An improved competitive Hopfield network with inhibitive competitive activation mechanism for maximum clique problem

Abstract

In this paper, we analyze the formula of weights definition in the discrete competitive Hopfield network (DCHOM) and point out its flaw when using it to solve some special instances of maximum clique problem (MCP). Based on the analysis, we propose an improved competitive Hopfield network algorithm (ICHN). In ICHN, we introduce a flexible weight definition method which excites the competitive dynamics, and we also present an initial values setting strategy which efficiently increases the probability of finding optimal solutions. Furthermore, an inhibitive competitive activation mechanism is introduced to form a new input updating rule which reduces significantly the number of neurons with an intermediate level of activations. Our algorithm effectively overcomes the flaw of the DCHOM, and exhibits powerful solving ability for the MCP. Experiments on the benchmark problems and practical applications verify the validity of our algorithm.