The Kohonen network incorporating explicit statistics and its application to the travelling salesman problem

In this paper we introduce a new self-organizing neural network, the Kohone n Network Incorporating Explicit Statistics (KNIES) that is based on Kohone n's Self-Organizing Map (SOM): The primary difference between the SOM and t he KNIES is the fact that every iteration in the training phase includes tw o distinct morlules-the attracting module and the dispersing module. As a r esult of the newly introduced dispersing module the neurons maintain the ov erall statistical properties of the data points. Thus, although in SOM the neurons individually find their places both statistically and topologically , in KNIES they collectively maintain their mean to be the mean of the data points, which they represent. Although the scheme as it is currently imple mented maintains the mean as its invariant, the scheme can easily be genera lized to maintain higher order central moments as invariants. The new schem e has been used to solve the Euclidean Travelling Salesman Problem (TSP). E xperimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSP LIB-A travelling salesman problem library. ORSA Journal on Computing, 3, pp . 376-384] indicate that it is a very accurate NN strategy for the TSP-prob ably the most accurate neural solutions available in the literature. (C) 19 99 Elsevier Science Ltd. All rights reserved.