Neural Network Algorithms for the p-Median Problem

In this paper three recurrent neural network algorithms are proposed for the p-median problem according to different techniques. The competitive 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 analyzed. The results indicate that the best technique depend on the scale of the problem and the number of medians.