 7 of 8
Fgure.3: Pseudo code of the dynamc optmal WSN desgn algorthm (DODA) Apply ODA 7. Holland JH (1975) Adaptaton n natural and artfcal systems. Unversty of Mchgan Press, Ann Arborn. 8. Sen S, Narasmhan S, Deb K (1998) Sensor network desgn of lnear processes usng genetc algorthms. Comput Chem Eng 22: 385 390. 9. Jourdan DB, De Weck OL (2004) Layout optmzaton for a wreless sensor network usng a mult-objectve genetc algorthm. n: IEEE Semannual Vehcular Technology Conference, Mlan, Italy. 10. Sohrab DB, Gao J, Alawadh V, et al.(2000) Protocols for self-organzaton of a wreless sensor network. IEEE Personal Commun Mag 7: 16 27. 11. Youns S, Fahmy S (2000) Dstrbuted clusterng n adhoc sensor networks: a hybrd, energy-effcent approach. n: INFOCOM, Hong Kong. Ctaton: Ismal Abdullah (2017) Sngle Ftness Functon to Optmze Energy usng Genetc Algorthms for Wreless Sensor Network. SF J References 1. Mchalewcz Z, Fogel DB (2002) How to Solve It: Modern Heurstcs. Sprnger-Verlag, Berln, Germany. 2. Ghas S, Srvastava A, Yang X, et al. (2002) Optmal energy aware clusterng n sensor networks.sensors 2: 258 269. 3. Goldberg DE (1989) Genetc Algorthms n Search, Optmzaton and Machne Learnng. Addson-Wesley, Readng, MA. 4. Konstantnos P. Ferentnos, Theodore A Tslgrds (2007), Parts of ths paper have been presented at the 2nd IEEE Conference on Sensor and Ad Hoc Communcatons and Networks (SECON 2005)Santa Clara, CA, USA, 26 29 September 2005/ Computer Networks 51: 1031 1051. 5. Akyldz IF, Su W, Sankarasubramanam Y, et al. (2002) Wreless sensor networks: a survey. Computer Networks 38: 393 422. 6. Ferentnos KP, Tslgrds TA (2006) Heurstc dynamc clusterng n wreless sensor networks towards unform sensng. n: 15th IST Moble and Wreless Communcatons Summt, Myconos, Greece. page 8 of 8