Eighth International Conference on Hybrid Intelligent Systems. Barcelona, 10-12 September 2008The goal of this paper is twofold. First, we want to make a study about how evolutionary computation techniques can efficiently solve the radio network design problem. For this goal we test several evolutionary computation techniques within the OPLINK experimental framework and compare them. Second, we propose a clustering approach and a 2-OPT in order to improve the results obtained by the evolutionary algorithms. Experiments carried out provide empirical evidence of how clustering-based techniques help in improving all algorithms tested. Extensive computational tests, including ones without clustering and 2-OPT, are performed with three evolutionary algorithms: genetic algorithms, memetic algorithms and chromosome appearance probability matrix algorithms.Publicad

Isasi, Pedro

Sáez Achaerandio, Yago

Zazo, Fernando

English

Sáez, Yago

Name not available

A study of the effects of clustering and local search on radio network design: evolutionary computation approaches

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A Study of the Effects of Clustering and Local Search on Radio Network Design: Evolutionary Computation Approaches

Universidad Carlos III de Madrid e-Archivo

A Study of the effects of clustering and local search on Radio Network Designevolutionary computation approachesY. Saez, F. Zazo, P. Isasi,Departamento de Informa´tica, Inteligencia Artificial, Universidad CARLOS III de MadridAve. de la Universidad 30 Legane´s 28911, SPAINyago.saez@uc3m.es, fernando.zazo@alumnos.uc3m.es, isasi@ia.uc3m.esAbstractThe goal of this paper is twofold. First, we want to makea study about how evolutionary computation techniques canefficiently solve the radio network design problem. For thisgoal we test several evolutionary computation techniqueswithin the OPLINK experimental framework and comparethem. Second, we propose a clustering approach and a 2-OPT in order to improve the results obtained by the evo-lutionary algorithms. Experiments carried out provide em-pirical evidence of how clustering-based techniques help inimproving all algorithms tested. Extensive computationaltests, including ones without clustering and 2-OPT, are per-formed with three evolutionary algorithms: genetic algo-rithms, memetic algorithms and chromosome appearanceprobability matrix algorithms.1 IntroductionThe extraordinary success of radio mobile telecommu-nication systems has led service providers to dynamicallyadapt network infrastructures to continuously increasing de-mand. As the demand of the Personal Communication Ser-vices (PCS) is increasing, capacity has now become a criti-cal issue for all of these services. In response, all of the mo-bile service operators are investigating different techniquessuch as cell splitting, allocation of new spectrum (digi-tal switchover), alternative access architectures or dynamicchannel allocation. The design of large cellular networksis a complex problem with a large impact on the deploy-ment costs, the availability and coverage, and the quality ofservice. In this scenario, the optimal selection of base sta-tions (BSs) sites and the use of optimal frequency planningmethods becomes imperative. As we know, the engineer-ing of radio mobile telecommunication networks presentsbasically two problems: the radio network design problem(RND) and the frequency assignment problem (FAP) [11].In this paper, we address the first, the RND problem.2 The radio network problemThe RND problem, also known as the antenna or BSplacement problem (APP) can be informally described asfollows: given a set of candidate places for antennas, theproblem consists of deciding on the best positioning of BSsin order to accomplish some objectives and constraints. Al-though different versions can be defined for the RND, themost usual objectives are maximizing the coverage whileminimizing the number of antennas used. The constraintsconcern a large number of predefined candidate positions,the number of BSs needed, the population density, pecu-liarities of the terrain, bandwidth requirements, handoverareas, etc. This problem has been tackled in literature bydifferent approaches, [5], [13], [14], [6], [17], [9]. Onlya few attempts are known whose approach is an analyticformulation of the complete RND problem, [8]. In gen-eral, the analytical models show great improvement over theclassical geometry-oriented designs, however, as the size ofthe search space for the complete problem was enormous(exponential), it was impossible to carry out a optimiza-tion. Therefore, computational numerical methods were re-quired, [18], i.e. software tool GRAND, [7].3 The OPLINK domainThe instance of the RND problem used in this paper canbe found in [1],[12]. It belongs to a Technology and ScienceCouncil project called OPLINK and it makes the followingassumptions:- Geographic information about the terrain: in this do-main a rectangular area modelled by a grid of 4.25 x 6.4kilometers is used. Each cell represents approximately 15x 15 meters. The grid is extracted from real data aboutEighth International Conference on Hybrid Intelligent Systems978-0-7695-3326-1/08 $25.00 © 2008 IEEEDOI 10.1109/HIS.2008.99951Authorized licensed use limited to: Univ Carlos III. Downloaded on March 26, 2009 at 10:49 from IEEE Xplore.  