Stochastic competitive Hopfield network and its application to maximum clique problem

In this paper, introducing a stochastic hill-climbing dynamics into an optimal competitive Hoplield network model (OCHOM), we propose a new algorithm that permits temporary energy increases, which helps the OCHOM escape from local minima. In graph theory, a clique is a completely connected subgraph and the maximum clique problem (MCP) is to find a clique of maximum size of a graph. The MCP is a classic optimization problem in computer science and in graph theory with many real-world applications, and is also known to be NP-complete. Recently, Galan-Marin et al. proposed the OCHOM for the MCP. It can guarantee convergence to a global/local minimum of energy function, and per-forms better than other competitive neural approaches. However, the OCHOM has no mechanism to escape from local minima. The proposed algorithm introduces stochastic hill-climbing dynamics which helps the OCHOM escape from local minima, and it is applied to the MCP. A number of instances have been simulated to verify the proposed algorithm.