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Many-objective optimization has posed a great challenge to the classical Pareto dominance-based multiobjective evolutionary algorithms (MOEAs). In this paper, an evolutionary algorithm based on a new dominance relation is proposed for many-objective optimization. The proposed evolutionary algorithm aims to enhance the convergence of the recently suggested nondominated sorting genetic algorithm III by exploiting the fitness evaluation scheme in the MOEA based on decomposition, but still inherit the strength of the former in diversity maintenance. In the proposed algorithm, the nondominated sorting scheme based on the introduced new dominance relation is employed to rank solutions in the environmental selection phase, ensuring both convergence and diversity. The proposed algorithm is evaluated on a number of well-known benchmark problems having 3-15 objectives and compared against eight state-of-the-art algorithms. The extensive experimental results show that the proposed algorithm can work well on almost all the test functions considered in this paper, and it is compared favorably with the other many-objective optimizers. Additionally, a parametric study is provided to investigate the influence of a key parameter in the proposed algorithm.
Yuan et al. (Mon,) studied this question.