Solving the Traveling Salesman Problem Using Elastic Net Integrate with SOM

The traveling salesman problem (TSP) is a prototypical problem of combinatorial optimization and, as such, it has received considerable attention from neural-network researchers seeking quick, heuristic solutions. This paper is to present an Elastic Net (EN) algorithm, by integrating the ideas of the Self-Organization Map (SOM). The proposed solution is based on a self-organizing map structure, initialized with as many artificial neurons as the number of targets to be reached. In the competitive relaxation process, information about the trajectory connecting the neurons is combined with the distance of neurons from the target. The gradient ascent algorithm attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. We present a simple but effective modification to the elastic net of Durbin and Willshaw which shifts emphasis from global to local behavior during convergence, so allowing the net to ignore some image points. Results of tests indicate that the proposed algorithm is efficient and reliable for Traveling Salesman Problem (TSP).