Hop eld-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-Hop eld (ALH) method, to improve Hop eld-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 e ectively solve the dilemma. Experimental results on the TSP show superiority of the ALH method over the existing Hop eld-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 di erent random initializations. For larger size problems, it also nds remarkably better solutions than the compared methods while always converging to valid tours.
It uses the augmented Lagrange method, which combines both the Lagrange and the penalty methods, to effectively solve the dilemma REF .
Improving Convergence and Solution Quality of Hopfield-Type Neural Networks with Augmented Lagrange Multipliers
IEEE Transactions On Neural Networks
Computer Science Medicine