Research Article A Double Herd Krill Based Algorithm for Location Area Optimization in Mobile Wireless Cellular Network

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1 e Scentfc World Journal Volume, Artcle ID 78, 9 pages Research Artcle A Double Herd Krll Based Algorthm for Locaton Area Optmzaton n Moble Wreless Cellular Network F. Vncylloyd and B. Anand RVS Techncal Campus, Combatore, Inda Hndusthan College of Engneerng and Technology, Combatore, Inda Correspondence should be addressed to F. Vncylloyd; vncylloyd@gmal.com Receved August ; Revsed 7 October ; Accepted 8 October AcademcEdtor:S.N.Deepa Copyrght F. Vncylloyd and B. Anand. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. In wreless communcaton systems, moblty trackng deals wth determnng a moble subscrber (MS) coverng the area servced by the wreless network. Trackng a moble subscrber s governed by the two fundamental components called locaton updatng (LU) and pagng. Ths paper presents a novel hybrd method usng a krll herd algorthm desgned to optmze the locaton area (LA) wthn avalable spectrum such that total network cost, comprsng locaton update (LU) cost and cost for pagng, s mnmzed wthout compromse. Based on varous moblty patterns of users and network archtecture, the desgn of the LR area s formulated as a combnatoral optmzaton problem. Numercal results ndcate that the proposed model provdes a more accurate update boundary n real envronment than that derved from a hexagonal cell confguraton wth a random walk movement pattern. The proposed model allows the network to mantan a better balance between the processng ncurred due to locaton update and the radobandwdthutlzedforpagngbetweencallarrvals.. Introducton Locaton areas represent a sgnfcant strategy of locaton management, used to reduce sgnallng traffc mposed by locatonupdatngandpagngmessagesnmoblecellular networks. Due to the ncreasng dmenson spaces to be searched, the locaton of optmal LAs represents a NP-hard optmzaton problem. In contrast to a landlne telephonc network, moble wreless cellular network (MWCN) accommodates dynamcally relocatable servce users wth whom locaton uncertanty s always assocated. To reduce ths locaton uncertanty, each moble termnal has to report ts locaton nformaton n regular nterval, whch s called an LU procedure. In dynamc LU scheme, the frequency of LU performed by a moble termnal (MT) depends upon a stochastc phenomenon, whch s user s movement behavor [ ]. Upon the arrval of a moble-termnated call, t s the responsblty of the network to search for the termnal for delverng the call successfully. Ths search s an teratve process, whch contnues untl the termnal s successfully located. The frequency of pagng to be performed by the network, per user, depends upon another stochastc phenomenon, whch s ncomng call arrval process for each user [7]. Snce LU and pagng process both consume suffcent amount of rado resource, cost s ncurred for performng an LU as well as for pagng. Both of these processes are coupled n a sense that there s an nherent trade-off between these two cost components, and these two together determne the total network cost. The sze of the LA, n partcular, affects thesgnallngloadgeneratedduetopagngandlu.froma desgner s pont of vew, t s requred to fnd out an optmum sze of LA such that the desred cost effectveness can be acheved. More precsely, the locaton area (LA) plannng represents a vtal role n cellular networks because of the trade-off created by pagng and regstraton sgnalng. The upper boundontheszeofanlastheservceareaofamoble swtchng center (MSC). In that extreme case, the cost of pagng s at ts hghest, but no regstraton s needed. On

2 The Scentfc World Journal M Fgure : Cellular network archtecture for the movement of MTs. the other hand, f each cell s an LA, the pagng cost s mnmal, but the regstraton cost s the most. In general, the most mportant component of these costs s the load on the sgnalng resources. Between the extremes le one or more parttons of the MSC servce area that mnmze the total cost of pagng and regstraton. The present work falls nto the class of locaton area plannng (LAP) problem [8, 9]. Forhexagonalcellconfguraton,[] hadtredtofnd out optmum movement threshold value, whch would, n effect, determne the number of cells, whch collectvely could be consdered as a dynamc optmal LA (as t depends upon two stochastc phenomena, namely, call arrval pattern and mcroscopc behavoural pattern of termnal