Evolutionary Many-Objective Optimization Based on Adversarial Decomposition

The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each of which is usually defined as a scalarizing function using a weight vector. Due to the characteristics of the contour line of a particular scalarizing function, the performance of the decomposition-based method strongly depends on the Pareto front's shape by merely using a single scalarizing function, especially when facing a large number of objectives. To improve the flexibility of the decomposition-based method, this paper develops an adversarial decomposition method that leverages the complementary characteristics of two different scalarizing functions within a single paradigm. More specifically, we maintain two co-evolving populations simultaneously by using different scalarizing functions. In order to avoid allocating redundant computational resources to the same region of the Pareto front, we stably match these two co-evolving populations into one-one solution pairs according to their working regions of the Pareto front. Then, each solution pair can at most contribute one mating parent during the mating selection process. Comparing with nine state-of-the-art many-objective optimizers, we have witnessed the competitive performance of our proposed algorithm on 130 many-objective test instances with various characteristics and Pareto front's shapes.

Matching-Based Selection with Incomplete Lists for Decomposition Multi-Objective Optimization

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.