A new acquisition function for robust Bayesian optimization of unconstrained problems

A new acquisition function is proposed for solving robust optimization problems via Bayesian Optimization. The proposed acquisition function reflects the need for the robust instead of the nominal optimum, and is based on the intuition of utilizing the higher moments of the improvement. The efficacy of Bayesian Optimization based on this acquisition function is demonstrated on four test problems, each affected by three different levels of noise. Our findings suggest the promising nature of the proposed acquisition function as it yields a better robust optimal value of the function in 6/12 test scenarios when compared with the baseline.Horizon 2020(H2020)766186Algorithms and the Foundations of Software technolog

Robust optimisation of computationally expensive models using adaptive multi-fidelity emulation

Computationally expensive models are increasingly employed in the design process of engineering products and systems. Robust design in particular aims to obtain designs that exhibit near-optimal performance and low variability under uncertainty. Surrogate models are often employed to imitate the behaviour of expensive computational models. Surrogates are trained from a reduced number of samples of the expensive model. A crucial component of the performance of a surrogate is the quality of the training set. Problems occur when sampling fails to obtain points located in an area of interest and/or where the computational budget only allows for a very limited number of runs of the expensive model. This paper employs a Gaussian process emulation approach to perform efficient single-loop robust optimisation of expensive models. The emulator is enhanced to propagate input uncertainty to the emulator output, allowing single-loop robust optimisation. Further, the emulator is trained with multi-fidelity data obtained via adaptive sampling to maximise the quality of the training set for the given computational budget. An illustrative example is presented to highlight how the method works, before it is applied to two industrial case studies

Metaheuristics for black-box robust optimisation problems

Our interest is in the development of algorithms capable of tackling robust black-box optimisation problems, where the number of model runs is limited. When a desired solution cannot be implemented exactly (implementation uncertainty) the aim is to find a robust one. Here that is to find a point in the decision variable space such that the worst solution from within an uncertainty region around that point still performs well. This thesis comprises three research papers. One has been published, one accepted for publication, and one submitted for publication. We initially develop a single-solution based approach, largest empty hypersphere (LEH), which identifies poor performing points in the decision variable space and repeatedly moves to the centre of the region devoid of all such points. Building on this we develop population based approaches using a particle swarm optimisation (PSO) framework. This combines elements of the LEH approach, a local descent directions (d.d.) approach for robust problems, and a series of novel features. Finally we employ an automatic generation of algorithms technique, genetic programming (GP), to evolve a population of PSO based heuristics for robust problems. We generate algorithmic sub-components, the design rules by which they are combined to form complete heuristics, and an evolutionary GP framework. The best performing heuristics are identified. With the development of each heuristic we perform experimental testing against comparator approaches on a suite of robust test problems of dimension between 2D and 100D. Performance is shown to improve with each new heuristic. Furthermore the generation of large numbers of heuristics in the GP process enables an assessment of the best performing sub-components. This can be used to indicate the desirable features of an effective heuristic for tackling the problem under consideration. Good performance is observed for the following characteristics: inner maximisation by random sampling, a small number of inner points, particle level stopping conditions, a small swarm size, a Global topology, and particle movement using a baseline inertia formulation augmented by LEH and d.d. capabilities

An exploration of building design and optimisation methods using Kriging meta-modelling

