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Fast grouping for large scale optimization problem

When dealing with the problem of less variables, there are usually many simple and practical methods to solve this kind of problem. However with the scale of the problem continues to grow, the effect of these methods will decline linearly or even exponentially. At the same time, many real problems have the large amount of variables which leads to a significant increase in the dimension of the problem. Usually, we call this kind of problem as large-scale optimization problem. At present, the common idea for large-scale problems is to reduce the dimension of the problem, that is, the decomposition of problem variables. At present, coevolution framework is a very effective method to solve large-scale problems. On this basis, considering the problem of resource allocation, a contribution based CC framework is produced. However, the accuracy and efficiency of problem decomposition are difficult to meet at the same time. In this paper, based on the contribution knowledge of variables, a new decomposition method combining differential grouping(DG) and matrix filling is proposed to realize the fast dynamic decomposition of large-scale problems. Firstly, in the initial stage, DG is used to calculate the correlation between some high contribution variables. These variables are obtained by calculating their contribution ranking to the problem. The correlation between other low contribution variables is finally decomposed by matrix filling. The experimental results on CEC2010 testing benchmark problems confirm the effectiveness of the method proposed in this paper.