Neural network methods in combinatorial optimization

Abstract

We describe two basic approaches to using neural networks for optimization. The more popular approach is to formulate a combinatorial optimization task in terms of minimizing a cost function. Neural network models have been developed or interpreted as minimization machines. Before using a network to solve a problem, one must express the problem as a mathematical function that is to be minimized. The other basic approach is to design competition-based neural networks in which neurons are allowed to compete to become active under certain conditions. These approaches suggest neural network methods as an alternative for solving certain optimization tasks as compared to classical optimization techniques and other novel approaches like simulated annealing. Theoretical results on the power of neural networks for solving difficult problems will be reviewed. We provide a list of optimization problems which have been tested on neural networks. In particular, we take a closer look at the neural network methods for solving the traveling salesman problem and provide a categorization of the solution methods. We also discuss the application of neural networks to constraint satisfaction problems. A comprehensive bibliography is provided to facilitate further investigation for the interested reader.