The impact of energy function structure on solving generalized assignment problem using Hopfield neural network

In the last 20 years, neural networks researchers have exploited different penalty based energy functions structures for solving combinatorial optimization problems (COPs) and have established solutions that are stable and convergent. These solutions, however, have in general suffered from lack of feasibility and integrality. On the other hand, operational researchers have exploited different methods for converting a constrained optimization problem into an unconstrained optimization problem. In this paper we have investigated these methods for solving generalized assignment problems (GAPs). Our results concretely establish that the augmented Lagrangean method can produce superior results with respect to feasibility and integrality, which are currently the main concerns in solving neural based COPs.