Abstract
Sorting solutions play a key role in using evolutionary algorithms (EAs) to solve many-objective optimization problems (MaOPs). Generally, different solution-sorting methods possess different advantages in dealing with distinct MaOPs. Focusing on this characteristic, this article proposes a general voting-mechanism-based ensemble framework (VMEF), where different solution-sorting methods can be integrated and work cooperatively to select promising solutions in a more robust manner. In addition, a strategy is designed to calculate the contribution of each solution-sorting method and then the total votes are adaptively allocated to different solution-sorting methods according to their contribution. Solution-sorting methods that make more contribution to the optimization process are rewarded with more votes and the solution-sorting methods with poor contribution will be punished in a period of time, which offers a good feedback to the optimization process. Finally, to test the performance of VMEF, extensive experiments are conducted in which VMEF is compared with five state-of-the-art peer many-objective EAs, including NSGA-III, SPEA/R, hpaEA, BiGE, and grid-based evolutionary algorithm. Experimental results demonstrate that the overall performance of VMEF is significantly better than that of these comparative algorithms.