Improving Convergence and Solution Quality ofHop eld - Type Neural Networks

Hoppeld-type networks convert a combinatorial optimization to a constrained real optimization and solve the latter using the penalty method. There is a dilemma with such networks: When tuned to produce good quality solutions, they can fail to converge to valid solutions; when tuned to converge, they tend to give low quality solutions. This paper proposes a new method, called the Augmented Lagrange-Hoppeld (ALH) method, to improve Hoppeld-type neural networks in both the convergence and the solution quality in solving combinatorial optimization. It uses the augmented Lagrange method, which combines both the Lagrange and the penalty methods, to eeectively solve the dilemma. Experimental results on the TSP show superiority of the ALH method over the existing Hoppeld-type neural networks in the convergence and solution quality. For the 10-city TSP's, ALH nds the known optimal tour with 100% success rate, as the result of 1000 runs with diierent random initializations. For larger size problems, it also nds remarkably better solutions than the compared methods while always converging to valid tours.