Only a small number of function evaluations can be afforded in many real-world multiobjective optimization problems (MOPs) where the function evaluations are economically/computationally expensive. Such problems pose great challenges to most existing multiobjective evolutionary algorithms (EAs), which require a large number of function evaluations for optimization. Surrogate-assisted EAs (SAEAs) have been employed to solve expensive MOPs. Specifically, a certain number of expensive function evaluations are used to build computationally cheap surrogate models for assisting the optimization process without conducting expensive function evaluations. The infill sampling criteria in most existing SAEAs take all requirements on convergence, diversity, and model uncertainty into account, which is, however, not the most efficient in exploiting the limited computational budget. Thus, this article proposes a Kriging-assisted two-archive EA for expensive many-objective optimization. The proposed algorithm uses one influential point-insensitive model to approximate each objective function. Moreover, an adaptive infill criterion that identifies the most important requirement on convergence, diversity, or uncertainty is proposed to determine an appropriate sampling strategy for reevaluations using the expensive objective functions. The experimental results on a set of expensive multi/many-objective test problems have demonstrated its superiority over five state-of-the-art SAEAs.

中文翻译：

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用于昂贵的多目标优化的克里金辅助双档案进化算法

在许多现实世界的多目标优化问题 (MOP) 中，只能提供少量的函数评估，其中函数评估在经济上/计算上很昂贵。此类问题对大多数现有的多目标进化算法（EA）提出了巨大挑战，这些算法需要大量的函数评估进行优化。代理辅助 EA (SAEA) 已被用于解决昂贵的 MOP。具体来说，使用一定数量的昂贵函数评估来构建计算成本低廉的替代模型，以帮助优化过程，而无需进行昂贵的函数评估。大多数现有 SAEA 中的填充抽样标准考虑了对收敛性、多样性和模型不确定性的所有要求，但是，在利用有限的计算预算方面不是最有效的。因此，本文提出了一种用于昂贵的多目标优化的克里金辅助双存档 EA。所提出的算法使用一个有影响的点不敏感模型来逼近每个目标函数。此外，提出了一种自适应填充标准，该标准确定了对收敛性、多样性或不确定性的最重要要求，以确定使用昂贵的目标函数进行重新评估的适当采样策略。一组昂贵的多目标/多目标测试问题的实验结果证明了其优于五个最先进的 SAEA。所提出的算法使用一个有影响的点不敏感模型来逼近每个目标函数。此外，提出了一种自适应填充标准，该标准确定了对收敛性、多样性或不确定性的最重要要求，以确定使用昂贵的目标函数进行重新评估的适当采样策略。一组昂贵的多目标/多目标测试问题的实验结果证明了其优于五个最先进的 SAEA。所提出的算法使用一个有影响的点不敏感模型来逼近每个目标函数。此外，提出了一种自适应填充标准，该标准确定了对收敛性、多样性或不确定性的最重要要求，以确定使用昂贵的目标函数进行重新评估的适当采样策略。一组昂贵的多目标/多目标测试问题的实验结果证明了其优于五个最先进的 SAEA。