Novel Ensemble of Surrogates-Based Infill Criterion for Engineering Design Optimisation

Abstract

The problem of finding optimal designs in complex optimisation problems has often been solved, to a large extent by evolutionary algorithms (EAs). In many cases, these algorithms are employed as black-box methods over the design space. Black-box problems arise frequently in engineering design, and the principal barrier to the general use of EAs for those problems, is the huge number of function evaluations that is often required. This makes EAs an impractical approach when the function evaluation depends on expensive computational design analysis tools, such as computational solid mechanics analyses and computational fluid-dynamics analyses. These tools are usually referred to as high fidelity models, and the computational cost involved typically places a strict limit on the number of candidate designs that can be effectively evaluated during the optimisation process. This normally rules out the direct application of an optimisation algorithm.

Therefore, in many situations, there is a need for a simplified model able to provide an efficient representation of the real system with a restricted computational budget. These simplified models are called surrogate models, as they emulate the true response, arising from a variety of performance analysis. Once constructed, the surrogate can replace the original expensive model and the optimisation process proceed, using in general, a limited number of function calls to the high fidelity-model.

Kriging is a particularly popular method of constructing a surrogate model due to its ability to accurately predict complicated landscapes, whilst providing at the same time an analytical error estimate of the prediction. However, its construction can become prohibitively expensive as the dimensionality of the optimisation problem increases. In this case, a large number of expensive analyses are required to build a reliable model. This high modelling cost can become a considerable issue when considering limited computational budget, or limited computational time. A different approach is to rely on less expensive surrogate models, such as Radial Basis Functions, or a proper combination of them (selective and combined ensemble of RBFs), for which the tuning cost is negligible in comparison with Kriging.

This thesis provides a survey on related modelling and optimisation strategies that may help to solve high-dimensional, expensive, black-box problems taking a look at some of the current surrogate-based optimisation approaches in order to suggest possible ways of combining and extending them to increase their efficiency and to make them more suitable for industrial purposes. In the first part, we investigate the performance of well established surrogate modelling tools with respect to their performance over a range of sampling plans, problem dimensionalities, objective functions and computational budgets. In the second part, two different new updating strategies are introduced and investigated. The first of these strategies involves an assessment of the level of local agreement between the surrogates comprising the ensemble in order to prevent updates in regions within which there is considerable disagreement between the constituent surrogates. The second update strategy is based on a weighted combination of local agreement and global accuracy using information gathered from an ensemble of RBFs.

Finally, in the last part of the thesis, we then look at how these new update strategies perform on real engineering problems, and how they can be set up for high efficiency and robustness.

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Identifiers

ORCID for David Toal: orcid.org/0000-0002-2203-0302

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