In this paper, we propose a new parallel algorithm for cellular radio channel assignment problem that can help the expanded maximum neural network escape from local minima by introducing a transient chaotic neurodynamics. The goal of the channel assignment problem, which is an NP-complete problem, is to minimize the total interference between the assigned channels needed to satisfy all of the communication needs. The expanded maximum neural model always guarantees a valid solution and greatly reduces search space without a burden on the parameter-tuning. However, the model has a tendency to converge to local minima easily because it is based on the steepest descent method. By adding a negative self-feedback to expanded maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm then is fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the expanded maximum neural network and the chaotic neurodynamics. Simulations on benchmark problems demonstrate the superior performance of the proposed algorithm over other heuristics and neural network methods.

In this paper, based on maximum neural network, we propose a new parallel algorithm that can escape from local minima and has powerful ability of searching the globally optimal or near-optimum solution for the maximum clique problem (MCP). In graph theory a clique is a completely connected subgraph and the 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. Lee and Takefuji have presented a very powerful neural approach called maximum neural network for this NP-complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to the local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm.