A systematic circular weight initialisation of Kohonen neural network for travelling salesman problem

Self-organising neural networks have since been employed by researchers in solving the travelling salesman problem. However, with these networks, the final tour length as well as the convergence time, largely depends on the initial weights of the networks. In this paper, systematic initialisation of Kohonen neural network weight in a circle is presented, that involves randomly initialising the weights to be along a circular path, with centroid equals the centroid of all the cities. Our major contribution is on having the circle exhibit different radius on each test run, in order to effectively encompass all the cities. This will increase the chance of attaining the global solution by preventing effect of local minima due to some cities that may be poorly covered by the circle having specific radius. Furthermore, a system of determining the most efficient number of neurons needed in the circle is devised. It was experimentally found that, having a circle of size 1.5 times the number of cities gives the best performance. Results generated indicate an average deviation error of 2.74% from the optimal solutions of 13 TSPLIB benchmark TSP instances.