cell planning with capacity expansion in mobile communications: a tabu search approach

1678 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 5, SEPTEMBER 2000

Cell Planning with Capacity Expansion in MobileCommunications: A Tabu Search Approach

Chae Y. Lee, Member, IEEE,and Hyon G. Kang

Abstract—Cell planning problem with capacity expansion is ex-amined in wireless communications. The problem decides the loca-tion and capacity of each new base station to cover expanded andincreased traffic demand. The objective is to minimize the cost ofnew base stations. The coverage by the new and existing base sta-tions is constrained to satisfy a proper portion of traffic demands.The received signal power at the base station also has to meet thereceiver sensitivity. The cell planning is formulated as an integerlinear programming problem and solved by a tabu search algo-rithm. In the tabu search intensification by add and drop move isimplemented by short-term memory embodied by two tabu lists.Diversification is designed to investigate proper capacities of newbase stations and to restart the tabu search from new base sta-tion locations. Computational results show that the proposed tabusearch is highly effective. A 10% cost reduction is obtained by thediversification strategies. The gap from the optimal solutions is ap-proximately 1 5% in problems that can be handled in appro-priate time limits. The proposed tabu search also outperforms theparallel genetic algorithm. The cost reduction by the tabu searchapproaches10 20% in problems with 2500 traffic demandareas (TDAs) in code division multiple access (CDMA).

Index Terms—AMPS, CDMA, cell planning, cellular communi-cation systems, parallel genetic algorithm, tabu search.

I. INTRODUCTION

I N CELL planning for mobile communication systems, weneed to consider the traffic demand to cover a specific re-

gion, availability of base station sites, available channel capacityat each base station, and the service quality at various poten-tial traffic demand areas (TDAs). Selection of good base sta-tion sites and channels will result in acceptable coverage per-formance at base stations both in coverage area and in signalquality. The problem discussed in this paper is to determine thenumber of base stations and location and capacity of each basestation to cover increased traffic demand. The coverage has tosatisfy a certain level of total traffic demand and the receivedsignal strength.

Optimal location of transmitters for microcellular system isstudied by Sheraliet al.[5]. The path loss at each subarea is rep-resented as a function of the base station location. A nonlinearprogramming problem is presented which minimizes a measureof weighted path-losses. Several nonlinear optimization algo-rithms are investigated to solve the problem. In [6], the radiocoverage optimization problem is converted to a maximum in-

Manuscript received October 29, 1998; revised March 28, 2000.The authors are with the Department of Industrial Engineering, Korea Ad-

vanced Institute of Science and Technology (KAIST), Taejon 305-701, Korea(e-mail: [email protected]).

Publisher Item Identifier S 0018-9545(00)07883-X.

dependent set problem. The objective is to achieve a large cov-erage of TDAs with a small number of base stations. A simu-lation method is employed to examine the relationship betweenthe number of base stations and the relative coverage of TDAs.

Tutschku [12] proposed an automatic cellular network designalgorithm without considering the capacity of transmitters. Thenetwork design problem is converted to a maximal covering lo-cation problem by using demand node concept. The location oftransmitter is optimized by minimizing cochannel interference.He [9] also proposed a greedy heuristic to solve the maximalcoverage location problem of transmitters. The heuristic takesinto account all the RF design objectives as well as the capacityand the network deployment constraints.

Ye et al. [10] solve the cell planning in a CDMA network.They maximize the cell coverage for given traffic and find op-timal location configuration by considering nodes covered viasoft handoff by two or three base stations.

A genetic algorithm approach is presented by Calegariet al.[7], [8]. The selection of base stations is represented in a bitstring. Selection based on fitness value, one-point crossover andmutation operators are employed. The fitness value combinestwo goals of maximizing the cover rate and minimizing thenumber of transmitters. To speed up the procedure a parallelgenetic algorithm is implemented by using island model. Theircomputational results show that the solution quality is signifi-cantly influenced by the number of islands.

Most of the research in the optimization of the radio cov-erage in cellular system is restricted to the selection of base sta-tion locations. Base stations are considered to start service atthe same time. In this paper we consider two types of base sta-tions. Some existing base stations are currently in service for aspecified region. The increased traffic demand in the region re-quires capacity expansion with additional base stations. We thusneed to determine the location and the capacity of each new basestations.

The remainder of this paper is organized as follows. In Sec-tion II, we discuss the capacity of a base station in various mul-tiple access technologies and the potential service area of a basestation. We also provide a mathematical model for the cell plan-ning problem. Section III presents a tabu search procedure tosolve the problem. Construction of initial solutions, intensifi-cation, and diversification strategies are examined. The perfor-mance of various tabu operators and the efficiency of the pro-posed tabu search procedure are presented and compared witha genetic algorithm and an excellent integer programming algo-rithm CPLEX [16] in Section IV. Finally, we conclude the paperin Section V.

