Ant colony algorithm for cell assignment is PCS Network

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Proceedingsof the 2004 IEEEInternational Conference on Networking, Sensing & Control

Taipei, Taiwan, March 21-23. 2004

An A nt Algorithm for Cell Assignm ent in PCS NetworksS.J. Shyu . B e r t r a n d M.T. Lin T.S. HsiaoDepartment of Computer Science Department of Information Management Department of Computer Scienceand Information Engineering National Chi Nan University, Taiwan and Information Engine eringMing Chuan University, Taiw an mtlin@,ncnu.edu.tw Ming Chuan University, [email protected]

Abstract - Even though signiifcant improvemeni iocommunicaiions infrastructure has been atiained in thepersonal communication service industry, the issuesconcerning the assignment of cells io switches in order iominimize the cabling and handoff costs in a reasonabletime remain challenging and need io be resolved. In thispaper, we propose an algorithm based upon the AniColoq Optimization (ACO) approach to solve this cellassignment problem, which is alreo& known to be A@hard. AC O is a metaheuristic inspired b y the fora gingbehaviors of ani colonies. We model the cell assignmentproblem as a form of mulching pro blem in a compleiebipartite graph so ihai our artifcia2 ants can constructtheir tours on the graph. Experimental resulisdemonshate that the proposed ACO algoriihm is aneffective and promising approach in composing betterapproximaie assignments f o r the cell assignmeni prob lemas compared with some . exisiing heuristics andmetaheuristics. The time needed b y the ACO algorithm isalsopraciically reasonable.Keywords: Cell assignment, ant colony optimization,metaheu ristic, multi-agent.1 Introduction

Since the last decade, there have been significantadvances in the development of mobile communicationsystems. Mobile networks in the next few years could heefficiently migrated to broadband services based on high-speed wireless access technologies (Cheng, Rajagopalan,Chang, Pollini and Barton, 1997). The backbone networksthat are fostering current research include the public landmobile networks (PLMN), mobile Internet protocolnetworks, wireless asynchronous transfer mode (W ATM )networks, and low earth orbit satellite netwo rks (Akyildiz,McNair, Ha, U zunalioglu and Wan& 1998). Even thoughsignificant improvement to communications infrastructurehas been attained in the personal communication serviceindustry, the issues concerning the assignment of cells toswitches in order to minimize the cabling and handoffcosts in a reasonable time remain challenging and need tohe resolved. In this paper, we address one of the criticalproblems concerning how to assign cells to switches tominimize the cost that is usually considered by thedesigners of such mobile communication services orpersonal communication services (PCS).

In PCS networks, each cell has an antenna that isused to communicate with subscribers over some pre-assigned radio frequencies. Groups of cells are connectedto a switch, through which the cells are then routed to theterrestrial (PLMN, ATM, Internet) or satellite networks.Consider the example where cells A and B are connectedto switch sIwhile cells C and D re connected to switch sz.Suppose that a subscriber is currently talking to sonleoneand this call is transmitted through cell B and switch SI . Ifthe subscriber moves from cell B to cell A , switch sIwillperform a handoff for this call. This call does not m ggerany location update in the database that records theposition of the subscriber. Besides, the handoff does notentail any network entity other than switch s ,. Supposethat the subscriber moves from cell B to cell C. Then thehandoff involves not only the modification of the locationof the subscriber in the database but also the execution ofa fairly complicated protocol between switches sI nd SZ.Therefore, there are two types of handoffs, one involvesonly one switch and the other involves two switches. Thelatter is relatively more difficult and costly than theformer. For a more comprehensive description ofhandoffs, the reader is referred to Yacoub (1993) andMerchant and Sengupta (1995). Obviously, the cellsamong which the handoff frequency is high should beassigned to the same switch (if possible) to reduce thehandoff cost. Incorporating the cabling cost that occurswhen a call is connected between a cell and a switch, wehave an optimization problem, called the cell assignmentproblem (Merchant and Sengupta, 1995), of assigning thecells to switches such that the total hybrid cost isminimized und er the constraint of call handling capacity.

Heuristic approaches to solving the cell assignmentproblem have been proposed in the literature since themiddle of 1990s. For example, Merchant and Sengupta(1995) proposed a heuristic based upon a greedy strategy(denoted as H). More heuristics (H-11 and H-IV) an dexperiments could be found in Bhattacharjee, Saha andMukherjee (1999). Bhattacharjee, Saha and Mukherjee(1999) designed experiments and the results show thatheuristics H-11or H-IV outperforms other heuristics in thecases where the number of cells ranges from 25 to 484.

