Optimization with neural networks: a recipe for improving convergence and solution quality

Abstract

Artificial Neural Networks, particularly the Hopfield Network have been applied to the solution of a variety of tasks formulated as optimization problems. However, the network often converges to invalid solutions, which have been attributed to an improper choice of parameters and energy functions. In this letter, we propose a fundamental change of viewpoint. We assert that the problem is not due to the bad choice of parameters or the form of the energy function chosen. Instead, we show that the Hopfield Net essentially performs only one iteration of a Sequential Unconstrained Minimization Technique (SUMT). Thus, it is not surprising that unsatisfactory results are obtained. We present results on an SUMT-based formulation for the Travelling Salesman Problem, where we consistently obtained valid tours. We also show how shorter tours can be systematically obtained.