Soft-computing based heuristics for location on networks: The p-median problem

We propose a genetic algorithm for the fuzzy p-median problem in which the optimal transport cost of the associated crisp problem is unknown. Our algorithm works with two populations: in one, the solutions with a better crisp transport cost are favored by the selection criterion, whereas in the second one, solutions with a better fuzzy satisfaction level are preferred. These populations are not independent. On the contrary, the first one periodically invades the second one, thus providing new starting points for finding fuzzy improvements.Our computational results also reveal the importance of choosing adequate functions for selecting the parents. Our best results are obtained with functions which are more sensitive to both objectives (crisp and fuzzy) and by increasing the invasion and mutation rates. We compare these results with other heuristic procedures.