A recurrent neural network model for the p-hub problem

Abstract

The p-hub problem is a facility location problem that can be viewed as a type of network design problem. Each node, within a given set of node, sends and receives some type of traffic to and from the other nodes. The hub location must be chosen from among these nodes to act as switching points for the traffic. Hubs are facilities that serve as transshipment and switching points for transportation and telecommunication systems with many origins and destinations. In this paper we consider the uncapacitated, single allocation, p-hub median problem. In the single allocation, each nonhub node must be allocated to exactly one of the p hubs. We provide a reduced size formulation and a competitive recurrent neural model for this problem. The neural network consists of a two layers (allocation layer and location layer) of np binary neurons, where n is the number of nodes and p is the number of hubs. The process units (neurons) are formed in groups, where one neuron per group is active at the same time and neurons of different groups are updated in parallel. Computational experience with another neural networks is provided using the data given in the literature.