Restrictions apply.the city of Malaga, Spain. It can be downloaded fromhttp://oplink.unex.es.- Information about the BSs: in this domain the antennatype is omnidirectional (circular) with radio 450 meters.For the coverage calculation parameters such as transmittedpower, height, tilt, azimuth, or signal propagation (strength,noise, obstacles, etc.) are not taken into account.- Information about aims: the objective function is cal-culated through equation 1 and is imposed by the project inorder to normalize the results obtained by different institu-tions.Fitness =(coverage)2number of base stations(1)As can be seen, even when relaxing the problem, thereis still a complex task to solve since there are one thousandcandidate positions for the BSs, which means a large searchspace of 21000  1.07 ∗ 10301.4 Evolutionary computation for radio net-work design problemsAs mentioned before, the OPLINK environment is acomplex NP-hard optimization problem with a large searchspace. Evolutionary Computation (EC) techniques are well-known for their performance when solving this kind ofcomplex problems, and it is not the first time evolution-ary algorithms have been applied to solve this problem, [2].This paper concentrates on three evolutionary computationtechniques: genetic algorithms (GAs), memetic algorithms(MAs) and chromosome appearance probability matrix al-gorithms (CAPMs). Starting from these techniques we pro-pose two ideas which can improve the results of the tech-niques tested: clustering the BSs and performing a 2-OPTsearch.4.1 ClusteringThe imperative objective in this domain is to maxi-mize the coverage and to minimize the number of antennasneeded. Therefore, if we make an antenna clustering be-fore the search, and we permit only one active antenna percluster, we are minimizing the overlapping between anten-nas without causing negative effects in the solutions. Theclustering technique used is the simple k-means [10] be-cause it is simple to use and very well-known. In the Figure1 a real distribution of 70 clusters is represented over thecity of Malaga. To compare the results found by the simplek-means an expectation maximization(EM) technique hasbeen also developed. The distribution of clusters with theEM is very similar and no relevant differences were foundbetween both methods.Figure 1. Distribution for 70 clusters with sim-ple k-means (Malaga city)4.2 2-OPT SearchAll the proposed algorithms give their best solution forthe problem. But we consider it useful if a lightweight al-gorithm can check if it is possible to improve the fitness ofthe final solution. The 2-OPT search is a well-known lo-cal search algorithm first proposed by Croes in 1958 [3].Basically it consists of looking for neighbor solutions ina specific layout of transmitters. This search is done se-lecting two antennas under defined proximity criteria andtesting all possible combinations around their neighbors foreach active antenna. The neighbor vector stores a numberof neighbor active antennas for each active antenna. Theneighbors are calculated with a distance matrix. Once theactive antennas are selected, all the possible combinationsof the neighbor vector are evaluated. If the solution is im-proved then the search starts from the new individual found.Once the neighbor vector is completed, then the stop criteriais checked (fitness has improved or the number of iterationsdesired has been completed). To show the importance ofhow these ideas can help to all these algorithms, we presenttwo set of experiments in Section 5, one with the raw ECtechniques (bit representation) and the other with the ECtechniques adapted to our proposals (clustered versions).4.3 Genetic AlgorithmIn the GA with cluster representation (GAC) an individ-ual has the same number of genes as clusters. A gene ismade of a list of transmitters in the cluster and the numberof the active transmitter. If there is a transmitter which isinactive it is selected by −1. The first step in the algorithmis to determine the clusters. We have used different cluster-ing methods but for experimental results the simple k-meansmethod was chosen. Once the clusters are found, the pop-ulation is randomly created and evaluated for the first time.952Authorized licensed use limited to: Univ Carlos III. Downloaded on March 26, 2009 at 10:49 from IEEE Xplore.  