This project will attempt to develop new neural network approaches to solving geometric combinatorial optimization problems. It will focus on the classical Traveling Salesman Problem (with Euclidean distances) as an easy to state, NP- complete problem needing efficient procedures yielding consistently good tours. The much publicized Hopfield neural network approach to the TSP disappoints operations researchers as cannot guarantee feasibility; hence, this project will investigate adaptive neural network procedures which correspond to geometric heuristic approaches, which exploit the "neural" property of learning, and which have shown great promise in application to the problem. The procedures to be considered will have to potential to be implemented as a neural system. Such systems consist of processing units and weighted connections among them. They exploit parallelism, and computations use local information (thus storage is minimal). As chip technology expands and so-called "neural" chip become available, the ability to find amendable methods will yield improved solution approaches to many combinatorial optimization problems.
