Designing an Expanded SOM for the Traveling Salesman Problem by Genetic Algorithms

The underlying idea of the ESOM [2] is to incorporate the topological neighborhood preserving property of Self-Organizing Map (SOM) and the convex-hull property (a global optimality) of TSP together. The learning rule of its generalized version is as follows: ! w j(t+ 1) = cj(t) [ ! w j(t) + j(t) ( ! x t !w j(t))] where !w j is the weight of jth neuron, !x t the input city coordinate, cj(t) the expanded coe cient and j(t) the learning rate. Note that ESOM becomes a traditional SOM when cj(t) = 1. While in ESOM, the expanded coe cient cj(t) (normally > 1) re ects the convex-hull property skillfully and then drives ESOM to learn the global optimality gradually. Furthermore, it should cooperate well with the traditional SOM learning rule so as to achieve a topological neighborhood preseving map. Thus, its e cient manual design seems intractable.