Restrictions apply.In each successive generation, part of the population is se-lected to breed the new offspring. The crossover does notneed to be changed: it is the same as in the canonical GA:simple and uniform. The mutation operator now changesthe active transmitter of a cluster randomly.4.4 Memetic AlgorithmThe memetic algorithm (MA) is a combination betweenlocal search (LS) techniques and evolutionary algorithms(EA). It is based on the concept of meme introduced byDawkins, [4]. The key idea of a meme is that an individualcan change his genetic code during his life thus improvingthe evolution process. To simulate this concept of meme anLS on the reproduction operators (crossover and mutation)is included. For many domains the MAs enhance the perfor-mance of the GAs. In contrast, LS methods are less genericand difficult to customize. They redefines the crossover andmutation operators proposed by the standard GA:- The crossover operator is similar to the one usedin the GA, but an LS is done in order to find the bestpossible crossover. The developed LS selects a prede-fined percentage of individuals randomly and then finds thebest crossover for those individuals. At this point, whencrossover is done, both parents are marked in order to avoididentical crossovers within the same iteration.- The mutation operator is the same as the one used inthe GA plus an LS. In this case, na LS is done to try to findthe best possible mutation. The operator first calculates thenumber of mutations for each individual and then makes anLS limited to blocks of 2 genes. The size of the block canbe changed and is determined depending on an admissiblecomputational cost.The other decisions about evaluation, selection and stopcriteria are the same as the ones used for the GA.4.5 Chromosome Appearance ProbabilityMatrix ClusteredThe Chromosome Appearance Probability Matrixmethod (CAPM) is GA modified in order to deal withmicropopulations. Basically, it consists of a GA which usesa probability matrix which drives the mutation towardsthe solution, speeding up the convergence during thefirst generations. It includes a statistical-driven mutationoperator and a clone remover operator. The CAPM methodis less accurate than GAs, however, because on average, itconverges faster. This is because the CAPM method hasmore selective pressure and reduces the effect of random-ness in the mutation operator. All steps are explained indetail in [16] and [15]. In this approach, the probabilitymatrix will have the same dimensions as the number ofclusters determined by the simple k-means. This numberdepends on the problem, but for the city of Malaga instanceno more than 100 clusters were found in all executions.5 Experimentation and ResultsThe first set of experiments with the raw EC techniques(bit representations) shows that the problem is not easy tosolve. The Genetic Algorithm (GA) achieves better resultsthan the Memetic Algorithm (MA) and the ChromosomeAppearance Probability Matrix (CAPM) is not a feasibleapproach. The results achieved by both algorithms could beimproved with more generations. TheMA has a slower evo-lution than the GA because it has a high local search cost.If we observe Table 1, we can see how the average fitnessis better for the GA during all iterations until the 2-OPT isrun. The standard deviation (σ) is also lower for the GA;this is because in the MA, the convergence is sometimespremature. Finally, all the results given by the algorithmsare refined with a 2-OPT search. The 2-OPT search im-proves the fitness and the standard deviation in almost alltested cases. In these experiments the 2-OPT improved theresults of the MA surpassing the best results found by theGA with 2-OPT. The CAPM is impossible to develop withbinary representation because the length of the chromosomeis 1, 000 bits and the size of the chromosome matrix is nottractable.GA MAEval. Average σ Average σ25000 138.72 2.037 101.31 3.96150000 140.74 1.280 107.92 3.914100000 142.85 1.730 120.29 4.257200000 145.57 1.313 132.42 2.459300000 147.13 1.840 137.67 1.678400000 148.24 1.735 140.09 1.814500000 149.47 2.155 141.54 1.885750000 151.33 1.784 143.98 1.9401000000 152.65 1.474 145.31 1.7632500000 156.27 1.447 151.63 1.6664750000 157.45 1.150 155.05 2.009(2-OPT) 161.38 1.028 162.54 0.532Table 1. Genetic algorithm and memetic algo-rithm results.The second set of experiments with the clustered ECtechniques achieves better results than the raw techniques,see Table 2. This is mainly because the search spacewhen working with clusters is significantly lower. TheGenetic Algorithm Clustered (GAC) improves all the re-sults obtained by the GA. The Memetic Algorithm Clus-tered (MAC) has the same problem as the MA. The MACdoes not achieve very good results because of the localsearch cost. It needs more evaluations to improve the fitnessachieved by the GA and the GAC. The Chromosome Ap-pearance Probability Matrix Clustered (CAPMC) is the bestduring the first 1, 000, 000 evaluations, because the statisti-cal oriented mutation performs surprisingly well. In fact, it953Authorized licensed use limited to: Univ Carlos III. Downloaded on March 26, 2009 at 10:49 from IEEE Xplore.  