Optimization and Engineering ( IF 2.1 ) Pub Date : 2020-05-25 , DOI: 10.1007/s11081-020-09510-1 Péter Zénó Korondi , Mariapia Marchi , Lucia Parussini , Carlo Poloni
In this work, a design optimisation strategy is presented for expensive and uncertain single- and multi-objective problems. Computationally expensive design fitness evaluations prohibit the application of standard optimisation techniques and the direct calculation of risk measures. Therefore, a surrogate-assisted optimisation framework is presented. The computational budget limits the number of high-fidelity simulations which makes impossible to accurately approximate the landscape. This motivates the use of cheap low-fidelity simulations to obtain more information about the unexplored locations of the design space. The information stemming from numerical experiments of various fidelities can be fused together with multi-fidelity Gaussian process regression to build an accurate surrogate model despite the low number of high-fidelity simulations. We propose a new strategy for automatically selecting the fidelity level of the surrogate model update. The proposed method is extended to multi-objective applications. Although, Gaussian processes can inherently model uncertain processes, here the deterministic input and uncertain parameters are treated separately and only the design space is modelled with a Gaussian process. The probabilistic space is modelled with a polynomial chaos expansion to allow also uncertainties of non-Gaussian type. The combination of the above techniques allows us to efficiently carry out a (multi-objective) design optimisation under uncertainty which otherwise would be impractical.
中文翻译:
计算预算有限的不确定性下的多保真设计优化策略
在这项工作中,提出了针对昂贵且不确定的单目标和多目标问题的设计优化策略。计算上昂贵的设计适用性评估禁止使用标准优化技术和直接计算风险度量。因此,提出了一种代理辅助的优化框架。计算预算限制了高保真模拟的数量,这使得无法准确估计景观。这鼓励使用廉价的低保真度仿真来获取有关设计空间未探索位置的更多信息。来自高保真度数值实验的信息可以与高保真度高斯过程回归融合在一起,以建立一个精确的替代模型,尽管高保真度仿真的数量很少。我们提出了一种自动选择替代模型更新的保真度级别的新策略。所提出的方法扩展到多目标应用。尽管高斯过程可以固有地对不确定过程进行建模,但是确定性输入和不确定参数在此分开处理,只有设计空间才能通过高斯过程进行建模。用多项式混沌展开对概率空间进行建模,以也允许非高斯类型的不确定性。上述技术的结合使我们能够在不确定的情况下有效地进行(多目标)设计优化,否则将是不切实际的。高斯过程可以固有地对不确定过程进行建模,此处确定性输入和不确定参数将分别处理,只有设计空间才能通过高斯过程进行建模。用多项式混沌展开对概率空间进行建模,以也允许非高斯类型的不确定性。上述技术的结合使我们能够在不确定性下有效地进行(多目标)设计优化,否则将是不切实际的。高斯过程可以固有地对不确定过程进行建模,此处确定性输入和不确定参数将分别处理,只有设计空间才能通过高斯过程进行建模。用多项式混沌展开对概率空间进行建模,以也允许非高斯类型的不确定性。上述技术的结合使我们能够在不确定性下有效地进行(多目标)设计优化,否则将是不切实际的。