Parameter analysis for removing the local minima of combinatorial optimization problems by using the inverse function delayed neural network

The Inverse function Delayed (ID) model is a novel neuron model derived from a macroscopic model which is attached to conventional network action. The special characteristic of the ID model is to have the negative resistance effect. Such a negative resistance can actively destabilize undesirable states, and we expect that the ID model can avoid the local minimum problems for solving the combinatorial optimization problem. In computer simulations, we have shown that the ID network can avoid the local minimum problem with a particular combinatorial optimization problem, and we have also shown the existence of an appropriate parameter for finding an optimal solution with high success rate experimentally. In this paper, we theoretically estimate appropriate network parameters to remove all local minimum states.