Exploring competition and co-operation for solving the Euclidean travelling salesman problem by using self-organizing map

In the last few years, several new results on self-organizing map algorithms applied to the Euclidean travelling salesman problem (ETSP) have emerged. All of them have attempted to find quasi-optimal solutions for this NP-complete combinatorial problem based on the functional role of the learning process mapping which is understood to occur in the brain. This paper brings an innovative computational investigation based on a new model of lateral interactions between neurons that can be thought of as introducing co-operation between them. Such interactions are now being observed in biological neural nets. Its application to ETSP obtained results never before achieved. Simulations using a sequential machine for well-known and difficult TSP library instances as well as for problems with over two thousands cities are discussed in this paper