A Kohonen-like decomposition method for the Euclidean traveling salesman problem-KNIES/spl I.bar/DECOMPOSE.

In addition to the classical heuristic algorithms of operations research, there have also been several approaches based on artificial neural networks for solving the traveling salesman problem. Their efficiency, however, decreases as the problem size (number of cities) increases. A technique to reduce the complexity of a large-scale traveling salesman problem (TSP) instance is to decompose or partition it into smaller subproblems. We introduce an all-neural decomposition heuristic that is based on a recent self-organizing map called KNIES, which has been successfully implemented for solving both the Euclidean traveling salesman problem and the Euclidean Hamiltonian path problem. Our solution for the Euclidean TSP proceeds by solving the Euclidean HPP for the subproblems, and then patching these solutions together. No such all-neural solution has ever been reported.

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.

Discrete vector quantization for arbitrary distance function estimation.

There are currently many vastly different areas of research involving adaptive learning. Among them are the two areas that concern neural networks and learning automata. This paper develops a method by which the general philosophies of vector quantization (VQ) and discretized automata learning can be incorporated for the computation of arbitrary distance functions. The latter is a problem which has important applications in logistics and location analysis. The input to our problem is the set of coordinates of a large number of nodes whose internode arbitrary "distances" have to be estimated. To render the problem interesting, nontrivial, and realistic, we assume that the explicit form of this distance function is both unknown and uncomputable. Unlike traditional operations research methods, which use optimized parametric functional estimators, we have utilized discretized VQ principles to first adaptively polarize the nodes into subregions. Subsequently, the parameters characterizing the subregions are learned by using a variety of methods (including, for academic purposes, a VQ strategy in the meta-domain). After an initial training phase, a system which achieves distance estimation attempts to yield an estimate of any node-pair distance without actually deriving an explicit form for the unknown function. The algorithms have been rigorously tested for the actual road-travel distances involving cities in Turkey and the results obtained are conclusive. Indeed, these present results are the best currently available from any single or hybrid strategy.