This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate set. Specifically, the acquisition function is formulated by penalizing the expected improvement with the variation of improvement, and the infill candidate set is composed of some global and local maxima of the expected improvement function which are identified to be “mutually non-dominated”. Some conditions necessary for setting the penalty coefficient of the acquisition function are investigated, and the definition of “mutually non-dominated infill candidates” is presented. The proposed method is demonstrated with a 1-D analytical function and benchmarked using six 10-D analytical functions and an underwater vehicle structural optimization problem. The results show that the proposed method is efficient for the optimization of expensive black-box design problems.

中文翻译：

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优化昂贵的黑盒问题，并惩罚预期改进


本文提出了一种新的填充准则，用于优化昂贵的黑盒设计问题。该方法通过考虑改进的分布而不仅仅是期望来补充经典的高效全局优化算法。在优化过程中，我们从专门收集的填充候选集中最大化一个被惩罚的预期改进获取函数。具体来说，获取函数是通过用改进的变化来惩罚预期改进来制定的，并且填充候选集由预期改进函数的一些全局和局部最大值组成，这些最大值被确定为“互不支配”。研究了设置获取函数的惩罚系数的一些必要条件，并提出了 “互不支配的填充候选者” 的定义。所提出的方法通过一个 1-D 解析函数进行了演示，并使用 6 个 10-D 解析函数和一个水下航行器结构优化问题进行了基准测试。结果表明，所提方法对于昂贵的黑盒设计问题的优化是有效的。