A hybrid Elastic Net method for solving the traveling salesman problem

The purpose of this paper is to present a new hybrid Elastic Net (EN) algorithm, by integrating the ideas of the Self Organization Map (SOM) and the strategy of the gradient ascent into the EN algorithm. The new hybrid algorithm has two phases: an EN phase based on SOM and a gradient ascent phase. We acquired the EN phase based on SOM by analyzing the weight between a city and its converging and non-converging nodes at the limit when the EN algorithm produces a tour. Once the EN phase based on SOM stuck in local minima, the gradient ascent algorithm attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. These two phases are repeated until the EN gets out of local minima and produces the short or better tour through cities. We test the algorithm on a set of TSP. For all instances, the algorithm is showed to be capable of escaping from the EN local minima and producing more meaningful tour than the EN.