Enhancing search efficiency in large-scale constrained multi-objective optimization using a decision variable importance matrix

Existing constrained multi-objective evolutionary algorithms (CMOEAs) encounter significant challenges in solving large-scale constrained multi-objective optimization problems (LSCMOPs), as the exponentially increasing search space severely restricts their optimization efficiency. To address this issue, this paper proposes a variable importance matrix-assisted large-scale constrained multi-objective evolutionary optimization method. First, multiple decision trees are constructed at the beginning of each generation based on historical population data. The resulting variable importance scores with respect to objectives and constraints are integrated to form a variable importance matrix (VIM). Second, the objective space is uniformly divided using reference vectors, and the VIM is employed to estimate the variable importance of individuals in different search subregions, resulting in the subregion-based variable importance matrix (SVIM). Finally, differentiated search directions are developed for different individuals according to the SVIM, thereby enhancing the search efficiency of the population. The proposed method can be seamlessly incorporated into existing CMOEAs and improve their performance to varying degrees. Extensive comparative experiments are conducted against nine state-of-the-art algorithms on 162 benchmark problems and an integrated coal mine energy system scheduling optimization problem. The results demonstrate the effectiveness and superiority of the proposed method.