0018–9545/00$10.00 © 2000 IEEE

LEE et al.: CELL PLANNING WITH CAPACITY EXPANSION IN MOBILE COMMUNICATIONS 1679

II. CELL PLANNING WITH CAPACITY EXPANSION

The cell planning we are interested in is to decide the locationand capacity of each new base station to cover increased trafficdemand. It causes cell splitting in urban area and requires newcell sites in suburban area. Thus, some of the existing TDAs areserved by the new base stations due to the cell splitting. Here,we consider the increased traffic demand, the capacity of eachnew base station to locate and the coverage of the base station.

A. Capacity of a Base Station

The capacity of a base station has experienced a greatimprovement due to the digital modulation, multiple accessschemes and other technological development. AdvancedMobile Phone Service (AMPS) employs the frequency divisionmultiple access (FDMA). It utilizes 50 MHz of spectrum inthe 800 MHz band. Each channel band of AMPS is 30 kHz.Assuming two competing carriers in the market, a carrier has416 channels [1]. Twenty one channels are used for controland the rest for traffic channels. When we assume 7-cell reusepattern, the number of traffic channels available in a cellbecomes 56. It corresponds to a base station capacity of 46Erlangs (Erlang B) when the blocking probability is 2%.

Global System for Mobile (GSM) is a typical standard ofthe time division multiple access (TDMA). GSM utilizes twobands of 25 MHz for forward and reverse links. The frequencyband is divided into 200 kHz wide channels called AbsoluteRadio Frequency Channel Numbers (ARFCNs). Each channel istime shared between as many as eight subscribers using TDMA.Since each radio channel consists of eight time slots, there arethus a total of 1000 traffic channels within GSM. In practicalimplementations, a guard band of 100 kHz is provided at theupper and lower ends of GSM spectrum, and only 124 channelsare implemented [1]. By assuming two companies as in AMPS,each carrier has 62 channels. Assuming the 4-cell reuse pattern,a BS can use 120 time slots. This corresponds to 107.4 Erlangswhen the blocking probability is 2%.

Interrim Standard 95 (IS-95) [14] is the standard of the codedivision multiple access (CDMA) and offers some advantagesover TDMA and FDMA. Each CDMA channel which is calledthe frequency assign (FA) occupies 1.25 MHz of spectrum. As-suming 25 MHz for both links, the number of available chan-nels becomes ten FAs. Since the reuse pattern in IS-95 is one,one cell use up to ten FAs. However, normally three to four FAsare used practically in a cell. Assuming four FAs and 36 trafficchannels [15] per 1 FA, 144 traffic channels are available in acell. If the system uses 120directional antenna, then the ca-pacity is increased approximately 2.5 times, which correspondsto 360 traffic channels. Assuming 2% blocking probability, thecapacity becomes 345.7 Erlangs at each base station.

B. Potential Service Area of a Base Station

Potential service area of a base station represents the TDAsthat can be served with sufficient quality by the base station. Inthis study, we are interested in a general propagation path-lossformula in a general mobile radio environment. By using thepath loss model the received signal power can be estimated as afunction of transmitted power, distance between the transmitter

and receiver, processing gains, and antenna heights. If we ignorefading, the following propagation model [2] may well be usedin computing potential service areas. In the model, the path lossexponent is assumed to be four.

wherereceived power;transmitted power;processing gains of receiver and transmitter;antenna heights of receiver and transmitter;buffer for fading;distance between transmitter and receiver.

From the above model, the radius of a cell site can be com-puted for a given receiver sensitivity. In other words, the TDAsthat can be covered by a base station are determined by com-paring the received power and the receiver sensitivity. Since weare interested in the location and the capacity of each new basestation, we consider the received power at a base station fromTDAs. We also assume that cochannel and adjacent channel in-terferences are negligible in the uplink analysis.

C. Problem Formulation

Suppose that mobile users are distributed over a designatedregion composed of TDAs. Each TDA has a traffic demand

.Assume that the region has existing base stations each of

which is denoted by BS . To satisfy increasedtraffic demands candidate cell sites are considered. It is as-sumed that the potential location of each candidate base stationBS is known. Let and be,respectively, the cost and capacity of each new base station.Note that the cost and capacity are mainly dependent on the wayof multiple access, number of user channels, and sectorization.We assume that the base station costis linear to the capacity

.To formulate the problem, we introduce two types of vari-

ables. Let be the wireless connection between TDAandBS such that

if TDA is covered by BS

otherwise

Also, let be the selection variable of BS, such that

if BS is selected

otherwise

The objective of our cell planning problem is to minimize thecost of newly installed base stations. Thus the objective functionof the problem is

Minimize


Now, TDA can be covered either by a new base station or byan existing base station. It can be covered by a new base stationonly if it has been selected. Thus, we have

for and

In the constraint above, the existing base stations are assumedselected, i.e.,

for

Note that due to the increased traffic demand from TDAs andcell splitting the coverage of existing base station may change.

