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A comparative study of multi-objective expected improvement for aerodynamic design

机译：空气动力学设计多目标预期改进的比较研究

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Multi-objective optimization in aerodynamics plays an important role in revealing trade-offs between conflicting objectives in order to discover important knowledge and insight for better future design. Of interest here is the use of Kriging surrogate models incorporated into a sequential Bayesian optimization (BO) strategy. In this paper, we studied four variants of multi-objective BO (MOBO) techniques that are based on expected improvement (EI), that is, Euclidean-based EI (EEI), expected hypervolume improvement (EHVI), ParEGO, and expected inverted penalty boundary intersection improvement (EIPBII) to understand their capabilities on handling multi-objective aerodynamic optimization problems. Numerical tests were performed on a set consisting of six generalized Schaffer problems (GSP), five low-fidelity, and one high-fidelity airfoil design problems. Results suggest that EHVI is the only method which consistently performed well on artificial and aerodynamic problems. EEI yields the worst performance and is not suitable to deal with various problem complexities. ParEGO, although it performs modestly on GSP, surprisingly works well on the low- and high-fidelity problems. On the other hand, EIPBII encounters the opposite case, where it is one of the best performer on GSP but yields modest performance on the aerodynamic problems. In light of the results, we suggest that EHVI is a highly potential MOBO method to be applied for multi-objective aerodynamic design optimization. (C) 2019 Elsevier Masson SAS. All rights reserved.
机译：空气动力学中的多目标优化在揭示相互冲突目标之间的权衡方面发挥着重要作用，以便了解更好的未来设计的重要知识和洞察力。这里的兴趣是使用Kriging代理模型，该模型纳入了顺序贝叶斯优化（BO）策略。在本文中，我们研究了基于预期改进（EI）的多目标Bo（MOBO）技术的四种变体，即欧几里德的EI（EEI），预期的超卓越化改善（EHVI），Parego和预期倒置罚款边界交叉口改进（EIPBII）了解他们对处理多目标空气动力学优化问题的能力。在由六个广义的Schaffer问题（GSP），五个低保真机构和一个高保真翼型设计问题组成的集合上进行数值测试。结果表明，EHVI是唯一在人工和空气动力学问题上持续表现良好的方法。 EEI产生最差的性能，不适合处理各种问题复杂性。 Parego，虽然它在GSP上谦虚地表演，但令人惊讶地效果很好，效果很好。另一方面，EIPBII遇到了相反的情况，在那里它是GSP上最好的表演者之一，但在空气动力学问题上产生适度的性能。鉴于结果，我们建议EHVI是应用于多目标空气动力学设计优化的高度潜在的MOBO方法。 （c）2019年Elsevier Masson SAS。版权所有。

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