Much attention has been paid to evolutionary multi-objective optimization approaches to efficiently solve real-world engineering problems with multiple conflicting objectives. However, the loss of selection pressure and the non-uniformity in the distribution of the Pareto optimal solutions in the objective space can impede both dominance-based and decomposition-based multi-objective optimizers when solving many-objective problems. In this work, we circumvent this issue by exploiting two performance indicators, and use these in an optimizer’s environmental selection via non-dominated sorting. This effectively converts the original many-objective problem into a bi-objective one. Our convergence performance criterion tries to balance the performance of individuals in different parts of the objective space. The angle between solutions on objective space is adopted to measure the diversity of each individual. Using these solutions can be separated into different layers easily, which is often not possible for the original many-objective optimization representation. The performance of the proposed method is evaluated on the DTLZ benchmark problems with up to 30 objectives, and MaF test suite with 10, 15, 20 and 30 objectives. The experimental results show that our proposed method is competitive compared to six recently proposed algorithms, especially for solving problems with a large number of objectives.

为了有效解决具有多个冲突目标的实际工程问题，进化多目标优化方法已引起了广泛关注。但是，在解决多目标问题时，选择压力的损失和目标空间中Pareto最优解的分布不均匀会阻碍基于优势的和基于分解的多目标优化器。在这项工作中，我们通过利用两个性能指标来规避此问题，并通过非主导排序将它们用于优化程序的环境选择中。这有效地将原始的多目标问题转换为双目标问题。我们的收敛绩效标准试图平衡目标空间不同部分中个人的绩效。采用目标空间解之间的角度来衡量每个个体的多样性。使用这些解决方案可以轻松地分为不同的层，这对于原始的多目标优化表示通常是不可能的。在具有多达30个目标的DTLZ基准问题以及具有10、15、20和30个目标的MaF测试套件中评估了所提出方法的性能。实验结果表明，与最近提出的六种算法相比，我们提出的方法具有竞争力，特别是对于解决具有大量目标的问题。在具有多达30个目标的DTLZ基准问题以及具有10、15、20和30个目标的MaF测试套件中评估了所提出方法的性能。实验结果表明，与最近提出的六种算法相比，我们提出的方法具有竞争力，特别是对于解决具有大量目标的问题。在具有多达30个目标的DTLZ基准问题以及具有10、15、20和30个目标的MaF测试套件中评估了所提出方法的性能。实验结果表明，与最近提出的六种算法相比，我们提出的方法具有竞争力，特别是对于解决具有大量目标的问题。