Abstract
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.
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Notes
Polynomial Chaos Expansion can be considered as a particular subclass of Gaussian process regression with particular regression functions and Kronecker delta covariance function (Schobi et al. 2015).
It is also possible to construct a multi-output GP. However, the training of a multi-output GP is challenging as a kernel should be found which can capture the correlation of both the input and output space (Press William et al. 2007).
For maximisation the appropriate signs must be changed.
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This work was partially supported by the H2020-MSCA-ITN-2016 UTOPIAE, Grant Agreement 722734.
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Korondi, P.Z., Marchi, M., Parussini, L. et al. Multi-fidelity design optimisation strategy under uncertainty with limited computational budget. Optim Eng 22, 1039–1064 (2021). https://doi.org/10.1007/s11081-020-09510-1
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DOI: https://doi.org/10.1007/s11081-020-09510-1