An efficient cooling algorithm for annealed neural networks with applications to optimization problems

Abstract

In this thesis we consider an efficient cooling schedule for a mean field annealing (MFA) algorithm. We combine the MFA algorithm with microcanonical simulation (MCS) method and propose a new algorithm called the microcanonical mean field annealing (MCMFA) algorithm. In the proposed algorithm, the cooling speed is controlled by the current temperature so that the amount of computation in MFA can be reduced without a degradation of performance. Unlike that produced by MFA, the solution quality produced by MCMFA is not affected by the choice of the initial temperature. Properties of MCMFA are analyzed and simulated with Hopfield neural networks (HNN). In order to compare MCMFA with MFA, we apply both algorithms to three problems namely, the graph bipartitioning problem, the traveling salesman problem and the weighted matching problem. Simulation results show that MCMFA produces a superior performance to that of MFA.