Multi-fidelity design optimisation strategy under uncertainty with limited computational budget

• Published in: Optimization and engineering 2021-06, Vol.22 (2), p.1039-1064
• Main Authors: Korondi, Péter Zénó, Marchi, Mariapia, Parussini, Lucia, Poloni, Carlo
• Format: Article
• Language: English
• Subjects: Accuracy; Budgets; Control; Design optimization; Engineering; Environmental Management; Financial Engineering; Gaussian process; Mathematics; Mathematics and Statistics; Multiple objective analysis; Normal distribution; Operations Research/Decision Theory; Optimization; Parameter uncertainty; Polynomials; Research Article; Simulation; Statistical analysis; Strategy; Systems Theory
• ISSN: 1389-4420; 1573-2924
• DOI: 10.1007/s11081-020-09510-1

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.