Extended Hopfield models of neural networks for combinatorial multiobjective optimization problems

In this paper, an extended Hopfield model of a neural network for solving NP-hard combinatorial multiobjective optimization problems has been proposed. Some models for satisfaction of representative constraints have been studied. Moreover, the Hopfield model for solving combinatorial constrained optimization problems with linear objective function has been considered. Afterwards, the network model for solving combinatorial constrained optimization problems with quasi-quadratic function has been considered. Finally, the family of extended Hopfield models for finding Pareto-optimal solutions have been developed. Some numerical examples related with the chosen two-objective optimization of operation allocations in distributed processing systems have been given.