进化高维多目标优化研究进展
Recent advances in evolutionary many-objective optimization

高维多目标优化问题是目标个数多于3的多目标优化问题. 尽管进化优化方法在多目标优化问题求解中显示了卓越的性能, 但是, 对于高维多目标优化问题, 已有方法存在目标维数难以扩展、Pareto占优关系无法区分进化个体, 以及多样性维护策略失效等困难. 因此, 高维多目标优化问题的高效求解引起进化优化界的高度关注. 本文将分别从新型占优关系、多样性维护策略、目标缩减、目标聚合、基于性能指标的选择、融入偏好、集合进化、变化算子、可视化技术, 以及应用等10个方面分类总结近年来进化高维多目标优化的研究成果, 通过分析已有研究存在的问题，指出今后可能的研究方向.
Many-objective optimization problems are multi-objective ones with more than three objectives. Evolutionary optimization methods have outstanding performances on multi-objective optimization problems. State-of-the-art evolutionary multi-objective optimization methods, however, exist a plenty of severe shortcomings when solving many-objective optimization problems, such as the curse of the objective dimensionality, the incapability of the Pareto dominance in distinguishing evolutionary individuals, and the inefficacy of the diversity maintenance strategies. Therefore, how to efficiently tackle many-objective optimization problems have been attracting scholars in the evolutionary optimization community. In this paper, we will comprehensively review recent advances in evolutionary many-objective optimization from such aspects as novel dominance relations, diversity maintenance strategies, objective reduction, objective aggregation, indicator-based selection, preference integration, set-based evolution, variation operators, visualization technology as well as applications, and suggest several important topics to be further researched by analyzing the existing problems.