An elastic net method for solving the traveling salesman problem

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