moblty). Due to the unqueness of desgn consderatons and problem formulaton n [], they used GA and SA method to solve the problem and have compared the qualty of solutons found by each for dfferent nputs. In fact, there s a growng body of lterature n the applcaton of emergng heurstcs to solve the optmzng problems n varous felds of scence and engneerng, but there s a huge vacuum n the applcaton of heurstcs for the locaton area (LA) problem. Ths paper proposes a Krll Herd based algorthm for mnmzng total network cost, comprsng locaton update (LU) cost and cost for pagng. Krll herd algorthm (KHA) s a recently developed powerful evolutonary algorthm proposed by Gandom and Alav []. The KHA s based on the herdng behavour of krll ndvduals. Each krll ndvdual modfes ts poston usng three processes, namely, () movement nduced by other ndvduals, () foragng moton, and () random physcal dffuson. Although some may dsagree that a sutable algorthm desgn would assure a hgh probablty of fndng soluton, populaton sze does ndrectly contrbute to the effectveness and effcency of the performance of an algorthm []. The prme decdng factor of populaton sze on any populatonbased heurstc algorthms s the executon cost. If an algorthm nvolves large populaton sze, t wll search thoroughly andncreasethechanceofexplorngtheentresearchspace and locatng possble good solutons but unavodably bear an unwantedandhghcomputatonalcost.theotherversons f an algorthm wth small populaton sze may suffer from premature convergence or may search partally the search space. Perhaps suggestng heurstcally a sutable populaton sze may be adequate because one need not know the exact ftness landscape to solve a complex optmzaton problem. Hence, a compromsed, yet effectve, soluton would be dynamcally adjustng the populaton sze to explore the search space n balance between computatonal cost and the attaned performance []. In ths paper, the basc KHA s enhanced by ncorporatng a dual populaton crteron to fnd an optmal soluton of the above problem. There are few lteratures that tackle the ssue of populaton sze wth varous heurstcs [ ]. The rest of paper s organzed as follows. In Secton, the system as well as the proposed model n [] srevsted.in Secton., the constraned cost optmzaton problem for LA plannng s mathematcally formulated. In Secton., thekhatechnquesovervewedngeneralandthenthe KHA based algorthm s proposed for solvng the problem of nterest. In Secton.., the dual herd KHA based algorthm s dscussed. In Secton., some representatve results are presented. Secton concludes the present work.. System and Model Descrpton.. System Descrpton. Fgure shows that the cellular network coverage area s comprsed of hexagonal shaped cells.

3 The Scentfc World Journal The entre coverage area s parttoned nto rngs of cells. The center cell s defned to be a cell where an MT has performed the last LU. An MT resdes n each cell t enters, for a generally dstrbuted tme nterval and then t can move to any of the neghbourng cells. The movement of an MT s assumed to be a smple random walk [7]. The next LU s performed by the MT, when the number of cell boundary crossngs, snce the last LU, equals a threshold value d. It s also assumed that MTs move n a radal drecton as shown n Fgure. If an MT makes, say, d movements n one partcular radal drecton, as shown n Fgure, then the LA wll be defned as the area wthn (d )rngsfromthecentercell.ifd assumes an optmum value, then the correspondng LA wll be an optmum LA [8]. If the LA conssts of D rngs, then D=(d ). () The number of cells wthn the LA, L D wll be N (D) = (D+) D+. () The permeter L(D) of the LA L D,canbecalculatedas L (D) = (D + ) R, () where R denotes the radus of the crcle nscrbng a hexagonal cell and the area of each cell s ( /)R and The area S(D) of the LA L D s d= R. () S (D) = [D (D+) +] (.) R. () Next, t s assumed that the ncomng call arrvals to each MT follow a Posson process. The pagng area s the entre LA that s the area wthn (d )rngsfromthecentercell... Analytcal Model. Let α(k) be the probablty that there are K boundary crossngs performed by an MT between two successve call arrvals. If the probablty densty functon of cell resdence tme t m has the Laplace-Steltjes transform F m (s) MT and mean /λ m, the call arrval to each termnal follows Posson process wth rate λ c. Based on these assumptons, the expresson of α(k) can be derved as follows []. Here, θ s the call-to-moblty rato (CMR), where CMR s defned as λ c /λ m []: { α (k) = θ [ F m (λ c)], K =, { { θ [ F m (λ c)] [F m (λ c)] K, K >. Consderng that cell resdence tme t m follows a Gamma dstrbuton, we get [] F m γ () (s) =[ (λ mγ) (s + λ m γ) ], (7) where γ= (V ar λ m ). (8) Let β(k, K) denote the probablty that the MT s k rngs away from the center cell, gven that the moble user has already performed K number of cell boundary crossngs. To depct the moblty pattern of an MT, a D random walk model s consdered. Let us assume that P K denotes the K K state transton matrx, where an element p,j,k n P K gves us the probablty that a moble termnal moves from one th rng cell to one jth n sngle step. Then, the probablty β(k, K) comes out to be [] β (k, K) ={ P K; Sngle step state transton matrx, P K P(n ) K ; n step transton matrx. (9) Snce we want to fnd out the optmum value of d, we express LU cost C u as a functon of d and the expresson s as follows (detaled dervaton s gven n [9]): C u (d) = U (Y [ F m (λ C)] /θ) ([F m (λ c)] d ) ( [F m (λ C)] d ). () Smlarly, we derve pagng cost C V as a functon of d and t s as follows (detaled dervaton s n [9]): d C V (d) =V k= ρ k N (k) πφ k, () where Y sthenumberofmtattachedtothenetworkwthn the LA and U and V are respectve cost coeffcents for performng an LU and pagng and φ k s the probablty of fndng the MT wthn the LA, L k ; the densty of the MT n that area s denoted by ρ k.sothetotalcosts or C T (d) =C u (d) +C V (d) () U (Y[ F m (λ C)] /θ) ([F m (λ C)] d ) C T (d) = ( [Fm (λ C)] d ) d +V k= ρ k N (k) φ k. ().. Problem Formulaton. The constraned optmzaton problem can be stated mathematcally as Mnmze (P) :C T (d) =C u (d) +C V (d) () Subject to: <p< () q k S (k) ρ k =N k p () R<R max. (7)

4 The Scentfc World Journal In constrant (), p denotes the penetraton factor. Constrant () gvesthetotalnumberofmtsnaservcearea where ρ k s the densty of the MTs n an LA L k,andthereare q k swtches. Ths number must be greater than or equal to the total number of attached moble users. In ths constrant N k denotes populaton sze wthn the LA. The maxmum radus s to be consdered so that the constrant on system power budget s not volated wth respect to (7).. Soluton Methodology The hgh complexty assocated wth the optmzaton problem (P) necesstates computatonally effcent and robust tools. Tradtonal technques lke gradent search, lnear programmng, quadratc programmng, and so forth were not frutful due to the complexty nvolved n the problem. Thsencouragedustoproposetwoheurstcswhchare based on krll herd algorthm and are presented n the next secton. However, the qualty of soluton (compared to classcal optmzaton technques) s often traded off aganst computaton tme, and one can always reach a near optmal soluton wthn bounded computaton tme... Krll Herd Algorthm: An Overvew. Krll herd algorthm (KHA) s a recently developed heurstc algorthm based on the herdng behavor of krll ndvduals. It has been frst proposed by Gandom and Alav []. It s a populaton-based method consstng of a large number of krll n whch each krll moves through a multdmensonal search space to look for food. In ths optmzaton algorthm, the postons of krll ndvduals are consdered as dfferent desgn varables andthedstanceofthefoodfromthekrllndvduals analogous to the ftness value of the objectve functon. In KHA, the ndvdual krll alters ts poston and moves to the better postons. The movement of each ndvdual s nfluenced by the three processes, namely, () nducton process, () foragng actvty, and () random dffuson. These operators are brefly explaned and mathematcally expressed as follows. () Inducton. In ths process, the velocty of each krll s nfluenced by the movement of other krll ndvduals of the multdmensonal search space and ts velocty s dynamcally adjustedbythelocal,target,andrepulsvevector.thevelocty of the th krll at the mth movements may be formulated as follows [9]: α = N S j= V m =α V max [ f f j f w f b +ω n V m, Z Z j Z Z j + rand (, )] +[rand (, ) + ]f best Z best, max (8) where V max s the maxmum nduced moton; V m and V m arethenducedmotonoftheth krll at the mth and (m )th movement; ω n s the nerta weght of the moton nduced; f w and f b aretheworstandthebestpostons,respectvely, amongallkrllndvdualsofthepopulaton;f and f j are the ftness value of the th and jth ndvduals, respectvely; N S s the number of krll ndvduals surroundng the partcular krll; and max are the current teraton and the maxmum teraton number. A sensng dstance (SD ) parameter s used to dentfy the