The parameter dependence of the inverse function delayed model on the success rate of combinatorial optimization problems

Abstract

Much research has been performed regarding attempts to solve NP hard or NP complete problems using neural networks, because high-speed solutions then become possible through parallel processing. However, there is still the local minima problem. The Inverse Function Delayed (ID) model used in this paper is shown to be a powerful avoidance algorithm for the local minima problem, because the dynamics of the model can cause negative resistance and the local minima can be destabilized by this negative resistance. In this paper, the differences with the conventional Hopfield model and the hysteresis neuron model, due to the parameters of the ID model, are discussed successively. Moreover, from a general energy function E of the optimization problem, when a static output state is the solution representation, it is shown that the global minima and the local minima can be separated using the ID model in a problem where E=0 in the global minimum state. Afterwards, the parameter dependence of the success rate is discussed. As a result, a numerical experiment confirmed that a wide optimal parameter range showing a 100% success rate is obtained, though there is a slight special oscillating state (limit cycle). © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 90(11): 41–54, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20402