A shrinking chaotic maximum neural network for maximum clique problem

Based on the analysis of the characteristic and theory on maximum neural network, we propose a shrinking chaotic maximum neural network to solve maximum clique problem. The shrinking chaotic maximum neural network contains most of the advantages of the chaotic maximum neural network algorithm, moreover it has a novel characteristic of gradually reducing network scale. Lee and Takefuji have presented that maximum neural network always guarantees a valid solution and reduces the search space greatly without a burden on the parameter-tuning. However we find that maximum neural network actually utilizes the graph structure of the problem to be solved which has potential competitive characteristic to produce network competition. Therefore to some special instances, maximum neural network still suffers the burden of parameter modification. By introducing and modifying a controlling parameter, our proposed algorithm obtains a shrinking ability to reduce the scale of the problem to be solved. With the solving problem scale lessening, the algorithm spends less time converging and has high probability to get optional solutions. Moreover it is especially suitable to solve large-scale maximum clique problems due to its shrinking characteristic. A large number of instances have been simulated to verify the proposed algorithm.