neghborng members of each krll ndvdual. If the dstance between the two ndvdual krll s less than the sensng dstance, that partcular krll s consdered as neghbor of the other krll. The sensng dstance may be represented by [9] n p SD = n Z Z k, (9) p k= where n p s the populaton sze; Z and Z k are the poston of the th and kth krll, respectvely. () Foragng Acton. Each ndvdual of krll updates ts foragng velocty accordng to ts own current and prevous food locaton. The foragng velocty of the th krll at the mth movement may be expressed by [9] V m f =. [ ( N S k= )f (Z k/f k ) max N S k= (/f k) +fbest X best ] +ω x V m f, () where ω X s the nerta weght of the foragng moton; V m f and V m f are the foragng moton of the th krll at the (m )th and m movement. () Random Dffuson. In KHA algorthm, n order to enhance the populaton dversty, random dffuson process s ncorporated n krll ndvduals. Ths process mantans or ncreases the dversty of the ndvduals durng the whole optmzaton process. The dffuson speed of krll ndvduals may be expressed as follows [9]: V m D =μv max D, () where V max D s the maxmum dffuson speed; μ s a drectonal vector unformly dstrbuted between (, ). (v) Poston Update. In KHA, the krll ndvduals fly around n the multdmensonal space and each of krll adjusts ts poston based on nducton moton, foragng moton, and dffuson moton. In ths way, KHA combnes local search wth global search for balancng the exploraton and explotaton. The updated poston of the th krll may be expressed as [9] Z m+ =Z m +(V m +V m f +V m D )P t (u j l j ), () where N d s the number of control varables; u j and l j are the maxmum and mnmum lmts of the jth control varable; P t s the poston constant factor. The above procedure wll be used to optmze () for locaton area (LA). N d j=

5 The Scentfc World Journal In order to speed up the convergence property and to fnd better results, the crossover and mutaton operatons of DE are combned wth the proposed algorthm to utlze the exploraton ablty of DE. These two operators are brefly descrbed below.... Mechansm of the Dual Herd Algorthm. Ths mechansm s adopted from [], whch uses ths for the dfferental evoluton (DE) algorthm. Specfcally, ths search mechansm s adopted to mantan the populaton dversty of the krll herd. Also, the orgnal krll herd algorthm s a good local search optmzer []. Step (ntalzaton). Ths step ntalzes the populaton for exploraton of the search space or else an equal of the herd truncated from the prevous ntalzaton wll be taken. Step. Evaluatng the new postons usng Z m+ =Z m r +F (Zm r Zm r ), () where F = rand(., ) and r, r, andr are random ntegers generated from truncated herd. Step. If rand(, ) CR and j where CR = rand(, ). =k,thensetz m+ =Z m, Step. Or f rand(, ) < PM, then Z m+ = rand(lb j, UB j ), where PM =.. Step. Repeat from Step, untl all the ndvduals n the truncated herd are updated. The above procedure wll ensure the algorthms thorough search of the soluton space as t confrms a random choce of canddates [] compared to a drectonal polcy.... A Double Herd Krll (DHK) Algorthm Developed for Constraned Optmzaton Problem (P). The proposed double herd KH (DHKH) algorthm problem of nterest n ths paper s descrbed as follows. Pseudocode for the DHK Algorthm Step (data structures). Defnng the smple bounds, determnng algorthm parameter(s), and so forth. Step (ntalzaton). Randomly creatng the ntal populaton n the search space. Step (ftness evaluaton). Evaluaton of each krll ndvdual accordng to ts poston. Step. Moton calculaton. Step. Moton nduced by the presence of other ndvduals: foragng moton, physcal dffuson. Implement the updatng steps of the dual herd algorthm (Secton..). Step (updatng). Updatng the krll ndvdual poston n the search space. Step 7 (repeatng). Go to Step untl the stop crtera are reached. Step 8. End Krll herd algorthm s appled twce n order to mantan the dversty n the search process. In a sngle herd algorthm, the search process towards the locaton area attempts to get hold wth that of the local optmal before reachng the convergent soluton. As a result, krll herd algorthm s carred out twce whch nvolves dversty n search process and ncreases the exploraton capablty durng search mechansm resultng n better convergence on the soluton n comparson wth that of the sngle krll herd algorthm consdered for fndng the optmal soluton.. Performance Analyss In ths secton, frst we have vared some system parameters to observe ther reflectons on the model