Sub-optimal solution screening in optimization by neural networks

The authors discuss a convergence condition of the Hopfield neural network to get the optimal or sub-optimal solutions of combinatorial optimization problems. For the TSP (traveling salesman problem), the condition to get its feasible solutions to coincide with the minimum points of the Hopfield neural network requires that the penalty parameter, which is the weight of a constraint function, must be greater than the distance between three consecutive cities in the solutions. It is proposed that by utilizing this condition, it would be possible to control the quality of solutions. The result was applied to TSPs with 4 and 16 cities, and confirmed that all the sub-optimal solutions could be eliminated. The optimal solution was obtained efficiently