Solving for multimodal function with high dimensions base on Hopfield Neural Network and immune algorithm

This paper analyzes immune theory and Hopfield Neural Network (HNN), and then proposes a new algorithm for multimodal function with high dimensions. This new algorithm uses the advantages of clustering analysis algorithm, HNN and immune algorithm, and it appears excellent characteristic in optimal problems of multimodal function with high dimensions. In detail, first, we obtain a group of solutions with variety by IA; and then the solutions are partitioned into some clusters by k-means algorithm. Finally we take cluster centurions returned by k-means algorithm as the initial value of each HNN, and run each Hopfield neural network to obtain all minima. Simulation experiment proves that the new algorithm has much higher accuracy and shorter running time, compared with IA. Especially, at high-dimensional function, the new algorithm has clearly advantage.