An adaptive weight optimization algorithm based on decision variable grouping for large-scale multi-objective optimization problems

Abstract

When solving large-scale multi-objective optimization problems (LSMOPs), the optimization effect of traditional multi-objective optimization algorithms deteriorates as the number of decision variables increases. The weight optimization method based on problem transformation can effectively address LSMOPs, demonstrating superior convergence compared to most evolutionary algorithms. However, existing problem transformation methods often fail to balance convergence and diversity, leading to get trapped in local optima. In order to effectively solve this problem, we propose an adaptive weight optimization algorithm based on variable grouping (GWOEA). The algorithm optimizes weights within groups to accelerate population convergence, while the adaptive control strategy boosts diversity, avoiding local optima and ensuring a balance between convergence and diversity during the optimization process. To reduce the size of solving LSMOPs, weight optimization is performed by grouping decision variables. The weights of variables within each group are first computed, and then these weights are directly optimized instead of the decision variables. The adaptive control strategy is designed to detect whether population evolution has stagnated and to handle stagnant populations, ensuring that the population retains its ability to explore. To evaluate the effectiveness of GWOEA, comprehensive comparative experiments are conducted on benchmark test problems, including variable sizes ranging from 500 to 5000. The results show that the proposed algorithm has relatively better optimization performance.