Graph partitioning using annealed neural networks

Abstract

A new algorithm, called mean field annealing (MFA), is applied to the graph partitioning problem. The MFA algorithm combines characteristics of the simulated annealing algorithm and the Hopfield neural network. MFA exhibits the rapid convergence of the neural network while preserving the solution quality afforded by stochastic simulated annealing (SSA). The MFA algorithm is developed in the context of the graph partitioning problem. The rate of convergence of MFA on graph bipartitioning problems is as much as 50 times that of SSA, yet does not degrade the quality of the final solution. The temperature behavior of MFA during bipartitioning is analyzed and shown to have an impact on the tuning of neural networks for improved performance. Also presented is a new modification to MFA that supports partitioning of random or structured graphs into three or more bins-a problem that has previously shown resistance to solution by neural networks. >