Restrictions apply.sometimes surpasses the results obtained by the GAC. Tak-ing into account that the CAPM works only with 10 indi-viduals its evolution and results are remarkable.GAC MAC CAPMCEval. Avg. σ Avg. σ Avg. σ25000 151.12 2.715 106.22 1.579 155.50 2.52350000 153.99 2.768 110.54 1.738 156.13 2.327100000 156.03 2.138 118.02 1.785 156.92 2.186200000 157.58 2.463 129.59 1.944 157.29 1.945300000 158.13 2.408 137.04 1.885 157.76 1.977400000 158.59 2.178 142.05 1.745 158.01 1.895500000 158.69 2.155 145.15 1.629 158.21 1.822750000 158.79 2.097 149.73 1.521 158.41 1.8661000000 159.00 2.172 152.12 1.665 159.11 1.8132500000 160.06 2.028 156.34 1.561 159.79 1.7744750000 160.68 1.994 157.68 1.504 160.78 1.5432-OPT 163.67 1.086 161,75 0,961 162.88 1.325Table 2. Comparison of GAC, MAC andCAPMC results (clustered versions).The 2-OPT search improves all the results achieved bythe algorithms with the exception of MAC. This happensbecause the local search on the MAC does a 2-OPT searchon each generation. The other algorithms outperform itsresults with a low cost technique. We recommend the 2-OPT search as an option to refine the solutions once theoptimization algorithm has finished. If we could only per-form 1, 000, 000 evaluations, the best algorithm would bethe CAPMC. The algorithm achieves high fitness at the be-ginning of the evolution. The best algorithm for 5, 000, 000evaluations is GAC, as it gets the highest average fitnessand in combination with 2-OPT, it achieves the best overallresult in all executions (164.72).6 Conclusions and Future WorkAnalyzing the RND problem in the selected instance andthe behavior of the proposed algorithms, we conclude thatthe clustering technique allows us to reduce the effectivesearch space without causing negative effects on solutions.In addition, the 2-OPT technique performs a final searchwhich may redefine the solution with low cost. The resultsobtained confirm that the algorithms tested perform betterwhen combined with clustering techniques, and that the 2-OPT is recommendable in all cases. However, for furtherdevelopments, other important issues must be considered,such as, different types of antenna, real propagation mod-els, the demand of the spot, the quality of service, or thehangover problem.References[1] E. Alba. Evolutionary algorithms for optimal placement ofantennae in radio network design. ipdps, 07:168, 2004.[2] E. Alba, M. A. Vega-Rodrı´guez, J. A. Go´mez-Pulido,D. Vega-Pe´rez, S.Priem-Mendes, and G. Molina. Differentevolutionary approaches for selecting the optimal numberand locations of omnidirectional bts in a radio network. InAlexis Quesada-Arencibia, et al. (Eds.). Eleventh Interna-tional Conference on Computer aided Systems Theory. EU-ROCAST, pages 292–294, Feb. 2007.[3] G. Croes. A method for solving traveling salesman prob-lems. Operations Research 6 (6), pages 792–812, 1958.[4] Dawkins, R. 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A high-capacity mobile radiotelephone system model using a coordinated small-zone approach. Vehicular Technology,

A method for solving traveling salesman problems.

A multiobjective genetic algorithm for radio network optimization.

An integrated approach to cellular radio network planning.

Cellular radio network planning.

Cellular system design using the expansion cell layout method. Vehicular Technology,

Cellular system design: An emerging engineering discipline.

Different evolutionary approaches for selecting the optimal number and locations of omnidirectional bts in a radio network.

Economic design of interference limited radiotelephone systems.

Evolutionary algorithms for optimal placement of antennae in radio network design. ipdps, 07:168,

Interactive evolutionary computation algorithms applied to solve rastrigin test functions.

Multiple radio zone plans in mobile radio systems. Vehicular Technology,

Optimal antenna placement using a new multiobjective chc algorithm.

Reference chromosome to overcome user fatigue in iec.

Remarks on radio network planning.

Some methods for classification and analysis of multivariate observations.

The effects of cochannel interference on the parameters of a small-cell mobile telephone system.

The selfish gene.

Isasi Viñuela, Pedro

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A study of the effects of clustering and local search on radio network design: evolutionary computation approaches

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