Large-Scale Evolutionary Optimization Approach Based on Decision Space Decomposition

Abstract

The identification of decision variable interactions has a crucial role in the final outcome of the algorithm in the large-scale optimization domain. It is a prerequisite for decomposition-based algorithms to achieve grouping. In this paper, we design a recognition method with higher efficiency and grouping accuracy. It is based on the decomposition strategy of min hash to solve large-scale global optimization (LSGO) problems, called MHD. Our proposed method focuses on discovering the interactions of decision variables through min hash and forming subcomponents with a principle that the interdependencies between these subcomponents are maintained at a minimal level. This is described as follows: first, the min hash performs several permutations of the vector composed of decision variables. Second, the index value of the first non-zero row of the vector after rearrangement is found to obtain the new feature vector. Third, the probability of identical data at each position is calculated based on the new feature vector to decide whether there are some certain interactions between the decision variables. The advantages of min hash are: simpler computation and greater efficiency improvement than comparison between two or two decision variables; ability to find similar decision variables very quickly; and ability to cluster decision variables in a simple way. Therefore, the efficiency as well as the reliability of MHD is guaranteed. On the accuracy aspect, the proposed algorithm performs well in various types of the large-scale global optimization benchmark test function. Finally, the experimental results analysis and summarize the performance competitiveness of our proposed MHD algorithm from several aspects when it is used within a co-evolutionary framework.