A Study of the Mean Field Approach to Knapsack Problems

The mean field theory approach to knapsack problems is extended to multiple knapsacks and generalized assignment problems with Potts mean field equations governing the dynamics. Numerical tests against "state of the art" conventional algorithms shows good performance for the mean field approach. The inherently parallelism of the mean field equations makes them suitable for direct implementations in microchips. It is demonstrated numerically that the performance is essentially not affected when only a limited number of bits is used in the mean field equations. Also, a hybrid algorithm with linear programming and mean field components is showed to further improve the performance for the difficult homogeneous N x M knapsack problem. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.