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206 Blas Pelegrín, Pascual Fernández, Juani L. Redondo, Pilar M. Ortigosa, and I. GarcíaFigure 2 shows four comparative graphics with computational results of the problems fordifferent values of the number of pre-existing facilities (q = 2, 4, 6, 8). Each graphic shows theaverage value of computational time (varying t) required for MSH and GASUB, for the fivevalues of s (2, 4, 6, 8, 10). For cases where MSH doesn’t find the solution at all runs, we havedrawn a circle and the corresponding percentage of success on finding the global solution(below 100%). Note that these are average values for different values of t. For those caseswhere GASUB finds the two optima we have drawn a square.5. Conclusions and future researchWe have shown some basic discrete location problems which can be solved, exactly and approximately,by the same type of algorithms. Then we have proposed a genetic-like heuristic,GASUB, to deal with large instances of these problems. This algorithm has been comparedwith an optimizer, Xpress-MP, and a well known heuristic used for many location problems,MSH. For this, 125 instances of MAXPROFIT have been solved by the three algorithms. Computationalexperiments show that optimal locations can also be obtained by the heuristics.MSH obtained optimal locations in 20% of the solved problems, while GASUB always foundoptimal locations in the tested problems. An additional advantage of GASUB is that this algorithmcan generate more than one global optimum (in 8 out of the 125 solved problems),the contrary happens with MSH and Xpress-MP which obtain only one optimum. Computationaltimes for both heuristics increase significantly when the s value increases, which isexplained by the fact that the number of location combination exponentially increases whenthe parameter s increases.As future research we will conduct more experiments with instances of the three mentionedmodels and we will compare GASUB with another genetic algorithm. Furthermore, a parallelizationof GASUB will be investigated in order to reduce computational times.References[1] G. Cornuejols, M.L. Fisher, and G.L. Nemhauser. Locations of bank accounts to optimize float: An analyticalstudy of exact and approximate algorithms. Management Science, 23:789–810, 1997.[2] M.S. Daskin. Network and Discrete location: Models, Algorithms and Applications. Dis Wiley, 1995.[3] H.A. Eiselt, G. Laporte, and J.F. Thisse. Competitive location models: a framework and bibliography. TransportationScience, 27:44–54, 1993.[4] P. Fernández, B. Pelegrín, M.D. García, and P. Peeters. A discrete long-term location-price problem under theassumption of discriminatory pricing: Formulations and parametric analysis. European Journal of OperationsResearch, pages –, 2005. forthcoming.[5] R.L. Francis, T.J. Lowe, and A. Tamir. Demand point aggregation for location models. In Z. Drezner andH. Hamacher, editors, Facility Location: Application and Theory, pages 207–232. Springer, 2002.[6] M.D. García, P. Fernández, and B. Pelegrín. On price competition in location-price models with spatiallyseparated markets. TOP, 12(2):351–374, 2004.[7] S.L. Hakimi. On locating new facilities in a competitive environment. European Journal of Operations Research,12:29–35, 1983.[8] H.W. Hamacher and S. Nickel. Classification of location models. Location Science, 13:229–242, 1998.[9] P.M. Ortigosa, I. García, and M. Jelasity. Reliability and performance of UEGO, a clustering-based globaloptimizer. Journal of Global Optimization, 19(3):265–289, 2001.[10] D. Serra and C. ReVelle. Competitive location in discrete space. In Z. Drezner, editor, Facility Location: ASurvey of Applications and Methods, pages 367–386. Springer, 1995.[11] Xpress-MP. Dashoptimization, 2004.