behavor, wthout consderng any constrants. Next, we have run our optmzaton algorthms and have presented some representatve results. Lastly, we have compared the performance of the heurstcs proposed... Model Varaton. To valdate the analytcal model, we have vared the value of movement threshold d and obtaned nature of varaton of LU cost, pagng cost, and total cost (Fgures ), wthoutconsdernganyconstrant. Theobjectve of ths endeavour s to valdate our model as well as our proposed heurstcs wth respect to that cted n []. Through ths effort, we fnd out the regon wthn the entre search space where optmal or near optmal soluton could be found. We take three dfferent values of CMR to demonstrate the effectofchangngmobltyandcallarrvalpatterns.foravery small value of d, the LU cost s very hgh as lesser number of d mples that the frequency of LU s hgher and vce versa. Ths fact can be corroborated from Fgure. FromFgure, t has also been seen that, for dfferent CMR values, the LU costsdfferent.lowcmrmeanstheprobabltyofboundary crossng s hgh by an MT between two successve calls, whch results n hgher locaton update cost. For hgher CMR values, thestuatonsjustthereverse.pagngcostalsovaresasd changes. If the value of d s small, the sze of the LA wll be small and the number of cells wthn the LA wll be less. It has been observed n Fgure that, for small values of d, pagng cost s mnmal. As we expected, the pagng cost also vares wth CMR. If the CMR s hgh, call arrval rate s hgh and for each call meant for a moble termnal, the network wll have to go through the call delvery process, whch wll rase the pagng cost sgnfcantly. The total cost C T vares as d changes, whch s plotted n Fgure. For smaller value of d, thetotalcostshgh.aswe have already explaned, even though the pagng cost s less, the LU cost s very hgh. For certan value of d,thetotalcost

6 The Scentfc World Journal Total cost ILM GLM Movement threshold Fgure:LUcostforvarousCMRvalues. Total cost GTM (dts =) GTM (dts = dms) Movement threshold. dms GTM (dts =) GTM (dts =) Fgure : Total cost for varous CMR values. Table : Parameter settngs for the DHK algorthm. Total cost Parameter Value Number of krll n the populaton (KN) Number of teratons (IN) Foragng speed V f. Dffuson speed D max. Intal volaton tolerance (ε). Decrement (dec). Ω mn ω max Movement threshold GLM U= GLM U= GLM U = Fgure : Pagng cost for varous CMR values. attans a mnmum value, whch s the optmum value of d. From Fgure, wefndthat,fortheunconstranedproblem for three dfferent values of CMR, the optmum value of d les n the nterval [, ]whenweusedourheurstcs.thenature of the cost varaton wth d as well as wth CMR s the same as presented n []wthdelayequaltoone... Results on Optmzaton of (P). In ths secton, we present the results obtaned after solvng the constraned optmzaton problem (P) usngkhaanddhka.toevaluatethe performanceofthelapproblem,wehavevaredthepopulatonandnetworkszeaswellascmrandhaveattemptedto fndoutoptmumcostforthesevaryngnputparameters.we have assumed that n our mcrocellular confguraton each hexagonal cell has a radus of km. Moderate user densty ( users/km ) s consdered. To calculate the cost coeffcent for LU (U) s and that for pagng (V) s. The parameter settngs for the proposed krll herd algorthm are delneated n Table. These values are commonly used for both krll herd algorthms used n ths research. Fgure shows the varaton of permeter of optmum LA wth varyng populaton sze. If the populaton sze s ncreased, optmum value of d ncreases and hence the sze of the LA s ncreased. It s obvous that f larger number of MTs, servced by a sngle MSC, are to be accommodated n a sngle LA, the number of MTs resdng closer to the boundary of an LA wll be hgh. Due to ths, the possblty of number of boundary crossngs by moble termnals also ncreases. To mnmze the total cost, the movement threshold value d would also ncrease so that after each boundary crossng one LU does not take place. However, Fgure shows that DHKA results n slghtly smaller LA. For a populaton sze of 8, DHKA fnds an optmum d value, whch s.% less