Approaches based upon metaheuristics for resolvingthe cell assignment problem can also be found in theliterature, including simulated annealing (SA) (Demirkol,Ersoy, Caglayan and Delic, 2001), tabu search (TQ

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(Pierre and Houeto, 2002a; Pierre and H oueto, 2002b) orgenetic and memetic algorithms (Auintero and Pierre,2002). It is beyond the scope of this paper to go into detailof these metaheuristics. The readers might refer theabove-mentioned papers.

The goal of this paper is to solve the cell assignmentproblem by applying the Ant Colony Optimization (ACO)approach to explore the possibility of composing bettersolutions. ACO utilizes a nature metaphor originatingfrom the food seeking behaviors of ant colonies. It hasbeen successfidly applied to cope with several classicaloptimization problems. In this paper, we shall design anACO algorithm and conduct experiments to study itseffectiveness in solving the cell assignment problem.

2. ACO D esign for Cell AssignmentAnt algorithms were first proposed by Dorigo andhis colleagues (Dorigo, Manieuo and Colomi, 1991;

Dorigo, 1992) as a multi-agent approach to solvingdifficult combinatorial optimization problems such as hetraveling salesperson problem and the quadraticassignment problem. ACO was inspired by someobservations on real ant colonies. While walking fromtheir colony to food sources back and forth, ants depositpheromone on the ground forming a pheromone trail. Ashorter path would accumulate more pheromone thanlonger ones. Ants thus prefer in probability to follow apath with more pheromone. As a positive feedbackmechanism, more ants traverse through a shorter path andin turn this path will accumulate more pheromone. As away, without visual cues ants are capable of finding theshortest path leading to food sources by exploitingpheromone information. The utilization of pheromone inthe meantime reflects the adaptive memory mechanism(Taillard, Gambardella, Gendreau and Potvin, 2001). Dueto the attractiveness about ant behaviors and simplicity inimplementations, ACO has been gaining more and moreresearch attention since the early 1990s.

In our study, we transform the original cellassignment problem into a structure that is suitable forants to search for solutions. In the literature, graphs havebeen widely adopted as such intrinsic structures. To namea few as examples, Dorigo and Gambardella (1997a;199%) used a directed graph with weighted edges torepresent TSP and a cycle in the graph corresponds to afeasible solution to TSP; Shyu, Yin, Lin and Haouari(2002) modeled the GMST as a undirected weightedgraph with weighted edges and a tree could be a feasiblesolution to GMST. W e shall model the cell assignmentproblem by a complete bipartite graph with weightednodes as described in the following.

Consider a cell assignment problem instance P withn cells and m switches. Let C denote the set o f the n cellsan d S enote the set of the m switches in P . We may use acomplete bipartite graph G = ( V , E ) with weightsassociated with nodes to represent P, here V =CUS,CnS = 0 and weights on nodes iaC denote the callvolume of cell i, while weights on nodes k enote thecapacity of switch k. As a way, a feasible assignment Acorresponds to a sub-bipartite graph G =(CU S, ) c G,where E ={(vl. v2 ) I v1 E C and v 2 E S) L E with theconstraints: (1) if edges e l =( a , b) , e2= c . d)E, then af c an d IEI =n, and (2) the constraint on switch capacityshould be satisfied. Note that each vertex in C shouldappear as an end vertex of exactly one ed ge in E. An edge(vl ,vz) ~E in dic ate she assignment of cell v, o switch v2.

Although the structure of G can dictate a feasibleassignment of P, he edges in G are not necessarilyconnected so as to form a tour. Thus it is not easy for ourartificial ants to traverse it out of G. A move of an antfrom cell i to switch k corresponds to the assignment ofcell i to switch k. However, once arriving switch k, hisant has to decide which cell to move on next to continuethe remaining cell-to-switch assignm ent. We thus appendedges Ec E in G for our ants to move from the switchesto the cells where E ={(vz, v I ) 1 V] E C and v 2 ~}L Ewith the constraint that if e l=(a ,b) and e 2 = ( c .d) elongto E, then b t d an d I E I =n-1. As a result, a subgraphG =(CIJ S, U E) of G,where E: E L E that satisfiesthe above-mentioned constraint would be suitable for ourants to traverse in G to consbuct the correspondingfeasible assignment. In fact, a femiibfeassignment couldbe interpreted as a tour of a sequence of 2n-1 alternatingedges in G ( 3 s4 1 3 ( s4 9 ), ( c,, , b, 1 9

