The balance between convergence and diversity is the cornerstone of evolutionary multiobjective optimization (EMO). The recently proposed stable matching-based selection provides a new perspective to handle this balance under the framework of decomposition multiobjective optimization. In particular, the one-one stable matching between subproblems and solutions, which achieves an equilibrium between their mutual preferences, is claimed to strike a balance between convergence and diversity. However, the original stable marriage model has a high risk of matching a solution with an unfavorable subproblem, which finally leads to an imbalanced selection result. In this paper, we introduce the concept of incomplete preference lists into the stable matching model to remedy the loss of population diversity. In particular, each solution is only allowed to maintain a partial preference list consisting of its favorite subproblems. We implement two versions of stable matching-based selection mechanisms with incomplete preference lists: one achieves a two-level one-one matching and the other obtains a many-one matching. Furthermore, an adaptive mechanism is developed to automatically set the length of the incomplete preference list for each solution according to its local competitiveness. The effectiveness and competitiveness of our proposed methods are validated and compared with several state-of-the-art EMO algorithms on 62 benchmark problems.
Bibliographical noteThis work was supported in part by the Hong Kong RGC General Research Fund GRF Grant 9042038 (CityU 11205314), in part by the ANR/RCC Joint Research Scheme through the Research Grants Council of the Hong Kong Special Administrative Region and France National Research Agency under Project A-CityU101/16 and in part by the National Science Foundation of China under Grant 61672443 and Grant 61473241.
- Adaptive mechanism
- convergence and diversity
- multiobjective optimization
- stable matching with incomplete lists