In cell planning, it is important to satisfy the coverage limit ofthe total traffic demand in the region. Specifically, the problemis handled with the minimum portion that has to be covered by awireless carrier in the specified region. The minimum portion isgiven either by the area or by the traffic demand. In this study, weemploy the minimum portion of traffic demand. In other words,at least of the total expected traffic demand hasto be covered by a set of base stations in the region. Thus, wehave the following constraint:

Now, consider TDAs that are covered by a base station.Clearly, the total traffic demand covered by the base stationcannot exceed the capacity. The capacity constraint is given asfollows:

for

Finally, we take into account the received signal powerstrength at BS which is transmitted from TDAs. Due to thepath-loss of radio propagation, if the received power from a TDAdoes not exceed the receiver sensitivity at BS, then the TDAcannot be covered by the BS. Let denotes the receivedpower at BS which is transmitted from the center of TDA.Also let be the minimum required power level at each basestation. Then we have the following path-loss constraint:

for and

From the above, the cell planning problem can be formulatedas the following linear integer problem:

Minimize

s.t. for (1)

for

and (2)

(3)

for (4)

for

and

(5)

The above cell planning problem is equivalent to the setcovering problem [6] when the coverage factor . Theproblem seeks a set of base stations that covers the TDAs ina specified region. When , all TDAs are covered bythe base stations. Note that the set covering which is a specialcase of the above cell planning problem is a well-knownNP-complete problem [11]. We thus propose a tabu searchprocedure (see Fig. 1) to solve the problem.

III. T ABU SEARCH FOR THECELL PLANNING PROBLEM

Tabu Search incorporates three general components [4]:

1) short-term and long-term memory structures;2) tabu restrictions and aspiration criteria;3) intensification and diversification strategies.

Intensification strategies utilize short-term memory function tointegrate features or environments of good solutions as a basisfor generating still better solutions. Such strategies focus on ag-gressively searching for a best solution within a strategically re-stricted region. Diversification strategies, which typically em-ploy a long-term memory function, redirect the search to unvis-ited regions of the solution space.

In our case, the short-term memory is implemented by meansof tabu lists and aspiration criteria. A tabu list records attributesof solutions (or moves) to forbid moves that lead to solutionsthat share attributes in common with solutions recently visited.A move remains tabu during a certain periods (or tabu size) tohelp aggressive search for better solutions. Aspiration criteriaenable the tabu status of a move to be overridden, thus allowingthe move to be performed, provided the move is good enough.

A. Initial Base Stations and Covering

To obtain an initial solution two strategies are adopted;“All Candidate Base Stations” and “Random Feasible BaseStations.” In the method of All Candidate Base Stations, basestations are located at every candidate cell site. For feasibility,sufficiently many candidate cell sites are initially prepared tosatisfy the capacity and path loss constraints. Each TDA isassigned to the nearest base station as far as the capacity issatisfied. In the method of Random Feasible Base Stations,base stations are selected in nonincreasing order of the capacityfrom candidate cell sites. Each TDA is covered by the nearestbase station within the capacity limit. The selection of basestations is terminated when all TDAs are covered.

B. Intensification with Short-Term Memory Function

We first define two types of moves. They are “Drop move”and “Add move.” Drop move makes a currently active base sta-tion inactive. In other words, a base station which is dropped canno more cover TDAs until it is selected again. This Drop move


Fig. 1. Proposed tabu search procedure for the cell planning.

is implemented by moving the base station from Active_List toCandidate_List. Add move is the opposite of Drop move. Addmove selects a base station to cover TDAs. Thus the base stationis moved from the Candidate_List to the Active_List.

The short-term memory function, embodied in the two tabulists, is implemented as an arrayTabu Time which recordsthe earliest iteration that BSis allowed to move: either to Can-didate_List or to Active_List. To prevent moving back to previ-ously investigated solutions, we define two different tabu times

and as the time that must elapse before a base stationis permitted to move from Candidate_List and Active_List, re-spectively. Both tabu times are measured in number of itera-tions. If by an Add move BSis moved from Candidate_List toActive_List, then theTabu Time Current Iteration

. If by a Drop move BS is moved from Active_List to Candi-

date_List, then theTabu Time Current Iteration .Thus BS is tabu ifCurrent Iteration Tabu Time . Thechoice of tabu times is important to the Tabu search algorithm.We will empirically select the tabu times ( ) which lead toreasonably good solutions.