1su , vS n. To minimize the total cost, the above tourshall be the one that minimize

whereassigned to the same swit chdetermines whether cell a , and cell a, ar e0, i f b , = bj ;1, othenvie.f O j O j =

Since each cell should be assigned to some switchexactly once in the cell assignment problem, w e provide ashort-term memory, called tabu, fo r our artificial ants tokeep track of the celkalready assigned. While multiplecells might be assigned to a switch if the capacity

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constraint is not violated, we afford each ant anothershort-term m emory, called fe w, to reflect the availabilityof switches. To find solutions to the cell assignmentproblem, an ant, say u, at cell i confronts two successivedecisions to make: (1) which switch to move on (namely,which switch kcfeas" cell i will be assigned to), and (2 )which cell to move on from the selected switch (namely,which cell ;E tabu" to continue). We call it a step for anant to make these two decisions in sequence to assign acertain cell to some switch. After n steps with theexception that the nth step makes only decision ( I ) , theant could construct a tour, which corres ponds to a feasibleassignment of the original problem. Such an n-stepprocess is called an teration.

In the following, we describe our detail design,including state transition rules and pheromone updatingN I ~ , or our ants to make their two decisions in each stepin the following.1. State Transition R ulesIn general, while constructing a solution using theACO heuristic, an ant moves on relying on th einformation given hy pheromone intensify and dynamicheuristicfunction. An ant at some cell i has to make twosuccessive decisions in each step. The two decisions referto different knowledge with respect to the problem status.Therefore, we em ploy diffe rent greedy heuristic functionsand define tw o pheromone trails to constitute thecorresponding state transition rules for our ants tostochastically make their decisions. Suppose that ant u iscurrently positioned at cell i . Our state transition rules forthe above tw o decisions are:

Once the ant chooses an edge to move from a cell toa certain switch in the r-th step of som e iteration, a partialcost incurred during the first r steps could be computed.We employ the partial cost built in the first r steps as thebasis of our heuristic. Let cell a,denote the cell on whichan t u is and b, denote the switch to which cell a, isassigned in step r, 1I 2 n. Thus cell a, is the startingcell of ant u . Let garb, denote the partial cost incurredwhen ant u moves from cell a, o switch 6 , after step r.The partial cost g O r b ,can be calculated byI i f r = l ;

0, ifb, =b l;1, otherwise,

We use the inverse value of the partial cost g,,b,during the first r steps as our heuristic function 7]& instep r of some iteration. Then, the probability for ant u atcell i to move to switch k (i.e., assigning cell i to switch k)in the r-th step of this iteration is defined as follows.

1 , i f q < q o a n d k = a r g may { r j 3 x ( q j s ) ~ ) ;E ea-

SEf e r n y0 , othenvise(k d &as") ,

where r,k denotes the amount of pheromone on edge (i,k), qo ( 0 9 0 5 ) is the relative preference for exploitationor exploration, p (0 t 0) is the relative importancebetween pheromone density and heuristic value, andfeas"denotes the feasible set of switches that the cells can beassigned to without violating the capacity constraints foran t u . Ant u at cell i picks up a pseudo random number q( O S q 5 1) to make its move in step r: if q< qo , it moves toswitch k through edge (i, k) that achieves the maximumvalue of r,k(q,k)' ; f q>qo, it moves to switch k in aprobabilistic way, which provides a biased exploration toavoid stagnation and to find better solutions. It is easy tosee that we prefer a switch k from cell i via an edge w ith ahigher pheromone density (more accumulated knowledge)and a highe r heuristic value (lower partial co st by a greedyapproach) to construct a solution path. Tuning the valuesof q0allows us to have an adaptive degree of exploration,Le., whether to exploit the steps that seem to be the mostpromising or to explore the search space probabilistically.(2 ) Following an edge from switch k o an un-visited cell;We employ a greedy heuristic for ants to choose acell not yet assigned to move on. The cell with the mostheavy call volume is considered first in each step. Ant umemorizes the cells that have been traversed in thecurrent iteration in tabu".

We define heuristic function 0 as the inverse valueof the call volume of cell J , which does not belong totabu" for ant u , i.e., rj, =(A,).'. Once ant u arrives at cellj from switch k, it deposits some pheromone, defined asT & , to communicate its experience about this edge withother ants. We use the following probability functionfor ant u at switch k o make its choice.where the value of 11a,4 depends on whether cell a, the

cell visited by a nt u in step I, l < k ) and cell a, the cell onwhich ant u is) areassigned to a same switch.

