Neural Network Algorithms for the p-Median Problem E. Dom´ ınguez Merino, J. Mu˜ noz P´ erez and J. Jerez Aragon´ es Department of Computer Science, E.T.S.I.Informatica Campus Teatinos s/n, 29071 University of Malaga – Malaga, Spain Abstract. In this paper three recurrent neural network algorithms are proposed for the p-median problem according to different techniques. The competi- tive recurrent neural network, based on two types of decision variables (location variables and allocation variables), consists of a single layer of 2Np process units (neurons), where N is the number of demand points or customers and p is the number of facilities (medians). The process units form N + p groups, where one neuron per group is active at the same time and neurons in the same group are updated in parallel. Moreover, the energy function (objective function) always decreases as the system evolves according to the dynamical rule proposed. The effectiveness and efficiency of the three algorithms under varying problem sizes are ana- lyzed. The results indicate that the best technique depend on the scale of the problem and the number of medians. 1 Introduction The traditional location problem is concerned with the location of one or more facilities, in some solution space, so as to optimize some specified criteria. The p-median problem concerns the location of p facilities (medians) in order to minimize a weighted sum of the distance from each node (population center or customer) to its nearest facility. Kariv and Hakimi [7] showed that the p-median problem on a general network is NP-hard. A number of solution procedure have been developed for general networks. Most of the proposed procedures have been based on mathematical program- ming relaxation and branch-and-bound techniques. However, recently have been developed new procedure based on tabu search, neural networks, tree search and heuristic techniques. Thus, some proposed procedures include tree search (Christofides and Beasley [1]), lagrangian relaxation with branch & bound (Galvao [4], Erlenkotter [3]), tabu search (Ohlem¨ uller [8])as well as ESANN'2003 proceedings - European Symposium on Artificial Neural Networks Bruges (Belgium), 23-25 April 2003, d-side publi., ISBN 2-930307-03-X, pp. 385-391