A Method for the Travelling Salesman Problem by Controlling two Parameters of the Hopfield Neural Network

Abstract

When the travelling salesman problem (TSP) is solved by the Hopfield Neural Network with analog output, it is difficult to determine two parameters of its energy function, that is, a penalty factor and a temperature. In this paper, by numerical experiments, we investigate the influence of both parameters upon the quality of _??_ solutions, and propose a method where the penalty factor is controlled so as to obtain a feasible solution and the temperature is optimized by the golden section search.
Computational results for the TSPs with random 5_??_40 cities, the proposed method improves the quality of the solution by 48% on the average, compared with the conventional method.