In a Drop move, a base station is selected to drop from theActive_List by considering base station costand normalizedresidual capacity NRC . The residual capacity is normalizedsuch that the total capacity is equal to the base station cost. Abase station whose sum of the two costs is the maximum is se-lected to drop.

In an Add move a base station is selected from Candidate_Listby comparing the coverage and the base station cost. A basestation that maximizes the number of TDAs covered with min-imum cost is selected to add.


The above two moves are explained in Steps 3 and 6 of theProcedure Tabu Search. Aspiration by default is applied whenthe coverage of TDAs is infeasible due to a Drop move. In thiscase the tabu status is overridden and the base station with theleastTabu Time Current Iteration from Candidate_Listis added to the solution.

C. Reassignment of TDAs

In the intensification process, reassignment is performed aftereach move. After a Drop move each TDA which was coveredby the dropped base station need to be covered by another basestation. Each TDA is now covered by a base station in the Ac-tive_List such that the received signal from the base station isthe strongest. The same is true after an Add move. When a basestation is added to satisfy feasibility of the covering problem,TDAs are selected which will be covered by the newly addedbase station. Each TDA whose received power from the addedbase station is stronger than that from the current base station isassigned to the new base station as far as the capacity is satis-fied. These two reassignments are explained in Steps 4 and 7 inthe tabu search procedure.

D. Diversification with Long-Term Memory Function

The diversification strategy is helpful to explore new unvis-ited regions of the solution space. It enables the search processto escape from local optimality. In our procedure the diversifi-cation is performed when no solution improvement results con-secutively for iterations in the intensification process.Also, a path is defined as the iterations between any two con-secutive diversifications. Two diversification strategies are em-ployed: capacity diversification and coverage diversification.

The capacity diversification is the process of determining anappropriate capacity at each new base station. It is implementedby examining the best solution in a path. When a BShas un-used residual capacity RC which is greater than the capacityvariation unit , then the capacity is reduced by . Whenthe capacity of a base station is fully employed to cover TDAs,then the capacity is increased by one unit, i.e., .

The coverage diversification is performed by usingActive Freq and Move Freq . Active Freq repre-sents the number of iterations BSwas in solution in theprevious path, whileMove Freq represents total numberof Add and Drop Moves performed on BS. In the coveragediversification the preference is given to the base stations withlow Active Freq and Move Freq . Base stations withrelatively lowerActive Freq Move Freq are selecteduntil all required traffic demands are covered. This diversifica-tion strategy has the effect of restarting the tabu search froma solution that is far away from the solutions obtained in theintensification procedure.

The above two diversification strategies described in Step 9of Procedure Tabu Search are designed to investigate proper ca-pacities of base stations and better coverage of the TDAs.

Procedure Tabu SearchStep 1. Initial Solution Method

Obtain Initial feasible solution by oneof the following two methods.

Method 1: All Candidate Base StationsMethod 2: Random Feasible Base Sta-

tions

Step 2. Starting Set upCurrent_Iteration , NoImprove ;MaxNoImprove Nmax, Diversification

;MaxDiversification Dmax, Tabu_Time(k)

;Move_Freq , Active_Freq ;Best_Solution_Value , Record_Solu-tion_Value ;

Tabu Time in Active_List;Tabu Time in Candidate_List;Number of TDAs;

Traffic Demand of TDA , Cov-erage Factor;Total_Traffic_Demand ;

Capacity of BS ;Construction Cost of BS ;

RC Residual Capacity of BS ;NRC Normalized residual capacity ofBS , i.e.,

NRCRC

Received power at BS which istransmitted from the center of TDA ;

Step 3. Drop Move(a) Evaluate the current solution ofBS’s in Active_List.

NRC .(b) Do in nonincreasing order of theevaluation value until a BS isselected.

For BSIf Tabu_Time Current_Iteration,

select the BS .Else if the BS satisfies the default

aspiration criterion then select theBS .

Otherwise repeat for the next BS inthe order.(c) Move the selected BS from Ac-tive_List to Candidate_List.Set Tabu_Time Current_Iteration

Move_Freq Move_Freq .(d) Go to Step 4.

Step 4. Reassignment after Drop Move(a) For each TDA that is not covered

(i) Find BS’s that can cover the TDAin Active_List.

