A mixed-integer programming approach for optimal configuration of artificial neural networks

Abstract

A mathematical programming approach for automatic computation of the optimal configuration of artificial neural networks (ANNs) is presented. Training of the network is modelled as a mixed-integer program (MIP) where 0–1 binary variables are introduced to represent the existence (binary variable = 1) and non-existence (binary variable = 0) of the nodes and the interconnections between the nodes. The objective is to minimize the number of nodes and/or interconnections to meet a given error criteria. From modelling point of view, the key advantage of the proposed approach is that the user does not have to try different configurations of the network, a solution of the proposed MIP formulation automatically generates the optimal configuration of the network. From the implementation of ANN point of view, a simplified representation of the network is obtained, where redundant nodes and interconnections have been eliminated. A number of examples are presented to demonstrate the applicability of the proposed approach.