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Proceedings of GO 2005, pp. 199 – 206.GASUB: A genetic-like algorithmfor discrete location problems ∗Blas Pelegrín, 1 Pascual Fernández, 1 Juani L. Redondo, 2 Pilar M. Ortigosa, 2 and I. García 21 Dpt. Statistics and Operational Research, University of Murcia, Spain, {pfdez,pelegrin}@um.es2 Dpt. Computer Architecture and Electronics, University of Almería, Spain, {inma, pilar, juani}@ace.ual.esAbstractKeywords:We propose a new genetic-like algorithm, GASUB, for finding solutions to different facility locationproblems which are hard to solve. We deal with the p-median problem, the maximum capture ,and the location-price problem with delivered prices. In each one of them, a given number s of facilitylocations must be selected in a set of potential locations, containing m location points, so as tooptimize a predetermined fitness function. Although these problems can be formulated as integerlinear optimization problems, they can only be solved by standard optimizers for moderately smallvalues of s and m. GASUB is compared with MSH, a multi-start substitution method widely usedfor location problems. Computational experiments with location-price problems (the ones with themore complex fitness function) show that GASUB obtains better solutions than MSH. Furthermore,the proposed algorithm finds global optima in all tested problems, which is shown by solving thoseproblems by Xpress-MP, an integer linear programming optimizer [11].Combinatorial optimization, Discrete location problems, Stochastic algorithms.1. IntroductionLocation models have been developed to help decision makers in a variety of situations inwhich new facilities have to be located to serve a set of users which are aggregated in a givennumber of demand points (see [5]). These models can be classified in two big groups: Noncompetitivemodels and Competitive models, depending on a single player in the market isconsidered or more than one. A detailed taxonomy can be found in the survey papers [3, 8].In a non-competitive environment, the most important objective is minimization of transportationcosts, which are due to the interaction between users and facilities, being the p-MEDIAN problem the basic model for many distribution systems (see [2]). In a competitiveenvironment, firms compete for users and the usual objective is profit maximization. Since usersare supposed to buy at the cheapest facility, strategic decisions on location and price have tobe made. Firms normally use either a mill price or a delivered price policy. Under mill pricing(the seller sets a factory price, equal for all the customers in the market, and the buyer takescare of carriage). A basic model is MAXCAP (see [10]) in which a common mill price is setby all competing firms; there is a finite set of possible facility locations; and the objective ismarket share maximization (which is equivalent to profit maximization in this setting). Underdelivered pricing (the seller charges a specific price in each market area, which includes thefreight cost, and takes care of transport), there exist equilibrium prices that are determined by∗ This research has been supported by the Ministry of Science and Technology of Spain under the research projects BEC2002-01026 and CICYT-TIC2002-00228, in part financed by the European Regional Development Fund (ERDF). We are very gratefulwith Dashoptimization for providing aXpress-MP license for testing.