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 Kohonen Network Incorporating Explicit Statistics (KNIES) that is based on Kohonen's Self-Organizing Map (SOM). The primary difference between the SOM and the KNIES is the fact that every iteration in the training phase includes two distinct modules-the attracting module and the dispersing module. As a result of the newly introduced dispersing module the neurons maintain the overall 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 implemented maintains the mean as its invariant, the scheme can easily be generalized to maintain higher order central moments as invariants. The new scheme has been used to solve the Euclidean Travelling Salesman Problem (TSP). Experimental results for problems taken from TSPLIB [Reinelt, G. (1991). TSPLIB-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-probably the most accurate neural solutions available in the literature.