(ii) Sort BS’s in nonincreasing orderof the received power .


(iii) If RC TDA is covered byBS (i.e. ) and set RC RC .

Otherwise repeat for the next BS inthe order.(b) Go to Step 5.

Step 5. Feasibility Check(a) Compute Covered_Traffic

RC .(b) If Covered_TrafficTotal_Traffic_Demand, go to Step 6.

Otherwise go to Step 8.

Step 6. Add Move(a) Evaluate the current solution ofBS’s in Candidate_List.

Number of TDAs which can becovered by BS

for TDA which can becovered by BS(b) Do in nonincreasing order of theevaluation value until a BS isselected.

For BS ,If Tabu_Time Current_Iteration,

select the BS .Else if , select the BS .Otherwise repeat for the next BS in

the order.(c) Move the selected BS from Candi-date_List to Active_List.

Set Tabu_Time Current_Iteration, Move_Freq Move_Freq .

(d) Go to Step 7.

Step 7. Reassignment after Add Move(a) For a new BS which is moved into Ac-tive_List

If new is the largest amongfor each TDA and BS in Active_List andRC(new) then

set (TDA is covered by newBS), RC(new) RC(new) ,

(TDA is not covered by oldBS), and RC(old) RC(old) .(b) Go to Step 4.

Step 8. Updating Solution(a) Compute the New_Solution_Value

(b) Set Active_Freq Active_Freqfor BS’s in Active_List.(c) If New_Solution_Value Best_Solu-tion_Value,

set Best_Solution_Value New_Solu-tion_Value, NoImprove and go to Step3.

Otherwise NoImprove NoImprove ;

(d) If NoImprove Nmax, then go to Step3.(e) If NoImprove Nmax and Best_Solu-tion_Value Record_Solution_Value,

set Record_Solution_Value Best_So-lution_Value and Best_Solution_Value

.(f) If Diversification Dmax, go toStep 9.

Otherwise STOP.Step 9. Diversification

(a) Two diversification strategies areperformed.

(i) Capacity Diversificationunit capacity variation in a

BS, unit cost variation in a BS;the number of units increased or

decreased ;Consider RC of BS’s in the

Best_Solution of the previous path.If RC and ,

and .If RC and ,

and .(ii) Coverage Diversification

Sort all new BS’s in nondecreasingorder of Move_Freq Active_Freq andstore the BS’s in Diverse_List.

Set Active_List .While the solution infeasible, move

BS’s one by one from Diverse_List to Ac-tive_List.(b) Set NoImprove , Move_Freq ,Active_Freq for .(c) Set Diversification Diversifica-tion .(d) Go to Step 3.

In the above procedure, notice that the main computationalburden occurs in Step 4 when TDAs are reassigned after a Dropmove. For each TDA the procedure sorts base stations innonincreasing order of received power. This procedure requires

steps. Since the ordering is performed for TDAspreviously covered by the dropped base station, the overall com-plexity reduces to in the worst case.

IV. COMPUTATIONAL RESULTS

In this section, we test the efficiency of the proposed algo-rithm for the cell planning with capacity expansion. The algo-rithm described in the previous section was implemented in Vi-sual C (Version 5.02), and run on a 200 MHz Intel Pen-tium based personal computer with 64 Mbyte of memory underWindows 95. We assume that all TDAs are square, as shown inFigs. 2 and 6. The traffic demand at each TDA has uniformly dis-tributed with integer values (in Erlang) over [1], [6], in AMPSand [1], [9] in CDMA. The locations of candidate base stationsare randomly generated.


Fig. 2. Received power levels in AMPS.

To compare the performance of the proposed tabu search,Parallel Genetic Algorithm (PGA) with island model is consid-ered. 500 chromosomes are divided into five islands and evolveduntil the best fitness at each island is equal to the average fit-ness of the island. At the end of each generation, the best solu-tion is copied to the next island. To represent the chromosomeGrouping GA [17] is employed which is known to be superiorin grouping problems including set covering. Each string hastwo parts: TDA part and BS part. In TDA part a base stationis assigned to each TDA. The base stations employed in theTDA part are then represented in the BS part. The superiorityof Grouping GA over standard GA is mainly due to group-ori-ented operators. Group-oriented crossover and mutation [17] areapplied to the chromosome. Tournament selection is performedto generate a population for the following generation.

A. Test on AMPS System

The capacity of each new base station is assumed 46 Erlangsas in Section II-A. The size of a TDA is assumed mwith traffic demand distributed uniformly over Er-langs.

