An extended Hopfield model for combinatorial optimization

A Hopfield model of order higher than two is considered by introducing high order monomials in the energy function to be minimized. The weights associated with each monomial of degree m allow to represent the links between m neurons of the network. The updating equation of the state of the neurons is obtained by deriving the generalized energy function. In this paper we show that the high order Hopfield neural network can be efficiently used for a particular family of combinatorial optimization problems. A simple case where the use of the high order Hopfield network appears to be very natural is considered and the good behavior of the proposed solution is illustrated by means of simulations