A two-space-decomposition-based evolutionary algorithm for large-scale multiobjective optimization

Large-scale multiobjective optimization problems (LSMOPs) pose a great challenge to maintaining the diversity of solutions. However, existing large-scale multiobjective optimization algorithms (MOEAs) prefer to directly use environmental selection methods designed for small-scale optimization problems. These methods are not effective in solving complex LSMOPs. To address this issue, this paper proposes a two-space (decision space and objective space) decomposition (TSD)-based diversity maintenance mechanism. Its main idea is to explicitly decompose the decision space and objective space into a number of subspaces, each of which may contain some Pareto-optimal solutions. Searching for Pareto-optimal solutions in these subspaces may help maintain the diversity of solutions. To this end, a diversity design subspace (DDS) is constructed to decompose the decision space. Then, a large-scale MOEA (MOEA/TSD) is designed by using the proposed TSD-based diversity maintenance mechanism. Experimental studies validate the effectiveness of the proposed TSD mechanism. Compared with nine state-of-the-art large-scale MOEAs on 112 benchmark LSMOPs, our proposed algorithm offers considerable advantages in overall optimization performance. The source code of MOEA/TSD is available at https://github.com/yizhizhede/MOEATSD.