Comparison of the criteria for updating Kriging response surface models in multi-objective optimization

K. Shimoyama, Koma Sato, S. Jeong, S. Obayashi
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引用次数: 24

Abstract

This paper compares the criteria for updating the Kriging response surface models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those combination (EHVI+EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has been recently proposed as the criterion considering the stochastic improvement of the front of non-dominated solutions in multi-objective optimization. EST is the value of each objective function, which is estimated non-stochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in a non-constrained case, EHVI keeps a balance between accurate and wide search for non-dominated solutions on the Kriging models in multi-objective optimization. In addition, the present experiments suggested future investigation into the techniques for handling uncertain constraints to enhance the capability of EHVI in a constrained case.
多目标优化中Kriging响应面模型更新准则的比较
本文比较了多目标优化中更新Kriging响应面模型的准则:期望改进(EI)、期望超体积改进(EHVI)、估计(EST)和组合(EHVI+EST)。传统上,EI作为单独考虑每个目标函数值的随机改进的准则,而EHVI作为多目标优化中考虑非支配解前端随机改进的准则最近被提出。EST是每个目标函数的值,由Kriging模型在不考虑其不确定性的情况下进行非随机估计。在焊接梁设计问题中进行了数值实验,实验结果表明,在无约束情况下,EHVI在多目标优化中能够在Kriging模型的非主导解的精确搜索和广泛搜索之间保持平衡。此外,本实验建议未来研究处理不确定约束的技术,以增强EHVI在约束情况下的能力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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