Parameter setting of the Hopfield network applied to TSP.

Abstract

The major drawbacks of the continuous Hopfield network (CHN) model when it is used to solve some combinatorial problems, for instance, the traveling salesman problem (TSP), are the non feasibility of the obtained solutions and the trial-and-error setting values process of the model parameters. In this paper, both drawbacks are avoided by introducing a set of analytical conditions guaranteeing that any equilibrium point of the CHN characterizes a tour for the TSP. In this way, any instance of the TSP can be solved with this parameter setting. Some computational experiences are also included, allowing the solution of instances with sizes of up to 1000 cities.