  The balance between convergence and diversity is a key issue of evolutionary
multi-objective optimization. The recently proposed stable matching-based
selection provides a new perspective to handle this balance under the framework
of decomposition multi-objective optimization. In particular, the stable
matching between subproblems and solutions, which achieves an equilibrium
between their mutual preferences, implicitly strikes a balance between the
convergence and diversity. Nevertheless, the original stable matching model has
a high risk of matching a solution with a unfavorable subproblem which finally
leads to an imbalanced selection result. In this paper, we propose an adaptive
two-level stable matching-based selection for decomposition multi-objective
optimization. Specifically, borrowing the idea of stable matching with
incomplete lists, we match each solution with one of its favorite subproblems
by restricting the length of its preference list during the first-level stable
matching. During the second-level stable matching, the remaining subproblems
are thereafter matched with their favorite solutions according to the classic
stable matching model. In particular, we develop an adaptive mechanism to
automatically set the length of preference list for each solution according to
its local competitiveness. The performance of our proposed method is validated
and compared with several state-of-the-art evolutionary multi-objective
optimization algorithms on 62 benchmark problem instances. Empirical results
fully demonstrate the competitive performance of our proposed method on
problems with complicated Pareto sets and those with more than three
objectives.