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I , if q


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experiments have demonstrated the effectiveness andscalability of ou r ACO algorithm in coping with the cellassignment problem. Although ACO takes a longer timethan the three heuristics H, H-ll an d H - r V, it finds muchbetter approximate solutions. When compared with othermctaheuristics, ACO requires less time and also deliversbetter solutions. Moreover the experimental resultsdemonstrate the scalability and robustness of ACO. Th etime needed by ACO is reasonable when compared withthat needed to derive an optimal solution. The concern ofsolution quality against temporal issue is a trade-off forPCS designers. For the cell assignment problem, ACO isan excellent and promising approach to delivering goodsolution quality within reasonable computational time.ReferencesI . I.F. Akyildiz, J. McNair, J. Ho, H. Uzunalioglu, andW. W ang, Mobility management in current and h tu re

communication networks, IEEE Network Magazine,August 1998.Auintero, A. and Pierre, S., Evolutionary approach tooptimize the assignment of cells to switches inpersonal communication networks, Submitted toComputer Communications.3. P. S. Bhattacharjee, D. Saha and A. Mukherjee,Heuristics for assignment of cells to switches in aPCSN: A comparative study, ICPWC99;pp.331-334,1999.B. Bullnbeimer, R. F. Hart1 and C. Strauss, Applyingthe Ant System to the vehicle routing problem, In: S.VoD, S. Martello, I.H. Osman, C. Roucairol (Eds.),Metaheuristics: Advances and Trendr in Local SearchParadigms for Optimization, Kluwer AcademicPublishers, Boston, MA, pp. 285-296, 1999.M. Cheng, S. Rajagopalan, L . F. Chang, G.P. Pollini,G. P. and M. Barton, PCS mobility support over fixedATM networks, I EEE Communication Magazine, Vol.35, pp. 82-92, 19 97.D. Costa and A. Hertz. Ants can color aaDhs. Journal

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Society Press, Los Alamitos, CA, 1998, pp. 74-83.9. G. Di Caro and M. Dorigo, AntNet: Distributedstigmergetic control for communications networks,Journal of Artificial Intelligence Research, Val. 9,1998,p p. 317-365.IO. M. Dorigo, Optim ization, Learning and NaturalAlgorithms. Ph.D. Thesis, Dipartimento di Elettronica,Politecnico di Milano, Italy (in Italian), 19 92.

1 1 . M. Dorigo, V. Maniezzo and A. Colorni, PositiveFeedback as a Search Stra tea , Technical Report 91-016, Dipartimento di Elettronica, Politecnico diMilano, Italy, 1991.12. M. Dorigo and L. M. Gambardella, Ant colony

system: A cooperative learning approach to thetraveling salesman problem, IEEE Transactions onEvolutionaiy Computation, Vol. 1, No. 1, pp. 53-66,199 l a .13. M. Dorigo and L. M. Gamhardella, Ant colonies forthe traveling salesman problem, BioSystems, Vol. 43,1997h , pp. 73-81.14. L. M. Gambardella, E. D. Taillard and G. Agazzi,M A C S -W T W : A mult ip le ant colony system forvehicle routing problems with time windows, In: D.Come, M. Dorigo, F. Glover (Eds.), New Ideas inOptimization, McGraw-Hill, London, UK, 1999, pp.63-16.15. V. Maniezzo and A. Colorni, The ant system appliedto the quadratic assignment problem, IEEETransactions on Knowledge and Data Engineering,Vol. 11 , No. 5, 1 999, pp. 2063-2070.16. P. R. McMullen, An ant colony optimizationapproach to addressing a JIT sequencing problemwith multiple objectives, Artificial Intelligence inEngineering, Vol. 15, No. 3,20 01, pp. 309-317.17. Merchant and B. Sengupta, Assignment of cells toswitches in PCS network, IEEE/ACM Transactionson Netwo rking, Vol. 3, No. 5, 1995, pp. 52 1-526.18. S. Pierre and F. Houito, A tabu-search approach forassigning cells to switches in cellular mob ile networks,Computer Communications, Vol. 25, No. 5, March2002a, pp. 464-477.19. S. Pierre and F. Houeto, Assigning cells to switchesin cellular mobile networks using taboo search, IEEETransactions on Systems, Man, And Cybernetics-Part B: Cybernetics, Vol. 32, No. 3, June 2002b, pp.351-35620. R. Schoondenvoerd, 0. Holland, J. Bruten and L.Rothkrantz, Ant-based load balancing intelecommunications networks, Adaptive Behavior,Vol. 5, No. 2, 1997, pp. 16 9-207.21. S. J. Shyu, P. Y. Yin and B. M. T. Lin, An ant colonyoptimization algorithm for the minimum weightvertex cover problem, accepted by Annals ofOperations Research, May 2003.22. S.J. Shyu, P.Y. Yin, B.M.T. Lin and M. Haouari, Ant-Tree: An Ant Colony Optimization Approach to theGeneralized Minimum Spanning Tree Problem,Journal of Experimental and Theoretic al ArtificialIntelligence,Vol. 15 ,N o. 1 , 2 0 0 3 , ~ ~ .03-112.23. E.D. Taillard, L. M., Ga mbardella, M. Gendreau, andJ.-Y. Potvin, Adaptive memory programming: Aunified view of metaheuristics, European Journal ofOperational Research, Vol. 135, No. 1, 2001, pp. 1-16 .

