Abstract
Maximum cut is an important of a class of combinatorial optimization problems. It has many important applications including the design of VLSI circuits and design of communication networks. The goal of this NP-complete problem is to partition the node set of an undirected graph into two parts in order to maximize the cardinality of the set of edges cut by the partition. In this paper, we propose a parallel algorithm using gradient ascent learning algorithm of the Hopfield neural networks for efficiently solving such optimization problems. The proposed learning algorithm is tested on a 2-variable quadratic polynomial and applied to the MAX CUT problem. Extensive simulations are performed and its effectiveness is confirmed.
