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GASUB: A genetic-like algorithm for discrete location problems 205jective function. This behavior is qualitatively different from genetic algorithms whichtypically run until a maximum number of function evaluations.4. Computational experimentsFor computational experiments we selected 1046 cities in Spain as nodes, and their populationsas demand. The geographic coordinates and population of each city was obtained fromhttp://www.terra.es/personal/GPS.2000 and http://www.ine.es, respectively. Distances were takenas the Euclidean distances between cities and each city demand was taken proportional to itspopulation. All cities were chosen as location candidates (the set J) in all test problems.In order to have an overall view on the performance of MSH and GASUB, we fixed p net = 1and generated different types of problems, varying the number of pre-existing facilities (q =2, 4, 6, 8, 10), the number of new facilities (s = 2, 4, 6, 8, 10) and the unit transportation cost(t = 0.001, 0.005, 0.01, 0.05, 0.1). These 125 problems were optimally solved by using Xpress-MP and their optimal values were used to evaluate the performance of both heuristics. All thecomputational results have been obtained under Linux on a Pentium IV with 3GHz CPU and2GB memory. The algorithms were implemented in C++.Results show that the parameter t practically doesn’t affect to the computational time, insuch a way that given fixed values for q and s, the required times to solve the problem aresimilar for different values of t. For this reason, graphics in Figure 2 showing the computationaltimes are average values from the computational times obtained for the different tvalues (0.001, 0.005, 0.01, 0.05, 0.1). Anyway it is interesting to remark that MSH do not getoptimal locations for some small values of t and high values of s. On the other hand, GASUBnot only finds the global solution for all runs of every problem but also finds more than oneexisting global optima. For instance, for q = 4 two global optima were found by GASUB.Computational results for q=2Computational results for q=4300300250MSHGASUB98%250MSHGASUB76%Computational time20015010098%84%Computational time20015010086%505002 4 6 8 10Number of new facilities ( s )300Computational results for q=602 4 6 8 10Number of new facilities ( s )300Computational results for q=8250MSHGASUB96%250MSHGASUB94%Computational time20015010084%Computational time20015010090%88%505096%98%02 4 6 8 10Number of new facilities ( s )02 4 6 8 10Number of new facilities ( s )Figure 2. Computational results for q=2, 4, 6, 8