The received power at BS from TDA is simplifiedas follows: Using the propagation model in Section II-B the cov-erage radius by a base station is computed which satisfies the re-ceiver sensitivity at the base station. For example, with receiversensitivity 112 dBm, the transmission power of a mobile is28 dBm ( mW), dB, dB, m,

m, and dB, the radius is computed askm from the propagation model.

In Fig. 2, the received power at the base station located inthe center is represented with ten different levels depending onthe location of each TDA. The ten levels are discretized de-pending on the received power such that level 1 corresponds to[ 112 dBm 110 dBm] and level 10 to [88 dBm ].

Now, we first test two initial solution strategies: 1) All Candi-date Base Stations and 2) Random Feasible Base Stations. Prob-lems of TDAs are tested for three different cases of cov-erage factor, i.e., and 0.99. For each case, teninstances are experimented and the average is shown in Fig. 3.As shown in the figure, the method of Random Feasible BaseStations is superior to that of All Candidate Base Stations inview of computational time. The solution quality seems to be

almost same in all three cases. Tabu parameters used in the testare chosen from the following experiments.

Before solving the cell planning problem we test the perfor-mance of tabu parameters: Tabu-Time size, , and .Tabu-Time size represents the number of iterations during whicha base station is not allowed to be added or dropped.represents the number of consecutive iterations allowed for thesearch to continue without cost improvement. A diversificationprocedure is followed if no cost improvement is obtained duringthe iterations. is the stopping criterion whichrepresents the number of diversifications in the search process.

Our test shows that the Tabu-Time size is dependent on thetabu list and problem size. In the test, since the size of Can-didate_List is larger than that of Active_List, it is clear thatTabu_Time size of a base station in the Candidate_List needsto be larger than that in the Active_List.

Larger Tabu-Time size showed better performance as theproblem size (number of TDAs to cover) increases. Test resultshows that the following pair of Tabu-Time sizes in Active_Listand Candidate_List are appropriate: ( ) for problems with

TDAs, ( ) for TDAs and ( ) forTDAs.

The test result of is presented in Fig. 4. By assumingthat an appropriate value of is proportional to thenumber of candidate base stations, test is performed forfive different values. Fig. 4 shows that isappropriate in view of iterations and objective function values.

The number of diversifications in tabu search is deeply re-lated to the solution quality. The test on is performedfor three different values of coverage factor. For each case, 50problems are experimented to determine the value of . Ineach case of , the portion among fifty problems which gives nofurther improvement for increased value of is plotted.Fig. 5 shows that the number of required diversifications in-creases with the increase of coverage factor. From the figure,it seems to be reasonable to perform 1, 3, and 5 diversificationsfor the coverage factor , 0.95, and 0.99, respectively.

Tables I–III show the performance of the proposed tabu searchwith operators and parameters obtained in the preliminary tests.CPLEX [16] is used to obtain optimal solutions. The parallel GAis also experimented. Since our attention is focused on the solu-tion quality, the PGA is run until the best solution at each islandbecomes equal to the average fitness of the island. The numberof new base stations and computational times are presented inthe tables. The performance of the proposed tabu search is out-standing for problems with coverage factors and .The gap from the optimal solution is approximately %even in problems with 900 TDAs. The gap is slightly increasedto % in problems with 900 TDAs with coverage factor

. The parallel GA gives near optimal solution in prob-lems with 100 TDAs. However, the performance is degraded asthe problem size increases. The gap from the optimal solution ap-proaches 20% in problems with 900 TDAs.

B. Test on CDMA System

The system capacity of CDMA is usually known to betimes of AMPS [1]. It means that CDMA is appropriate for the


Fig. 3. Test of initial feasible solutions.

Fig. 4. Test ofN max in problems with20 � 20 TDAs.

Fig. 5. Test ofDmax on problems with20 � 20 TDAs.

increased dense traffic area with microcells. We thus assumethat the size of a TDA is m with traffic demand dis-tributed uniformly over Erlangs.

The received power at a base station can be computed as in theAMPS of Section IV-A. Due to the reduced cell size, the trans-mission power of a mobile is reduced to mW as in PCS phones.

In Fig. 6, the received power at the base station located inthe center is represented with 15 different levels. The 15 levelsare discretized depending on the received power such that level

1 corresponds to [112 dBm 111 dBm] and level 15 to[ 76 dBm ].

For the capacity of base stations, we assume each existing basestation uses four FAs which is equal to 345 Erlangs. The capacityof each new base station is assumed to have either two, three, orfourFAs,whichcorrespond to 165,255, and 345Erlangs, respec-tively. Since the cost of a base station consists of fixed and vari-able parts, we assume the cost of base station to be six, eight, andten, respectively, for the two, three, and four FAs.


Fig. 6. Received power levels in CDMA.

