Ineffectiveness in solving combinatorial optimization problems using a Hopfield network: a new perspective from aliasing effect

A Hopfield network has been proposed as a novel approach to achieve memory associativity and to solve combinatorial optimization problems. The authors presently relate optimization problems to problems of memory association of a Hopfield network and show the limitations of the network when it is used to solve NP-complete problems from the viewpoints of the aliasing effect among pattern sets and the information capacity embedded in such a network. A simplest Hopfield network for solving the race traffic problem is constructed to manifest the similarity between memory association and optimization problem resolution as well as to discuss the stability of convergence in synchronous and asynchronous operation modes. By transforming the traveling salesman problem to a memory association problem, it is shown that the use of a Hopfield network for solving NP-complete problems is, in fact, overloaded