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Table 1. Relative deviation for different heuristics with respect to ACO(H-11- (H-IV- (sa- (E- (Ma -(n , m) (H-aco)iacoACO)/ACO aco)/Aco Aco)/aco ac0)laco aco)/acoX I 0 0 (%) lo o (%) x 100 (%) x LOO (%) x 100 (%) x 100(%)( 5 0 3 16.35 18.34 18.71 8.31 8.68 7.39(50,lO) I7.89 25.83 26.13 3.95 4.68 3.81( 5 0 , W 14.96 25.59 23.78 3.39 4.07 1.88( I O O S ) 12.40 16.23 19.43 10.28 9.55 7.68

( I 00,lO) 22.73 21.63 21.65 9.96 9.22 8.86(100,15) 20.83 29.21 25.50 9.07 8.98 8.60(150S) 30.72 16.30 12.63 3.02 2.56 1.77( I 50,lO) 30.31 30.73 28.77 9.30 6.70 2.89

(lSO,I5) 26.80 27.79 29.23 10.55 9.05 5.68(200s) 21.67 13.42 12.03 9.78 8.94 6.63(200,lO) 39.92 29.15 24.20 . 8.64 8.03 7.00(200,15) 46.87 33.26 33.41 13.41 12.00 9.501250.5) 25.91 19.07 11.74 9.68 7.55 0.46i l(250.10) 23.74 16.79 17.55 9.85 8.36 5.86(250.15) 32.66 31.60 26.05 8.81 7.32 5.47(350.20) 37.4 8 30.98 32.07 15.37 10.31 6.63

~(500.20) 38.0 1 32.50 31.18 17.01 11.54 7.82

Table 2. CPU time (sec.) needed by different heuristics(n .m) H H-I1 H-IY SA TS Ma ACO( 5 0 S ) 9.1 0.9 18.5 1.3(50.7) 9.9 1.3 19.4 1.7Cj0,'lO) 12.4 2.3 22.2 2.7(50.151 8.3 1.8 17.9 4.732.9 5.6 110.1 5.434.8 6.2 116.9 8.2(100,5)1100.10) 37.2 7.1 115.7 2.5(100,7)(100.15 i 42.5 10.0 115.8 23.6(150S) 65.7 19.3 728.4 13.3(150.7) 0.1 84.4 21.0 750.4 19.4(iso,io) 0.1 80.2 25.8 747.0 35.4(150.15) 0.I 92.6 40.2 751.8 49.0( 2 0 0 3 0.1 - 138.9 28.2 2,696.8 24.60.1 - 140.5 42.3 2,733.6 35.4(200.10) 0.1 - 139.0 60.0 2.807.0 66.1(200,71. . .(200.15) 0.2 - 169.9 62.4 2:SOS.S 117.4

0.1 86.8 42.3 7,748.1 43.7(250.71 0.2 - 228.0 73.4 7.813.0 68.0( 2 5 0 3(k0,lO) 0.3 - 234.6 97.2 7,437.0 100.0250.15 ~ 254.1 15.7 7,930.1 191.6(350,20) 1.3 0.1 0.1 1.1678.9 1,108.9 90,018.1 744.5(500,20) 3.2 0.2 0.2 2.7886.9 2.357.6 145,210.6 1,684.8

(-denotes that the CPU time i s less than 0.1 seconds.)

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Ant colony algorithm for cell assignment is PCS Network