TABLE ICOMPUTATIONAL RESULTS WITH10 � 10 TDAS

As in AMPS, the strategy of Random Feasible Base Stationsis employed to have initial feasible solution. Tabu-Time sizesin Active_List and Candidate_List are selected as (), ( ),and ( ) for problems with , , andTDAs, respectively.

In addition to the above fixed tabu time, we test the perfor-mance of dynamic tabu time. A sequence of Tabu-Time (),( ), and ( ) are repeatedly employed in problems with

TDAs. ( ), ( ), and ( ) for and ( ),( ), and ( ) for are tested. Fig. 7 shows the dy-


TABLE IICOMPUTATIONAL RESULTS WITH20 � 20 TDAS

TABLE IIICOMPUTATIONAL RESULTS WITH30 � 30 TDAS

namic tabu tenure is slightly better than the fixed one with rea-sonable increase of tabu iterations. We thus employ dynamictabu tenure in the tests to follow.

The test results on and are shown in Figs. 8and 9, respectively. Fig. 8 shows that diversification with ca-pacity change gives best performance. In other words, the per-


Fig. 7. Test of fixed/dynamic tabu tenure strategies

Fig. 8. Test ofN max in problems with30 � 30 TDAs.

Fig. 9. Test ofDmax in problems with30� 30 TDAs.

formance of tabu search is increased with the diversificationwhich increases or decreases the capacity of a new base sta-tion depending on the current usage of the capacity. When thecapacity of a base station is fully employed, the capacity is in-creased by 1 FA, and the residual capacity is decreased by 1 FA.The effectiveness of the restarting strategy is also illustrated inthe figure. Better solutions are obtained by starting base stationswith least frequencies in the old solutions and moves. Diversi-fication is performed when no functional improvement is ob-tained for consecutive iterations.

The number of diversifications required to stop tabu search islargely dependent on the problem complexity. The difficulty of aproblem is increased with the increase of traffic coverage factor.From Fig. 9 the reasonable number of diversifications seams tobe 9, 12, and 15, respectively, for , , and .

Tables IV–VI show the computational results of tabu searchfor problems under CDMA system. For problems with 400TDAs tabu search provides solutions which are within 5%from the optimal even in case of . However, inmost problems with 900 and 2500 TDAs, we failed to obtain


TABLE IVCOMPUTATIONAL RESULTS WITH20 � 20 TDAS

TABLE VCOMPUTATIONAL RESULTS WITH30 � 30 TDAS

optimal solutions with CPLEX within the CPU time limitof 10 000 s. Fortunately in problems with 900 TDAs, theproposed tabu search provides optimal solutions in almost allcases of and . Solutions by the tabu search

match with the lower bounds by CPLEX. For thegap from the lower bound is approximately 15% in 900 TDAs.In problems with 2500 TDAs, the gaps from the lower boundsare 1%, 5%, and 15%, respectively, for , , and


TABLE VICOMPUTATIONAL RESULTS WITH50 � 50 TDAS

. Note that the gaps remain same in problems with 900and 2500 TDAs.

The performance of the parallel GA is not promising com-pared to the proposed tabu search. In many problems the PGAfails to meet the coverage factor, which is due to the penaltymethod used in GA to handle the constraints in the problem.Moreover, the gaps from the lower bounds are 28–30% for prob-lems with 2500 TDAs regardless of the coverage factor.

V. CONCLUSION

Cell planning problem with capacity expansion is examinedin wireless communications. The problem decides the locationand capacity of each new base station to cover expanded and in-creased traffic demand. The objective is to minimize the cost ofnew base stations. The coverage by the new and existing basestations is constrained to satisfy a proper portion of traffic de-mands. The received signal power at the base station also hasto meet the receiver sensitivity. The cell planning is formulatedas an integer linear programming problem and solved by a tabusearch algorithm.

In the tabu search intensification by add and drop move is im-plemented by short-term memory embodied by two tabu lists:Candidate_List and Active_List. Different tabu times are ap-plied to the base stations to add among those in the Candi-date_List and to drop in the Active_List. Two diversificationstrategies are employed to explore new solution space. The ca-pacity diversification is designed to investigate proper capacitiesof new base stations. The capacity of each new base station isincreased or decreased depending on the usage of the capacity.The coverage diversification restarts the tabu search from new

assignment of bast station locations. It is implemented by exam-ining the base stations with least frequencies in the old solutions.

Computational experiments of the proposed tabu search areperformed for the cell planning problems in two different envi-ronments: AMPS and CDMA system. The proposed procedureillustrates outstanding performance in AMPS. The gap from theoptimal solution is % for coverage factor and0.95. The gap is slightly increased to % in problems with900 TDAs with . Compared to the PGA %cost reduction is obtained by the tabu search in problems with900 TDAs.

