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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]

In this paper, we study on how to achieve balance between minimizing the objectives, satisfying the constraints, and avoiding the population to stuck at locally optimal or locally feasible regions. We propose a new constraints handling technique based on diversity distance measure for constrained multiobjective optimization problems. We innovatively measure all effects of the constraints on the objectives by the interaction effects and direct effects of constraints on the objectives. The interactive effects of constraints on the objective functions are firstly expressed and quantified by using Mahalanobis distance and computing the value of the distance measure by involving a Lebesgue measure. Based on interactive and direct effects, we propose a new modified mechanism of objective space, called objective space modified mechanism based on diversity distance measure, so that the good infeasible solution could be more effectively used to find the optimal solution. The Pull and Push search is used to adaptively adjust the location of the Pareto front, which could preclude the population from being stuck at some locally optimal or locally feasible regions and could decrease time complexity. Comprehensive experiments completed for several benchmark problems demonstrate the competitiveness of the proposed algorithm, in comparison to the existing state-of-art constrained evolutionary multiobjective optimization. [ABSTRACT FROM AUTHOR]