Resultant projection neural networks for optimization under inequality constraints

In this paper we propose Resultant Projection Neural Networks, based on the idea of orthogonal projections onto convex sets for solving optimization problems under inequality constraints. The proposed network is capable of solving optimization problems with inequality constraints which cannot be solved directly using a Hopfield network. The effect of various network parameters on the optimization process are theoretically analyzed. A probabilistic analysis of the expected performance of the network has been carried out for the 0-1 knapsack problem. Simulation results for the 0-1 knapsack, multidimensional 0-1 knapsack and job processing with deadlines are also shown. The average performance (mean and median) of the network compare quite well with optimal and suboptimal solutions obtained using standard techniques in conventional computers. However, there are some instances which do produce bad solutions.