7 The Scentfc World Journal 7 LA permeter (km) Sze of the canddates SA GA GSO KRHA Table : Results obtaned for LA mnmzaton problem usng varous methods. No. of cells Method LU cost Pagng cost Total cost [] KHA DHKA [] KHA 87 9 DHKA [] 898 KHA 9 87 DHKA [] KHA 9 97 DHKA [] KHA 77 7 DHKA Fgure : Varaton of permeter of locaton area for change n canddate sze. Total cost ($) Iteratons Ref. [] GSO KRHA Fgure : Varaton of the optmum total cost for varous CMR values. than that generated by SA. However, for a populaton sze of,, usng GA, the optmum value that we obtan s 7.9% less than that obtaned by runnng SA. Fgure shows the nature of varaton of the optmum LU cost, pagng cost, and the total cost wth number of cells per LA wth λ C =. and CMR =.. In ths case, as done n [], the smulaton set-up vared the network sze consstng of 7 cells to 9 cells correspondng to movement threshold values n the nterval [, 7]. However, whle presentng the results, we have rounded up the values of the number of cells per LA to avod any confuson. For cell sze 7 onwards, the LU cost s almost nsgnfcant. However, the pagng cost ncreases as the sze of an LA ncreases. From Table,tsapparentthatanLAconsstngof cells n the nterval [9, ] results n mnmum total cost. Performancewse, both algorthms generate results whch are comparable; average pagng cost wth DHKA came out to be.% less than that obtaned by KHA; average total cost only vares by.%. Varaton n LU cost s almost neglgble. Here, all the LU cost, pagng cost, and subsequently the total cost are comparatvely less when the cell number s. Unlke the results n [], ths research has dentfed a new set of results, confrmng that the locaton area problem mnmzaton s much effectvely solved usng the DHKA algorthm compared to the GA and SA methods n []. Next, we have vared the value of CMR to nvestgate ts mpact on optmum total cost per call arrval. The nature of the varaton s shown n Fgure 7, wheretheoptmum cost per call arrval decreases wth ncrease n CMR. It s apparent that, for low CMR, call arrval rate s low and the moblty rate of the MT s hgh. In ths stuaton, the possbltyofboundarycrossngsbyanmtncreases.ths would ncrease the LU cost sgnfcantly, whereas pagng cost wll be mnmal. As CMR ncreases, the LU cost drastcally decreases and so does the total cost. Optmum movement threshold value d and hence the permeter of an LA obtaned DHKA come out to be less than those SSA calculates. Ths pattern becomes apparent as CMR value ncreases from. onwards... Comparatve Study of the Performance of the Proposed Soluton Methodology. To assess the performance of the two heurstcs we have used n ths research, we have compared

8 8 The Scentfc World Journal Total cost ($) Iteratons CMR =.8 CMR =.9 CMR =. CMR =. CMR =. Fgure 7: Varaton of the optmum total cost usng varous technques. Executon tme (μs) Proposed DHKA Ref. [] KHA Canddate sze Fgure 9: Smulaton tme of the proposed technques wth respect to canddate sze (Dummy). Executon tme (μs).... LA sze Proposed DHKA Ref. [] KHA Fgure 8: Smulaton tme of the proposed technques wth respect to LA sze (Dummy). the computaton tme taken by each algorthm to converge by varyng populaton sze and network as well. Fgures 8 and 9 show that, even as the network sze grows, theproposedkhabasedalgorthmtendstoconvergewthn tolerable run tme, whereas DHKA takes much more tme to converge. DHKA bascally has twce the sze of the herd compared to KHA and t contnues to search for the best member scannng through generatons. The populaton sze and the maxmum number of generatons conventonally assume large values for DHKA to work properly. On average, KHA based algorthm takes about. μsec whereas DHKA takes around.9 μsec. Despte ths fact, DHKA s a strong contender as a combnatoral optmzaton tool because of ts robustness.. Concluson Ths paper dscusses the problem of ever ncreasng concern for reducton of sgnallng loads generated n future moble wreless cellular network (MWCN) due to pagng and LU. In ths regard, the mplcaton of proper plannng for locaton area (LA) towards optmalty s demonstrated. The optmal LA problem was overvewed formally and mathematcally formulated consderng varous practcal constrants. Based on varous moblty patterns of users and network archtecture, the desgn of the LR area s formulated as a combnatoral optmzaton problem. The nondfferentable nature of the problem of nterest n ths paper has created room for some effcent, robust, and nontradtonal search algorthms. Ths research has proposed a double krll herd algorthm wheren the krll herd s dvded based on ther global search and local search mechansms derved from DE. Numercal smulaton wtnesses promsng results, wth the condton of wdely varyng nput parameters, some of whch are documented. Thus, the proposed DHKA appeared to be a strong alternatve for a complex, hard NP-complete optmzaton problem, such as LAP.

