State-of-the-Art Survey - The Traveling Salesman Problem: A Neural Network Perspective

This paper surveys the "neurally" inspired problemsolving approaches to the traveling salesman problem, namely, t h e Hopfield-Tank network, the elastic net, and the self-organizing map. The latest achievements in the neural network domain are repor ted and numerical comparisons are provided with the classical solution approaches of operations research. An extensive bibliography wi th more than one hundred references is also included. I n t r o d u c t i o n The Traveling Salesman Problem (TSP) is a classical combinatorial optimization problem, which is simple to state b u t very difficult to solve. The problem is to find the shortest possible tour through a set of N vertices so that each vertex is visited exactly once. This problem is known to be NP-complete, and cannot b e solved exactly in polynomial time. Many exact and heuristic algorithms have been devised in t h e field of operations research (OR) to solve the TSP. We refer readers to [15, 64, 65] for good overviews of the TSP. In the sections that follow, we briefly introduce the OR problem-solving approaches to the TSP. Then, the neural network approaches for solving that problem a r e discussed.