Solve large‐scale many‐objective optimization problems based on dual analysis of objective space and decision space

Abstract

A method based on decision variable partition is often utilized for large-scale optimization problems, but it only considers the convergence and diversity of decision variables. However, decision variables in the same group may still have different (strong or weak) correlations with objectives, even if they are only related to convergence or diversity. This situation not only reduces the accuracy of the grouping of decision variables, but also affects the allocation of computational resources. To address this issue, an algorithm based on dual analysis of objective space and decision space to group decision variables more accurately for solving large-scale many-objective optimization problems is proposed; this algorithm is called LM-DAS. It first divides decision variables into two categories: convergence-related variables and the diversity-related variables. Then, the correlation between convergence-related variables and objective functions is analyzed. The decision space is divided into several subspaces according to the objective importance. Next, the decision variables are grouped using the method of interaction analysis between two level variables. Under the premise of ensuring the correctness of the grouping as much as possible, the algorithm can allocate more search resources to decision variables that are related to more important objective functions. The performance of LM-DAS is compared with four representative algorithms for 71 test instances. These instances involved 5–10 objectives and 200–1000 decision variables. The experimental results demonstrate that the proposed algorithm is competitive and effective.