9 The Scentfc World Journal 9 Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. References [] K.-Y. Chung, J. Yoo, and K. J. Km, Recent trends on moble computng and future networks, Personal and Ubqutous Computng,vol.8,no.,pp.89 9,. [] I. Demrkol, C. Ersoy, M. U. Caglayan, and H. Delc, Locaton area plannng n cellular networks usng smulated annealng, n Proceedngs of the th Annual Jont Conference on the IEEE Computer and Communcatons Socetes (INFOCOM ), vol.,pp.,aprl. []A.Bar-Noy,P.Chelars,Y.Feng,andM.J.Goln, Pagng moble users n cellular networks: optmalty versus complexty and smplcty, Theoretcal Computer Scence, vol. 7, pp.,. [] S.K.Sen,A.Bhattacharya,andS.K.Das, Aselectvelocaton update strategy for PCS users, Wreless Networks, vol.,no., pp.,999. [] D. Feng, C. Jang, G. Lm, L. J. Cmn Jr., G. Feng, and G. Y. L, A survey of energy-effcent wreless communcatons, IEEE Communcatons Surveys and Tutorals, vol.,no.,pp.7 78,. [] G. P. Polln and I. Chh-Ln, A profle-based locaton strategy and ts performance, IEEEJournalonSelectedAreasnCommuncatons,vol.,no.8,pp.,997. [7]J.S.HoandI.F.Akyldz, Mobleuserlocatonupdateand pagng under delay constrants, Wreless Networks, vol.,no., pp., 99. [8] A. Bhattacharya and S. K. Das, LeZ-update: an nformatontheoretc approach to track moble users n PCS networks, n Proceedngs of the th Annual ACM/IEEE Internatonal Conference on Moble Computng and Networkng (MobCom 99),pp.,Seattle,DC,USA,August999. [9] I.F.Akyldz,J.S.M.Ho,andY.-B.Ln, Movement-basedlocaton update and selectve pagng for PCS networks, IEEE/ACM Transactons on Networkng,vol.,no.,pp.9 8,99. [] M.Matra,R.K.Pradhan,D.Saha,andA.Mukherjee, Optmal locaton area plannng for moble cellular network usng evolutonary computng methods, IETE Journal of Research,vol., no., pp.,. [] A. H. Gandom and A. H. Alav, Krll herd: a new bo-nspred optmzaton algorthm, Communcatons n Nonlnear Scence and Numercal Smulaton,vol.7,no.,pp.8 8,. [] K.C.Tan,T.H.Lee,andE.F.Khor, Evolutonaryalgorthms wth dynamc populaton sze and local exploraton for multobjectve optmzaton, IEEE Transactons on Evolutonary Computaton,vol.,no.,pp. 88,. [] W.-F. Leong and G. G. Yen, PSO-based multobjectve optmzaton wth dynamc populaton sze and adaptve local archves, IEEE Transactons on Systems, Man, and Cybernetcs Part B: Cybernetcs,vol.8,no.,pp.7 9,8. [] J.Arabas,Z.Mchalewcz,andJ.Mulawka, GAVaPS-agenetc algorthm wth varyng populaton sze, n Proceedngs of the IEEE World Congress on Computatonal Intellgence: Evolutonary Computaton,pp.7 78,99. [] J.-H. Zhong, M. Shen, J. Zhang, H. S.-H. Chung, Y.-H. Sh, and Y. L, A dfferental evoluton algorthm wth dual populatons for solvng perodc ralway tmetable schedulng problem, IEEE Transactons on Evolutonary Computaton, vol.7,no., pp. 7,. [] A. K. Qn, V. L. Huang, and P. N. Suganthan, Dfferental evoluton algorthm wth strategy adaptaton for global numercal optmzaton, IEEE Transactons on Evolutonary Computaton, vol., no., pp. 98 7, 9. [7] C. Rose and R. Yates, Mnmzng the average cost of pagng under delay constrants, Wreless Networks, vol., no., pp. 9, 99. [8] W.Wang,I.F.Akyldz,G.L.Stüber, and B.-Y. Chung, Effectve pagng schemes wth delay bounds as QoS constrants n wreless systems, Wreless Networks, vol.7,no.,pp.,. [9] S.-S.Km,J.-H.Byeon,J.Taher,andH.Lu, Swarmntellgent approaches for locaton area plannng, Journal of Multple- Valued Logc and Soft Computng, vol.,no.,pp.87,. [] B. Krshnamachar, R.-H. Gau, S. B. Wcker, and Z. J. Haas, Optmal sequental pagng n cellular wreless networks, Wreless Networks,vol.,no.,pp.,.

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