A new elastic net learning algorithm for traveling salesman problem

This paper introduces a gradient ascent the learning algorithm of the original elastic net(EN) and the optimal elastic net(OEN) for the traveling salesman problem(TSP). The learning algorithm minimizes the path through cities. The procedure is equivalent to gradient descent of an energy function; and lends to a local minimum of energy that represents a good solution to the problem. Once the EN (OEN) gets 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 phase are repeated until the EN (OEN) gets out of local minima and produces the shorted or better tour through cities. We test the algorithm on a set of TSP. For all instances, the new algorithm is showed to be capable of escaping from the EN (OEN) local minima and producing more meaningful tour than the original EN (OEN).