Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization
Updating Kriging Surrogate Models Based on the Hypervolume Indicator in Multi-Objective Optimization
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DOI：
10.1115/1.4024849
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发表时间：
2013-09
影响因子：
3.3
通讯作者：
K. Shimoyama;Koma Sato;Shinkyu Jeong;S. Obayashi
中科院分区：
文献类型：
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作者：
K. Shimoyama;Koma Sato;Shinkyu Jeong;S. Obayashi
本文比较了多目标优化中更新Kriging代理模型的准则：期望改进（EI）、期望超体积改进（EHVI）、估计（EST）以及它们的组合（EHVI + EST）。EI已被常规地用作单独考虑每个目标函数值的随机改进的准则，而EHVI最近被提出作为考虑多目标优化中非支配解前沿的随机改进的准则。EST是在不考虑其不确定性的情况下，利用Kriging模型对各目标函数的非随机估计值。数值实验中实施的焊接梁的设计问题，经验表明，在无约束的情况下，EHVI保持精度之间的平衡，蔓延，并在非支配的解决方案基于Kriging模型的多目标优化的均匀性。此外，目前的实验表明，未来的调查技术处理约束的不确定性，以提高能力的EHVI在约束的情况下。
This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI + EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Kriging-model-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases.