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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. [ABSTRACT FROM AUTHOR]

Recently, evolutionary algorithms (EAs) have shown their strong competitiveness in handling many-objective optimization problems (MaOPs) with different Pareto fronts (PFs). However, maintaining convergence and diversity simultaneously in high-dimensional problems can be further explored. This paper suggests an adaptive convergence-diversity balanced evolutionary algorithm (ACDB-EA) to handle the above issue, which maintains balance between convergence and diversity adaptively during the evolutionary process. In the proposed algorithm, a novel diversity maintenance mechanism based on the global and local diversities is developed to promote the diversity by considering them collaboratively. To be specific, the average similarity and the maximal similarity represent respectively the global and local diversities of the solution, where the similarity between two solutions is defined as the cosine similarity between their objective vectors. In the environmental selection, the proposed adaptive convergence-diversity balanced strategy is used to adjust weights of convergence (defined as the L 2 norm in the objective space), global diversity and local diversity according to the population adaptively. Under this strategy, each solution produces a score and the solution with the highest score will enter the next generation, which means it acquires the optimal performance in terms of convergence and diversity. In each iteration, scores of candidate solutions will be recalculated to continuously search for the most suitable one, which strengthens the selection pressure toward the true PFs. We conduct experimental study on 111 benchmark testing instances with 2-20 objectives. The proposed method is shown to be superior to seven state-of-the-art algorithms in maintaining balance between convergence and diversity. [ABSTRACT FROM AUTHOR]