Many-objective optimization problems (MaOPs) contain four or more conflicting objectives to be optimized. A number of efficient decomposition-based evolutionary algorithms have been developed in the recent years to solve them. However, computationally expensive MaOPs have been scarcely investigated. Typically, surrogate-assisted methods have been used in the literature to tackle computationally expensive problems, but such studies have largely focused on problems with 1–3 objectives. In this paper, we present an approach called hybrid surrogate-assisted many-objective evolutionary algorithm to solve computationally expensive MaOPs. The key features of the approach include: 1) the use of multiple surrogates to effectively approximate a wide range of objective functions; 2) use of two sets of reference vectors for improved performance on irregular Pareto fronts (PFs); 3) effective use of archive solutions during offspring generation; and 4) a local improvement scheme for generating high quality infill solutions. Furthermore, the approach includes constraint handling which is often overlooked in contemporary algorithms. The performance of the approach is benchmarked extensively on a set of unconstrained and constrained problems with regular and irregular PFs. A statistical comparison with the existing techniques highlights the efficacy and potential of the approach.

中文翻译：

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一种基于多代理辅助分解的昂贵多目标/多目标优化进化算法

多目标优化问题 (MaOP) 包含四个或更多要优化的冲突目标。近年来已经开发了许多有效的基于分解的进化算法来解决它们。然而，几乎没有研究过计算成本高的 MaOP。通常，文献中已使用代理辅助方法来解决计算成本高的问题，但此类研究主要集中在具有 1-3 个目标的问题上。在本文中，我们提出了一种称为混合代理辅助多目标进化算法的方法来解决计算成本高的 MaOP。该方法的主要特点包括：1）使用多个代理来有效地逼近各种目标函数；2) 使用两组参考向量来提高不规则帕累托前沿 (PF) 的性能；3) 在后代生成过程中有效使用存档解决方案；4) 产生高质量填充解决方案的局部改进方案。此外，该方法包括在当代算法中经常被忽视的约束处理。该方法的性能在一组具有规则和不规则 PF 的无约束和有约束问题上进行了广泛的基准测试。与现有技术的统计比较突出了该方法的功效和潜力。该方法包括在当代算法中经常被忽视的约束处理。该方法的性能在一组具有规则和不规则 PF 的无约束和有约束问题上进行了广泛的基准测试。与现有技术的统计比较突出了该方法的功效和潜力。该方法包括在当代算法中经常被忽视的约束处理。该方法的性能在一组具有规则和不规则 PF 的无约束和有约束问题上进行了广泛的基准测试。与现有技术的统计比较突出了该方法的功效和潜力。