IMPROVED PROJECTION HOPFIELD NETWORK FOR THE QUADRATIC ASSIGNMENT PROBLEM

Abstract

The continuous-valued Hopfield neural network (CHN) is a popular and powerful metaheuristic method for combinatorial optimization. However, it is difficult to select appropriate penalty parameters for constraints so as to obtain a feasible and desirable solution by CHN. Thus, various improved models have been proposed. Matsuda proposed a CHN named optimal CHN and showed theoretical results on selecting parameters. On the other hand, Smith et al. proposed the projection CHN which projects a solution onto the feasible region and thus needs not select penalty parameters. In this paper, we point out some drawbacks of these two models and propose a new CHN with an efficient projection technique for the quadratic assignment problem, which overcomes these drawbacks. Moreover, we show that the proposed model can always find a feasible solution and that it has the local convergence property. Finally, we verify advantages of the proposed model through some numerical experiments.