Evolutionary algorithms have shown their promise in addressing multiobjective problems (MOPs). However, the Pareto dominance used in multiobjective optimization loses its effectiveness when addressing many-objective problems (MaOPs), which are defined as having more than three objectives. This is because the Pareto dominance loses its ability to distinguish between individuals. In this paper, a many-objective evolutionary algorithm based on rotation and decomposition is proposed (MaOEA-RD) to overcome the shortcoming of insufficient selection pressure caused by the Pareto dominance. First, the coordinates system is rotated and a hyperplane is established to distinguish between the nondominated individuals. Then, a novel individual selection mechanism incorporating decomposition is adopted to maintain the diversity of the population. In order to compensate for the deficiency of the predefined reference vectors, a reference vector adjustment mechanism is proposed. Experimental studies on several well-known benchmark problems show that the proposed algorithm is competitive compared with nine state-of-the-art many-objective algorithms.

进化算法已经显示出其在解决多目标问题（MOP）中的希望。但是，在解决被定义为具有三个以上目标的多目标问题（MaOP）时，用于多目标优化的帕累托优势失去了有效性。这是因为帕累托优势失去了区分个人的能力。提出了一种基于旋转分解的多目标进化算法（MaOEA-RD），克服了帕累托优势导致选择压力不足的缺点。首先，旋转坐标系并建立超平面以区分非支配的个体。然后，采用一种新的结合分解的个体选择机制来维持种群的多样性。为了补偿预定参考矢量的不足，提出了一种参考矢量调整机制。对几个著名基准问题的实验研究表明，与九种最新的多目标算法相比，该算法具有竞争力。