Test on CDMA shows that two diversification strategies arehighly effective. Compared to the no diversification 6% cost re-duction is obtained by the coverage diversification and 10% byboth the coverage and capacity strategies. In problems with 400TDAs tabu search provides solutions which are within 5% fromthe optimal even in case of . The proposed proce-dure presents optimal solutions in almost all instances of 900TDAs with and 0.95. The gap from the lower boundis approximately 15% in problems with . However, thegap remains same in problems of 2500 TDAs with ,which shows the robustness of the proposed tabu search. Theproposed tabu search also outperforms the PGA. Approximately

% cost reduction is obtained in problems with 2500TDAs.

REFERENCES

[1] T. S. Rappaport,Wireless Communications. Englewood Cliffs, NJ:Prentice-Hall, 1996.

[2] W. C. Y. Lee, Mobile Cellular Telecommunications Systems. NewYork: McGraw-Hill, 1989.


[3] F. Glover, “Tabu search,”ORSA J. Comput., vol. 1, no. 3, pp. 190–206,Summer 1989.

[4] E. Rolland, H. Pirkul, and F. Glover, “Tabu search for graph parti-tioning,” Ann. Oper. Res., vol. 63, pp. 209–232, 1996.

[5] H. D. Sherali, C. M. Pendyala, and T. S. Rappaport, “Optimal locationof transmitters for microcellular radio communication system design,”IEEE J. Select. Areas Commun., vol. 14, no. 4, pp. 662–673, 1996.

[6] B. Chamaret, S. Josselin, P. Kuonen, M. Pizarroso, B. Salas-Manzanedo,S. Ubeda, and D. Wagner, “Radio network optimization with maximumindependent set search,”IEEE VTC, pp. 770–774, 1997.

[7] P. Calegari, F. Guidec, P. Kuonen, and D. Wagner, “Genetic approachto radio network optimization for mobile systems,”IEEE VTC, pp.755–759, 1997.

[8] P. Calegari, F. Guidec, P. Kuonen, and D. Kobler, “Parallel island-basedgenetic algorithm for radio network design,”J. Parallel Distrib.Comput., vol. 47, pp. 86–90, 1997.

[9] K. Tutschku, “Demand-based radio network planning of cellular com-munication systems,” inProc. IEEE Infocom’98, 1998, pp. 1054–1061.

[10] C. Yu, S. Subramanian, and N. Jain, “CDMA cell site optimization usinga set covering algorithm,” inProc. 8th Int. Network Planning Symp.,1998, pp. 75–78.

[11] M. R. Garey, D. S. Johnson, and L. Stockmeyer, “Some simplifiedNP-complete graph problems,”Theor. Comput. Sci., vol. 1, pp.237–267, 1976.

[12] K. Tutschku, “Interference minimization using automatic design of cel-lular communication networks,”IEEE VTC, pp. 634–638, 1998.

[13] M. H. Wright, “Optimization methods for base station placement inwireless application,”IEEE VTC, pp. 387–391, 1998.

[14] The CDMA Network Engineering Handbook, vol. 1, Qualcomm, Mar. 1,1993.

[15] 1994 CDMA Forum, San Diego, CA, 1994.2.28.-3.1.[16] CPLEX 4.0, CPLEX Optimization Inc., 1998.

[17] E. Falkenauer, “A new representation and operators for genetic algo-rithms applied to grouping problems,”Evolutionary Computation, vol.2, no. 2, pp. 123–144, 1994.

Chae Y. Lee(M’93) received the B.S. degree in in-dustrial engineering from Seoul National University,Seoul, Korea, in 1979 and the M.S. and Ph.D. de-grees in industrial engineering from Georgia Instituteof Technology, Atlanta, in 1981 and 1985, respec-tively.

He is a Professor of Industrial Engineeringat the Korea Advanced Institute of Science andTechnology (KAIST), Taejon, Korea. His researcharea includes mobile communication systems, datacommunications, and heuristic search.

Dr. Lee is a member of INFORMS.

Hyon G. Kang received the B.S. degree in mathe-matics in 1996 and the M.S. degree in industrial engi-neering in 1998, both from Korea Advanced Instituteof Science and Technology (KAIST), Taejon, Korea,where he is currently a doctoral candidate in indus-trial engineering.

He is interested in heuristic search, cell planning,and operation management of mobile communicationsystems, and data communications in Mobile IP.

cell planning with capacity expansion in mobile communications: a tabu search approach

Documents