An efficient algorithm for traveling salesman problems based on self-organizing feature maps

Kohonen´s self-organizing feature map (SOFM) has the topological characteristics that can be effectively used in solving traveling salesman problems (TSPs). B. Angeniol et al. (1988) applied SOFM in solving TSPs, but, due to the duplication of a new neuron as the winner for two different cities, their algorithm requires at least kN output neurons and 2 kN connections for N-city TSPs, where k is the number of the deletion process. The authors present, for large scale TSPs, an efficient SOFM algorithm in which a winner neuron for each city is not duplicated but excluded in the next competition. Therefore, the algorithm requires just only the N output neurons and 2N connections for N-city TSPs. Due to direct use of the output potential, the proposed algorithm can obtain better solutions. Simulation results show about 30% faster convergence and better solutions than the conventional algorithm for solving 30-city TSPs. Other simulation results for large scale TSPs with 1000 cities also show good performance of the proposed algorithm