This thesis investigates the application of Kriging meta-modelling techniques in the field of building design and optimisation. In conducting this research, there were two key motivational factors. The first is the need for building designers to have tools that allow low energy buildings to be designed in a fast and efficient manner. The second motivating factor is the need for optimisation tools that account, or help account, for the wide variety of uses that a building might have; so-called Robust Optimisation (RO). This thesis therefore includes an analysis of Kriging meta-modelling and first applies this to simple building problems. I then use this simple building model to determine the effect of the updated UK Test Reference Years (TRYs) on energy consumption. Second, I examine Kriging-based optimisation techniques for a single objective. I then revisit the single-building meta-model to examine the effect of uncertainty on a neighbourhood of buildings and compare the results to the output of a brute-force analysis of a full building simulator. The results show that the Kriging emulation is an effective tool for creating a meta-model of a building. The subsequent use in the analysis of the effect of TRYs on building shows that UK buildings are likely to use less heating in the future but are likely to overheat more. In the final two chapters I use the techniques developed to create a robust building optimisation algorithm as well as using Kriging to improve the optimisation efficiency of the well-known NSGA-II algorithm. I show that the Kriging-based robust optimiser effectively finds more robust solutions than traditional global optimisation. I also show that Kriging techniques can be used to augment NSGA-II so that it finds more diverse solutions to some types of multi-objective optimisation problems. The results show that Kriging has significant potential in this field and I reveal many potential areas of future research. This thesis shows how a Kriging-enhanced NSGA-II multi-objective optimisation algorithm can be used to improve the performance of NSGA-II. This new algorithm has been shown to speed up the convergence of some multi-objective optimisation algorithms significantly. Although further work is required to verify the results for a wider variety of building applications, the initial results are promising.EPSRC Centre for Energy and the Environment, University of Exete

Efficiency Improvements to Adjoint-Based Aeroelastic Optimisations using a Trim-Corrected and Hybrid Mesh Deformation Strategy

This purpose of this research is to increase the efficiency of the aeroelastic shape optimisation process for commercial aircraft. Aeroelastic simulations capture the interaction between aerodynamic loading and structural displacements. High-fidelity aeroelastic simulations are computationally expensive, hence an adjoint-based approach to aircraft shape optimisation is the most suitable approach when large numbers of design parameters are present. The coupled nature of the fluid-structure interaction (FSI) is reflected in the resulting adjoint equations that are used to find the gradient. Previous coupled-adjoint optimisations performed in literature have used high-fidelity solvers for both computational fluid dynamics (CFD) and computational structural mechanics (CSM) while also satisfying the trim constraints within the FSI simulation. This project builds on those studies by proposing a simple yet powerful control surface parameterisation method for satisfying the trim constraints within the FSI simulation. An additional contribution of this work is an investigation into the effects that different mesh deformation algorithms have on the rate of convergence of the coupled-adjoint. An important aspect of capturing the FSI is an effective mesh deformation strategy. The algorithm used for deforming the mesh in an FSI simulation needs to be robust to large deformations but also efficient due to the large number of times it will be required. The radial basis function (RBF) mesh deformation strategy with a data-reduction algorithm is a popular method for achieving robust and efficient deformations within FSI simulations. A key contribution of this work is the finding that the application of a data-reduction algorithm to the input field of the mesh deformation strategy has a significantly negative effect on the convergence of the coupled-adjoint whilst having only a negligible effect on the convergence of the FSI simulation. The Delaunay Graph Mapping (DGM) mesh deformation algorithm is employed to obtain faster convergence of the coupled-adjoint than the RBF approach. To increase the efficiency of optimisation process, a hybrid mesh deformation strategy is proposed by using the RBF approach within the FSI simulation and the DGM approach within the coupled-adjoint. The gradients that are obtained via the hybrid mesh deformation approach are successfully validated. The hybrid mesh deformation strategy is then applied to two optimisation scenarios in the transonic flow region. The first is a lift constrained wing optimisation. The second is a lift and trim constrained optimisation performed on a full transport aircraft configuration. The developed trim-corrected and hybrid mesh deformation optimisation strategy is shown to demonstrate a more efficient coupled-adjoint aeroelastic shape optimisation process

Otimização eficiente global dirigida por metamodelos combinados : novos caminhos abertos pela aproximação por mínimos quadrados

Orientador: Alberto Luiz SerpaTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O presente trabalho representa a compilação dos resultados anteriores dessa pesquisa no campo de metamodelos combinados e otimização eficiente global (EGO), os quais foram sumetidos para publicação em periódicos especializados. Recentemente foi implementado nesse trabalho de doutorado o algoritmo LSEGO que é uma abordagem para conduzir algoritmos tipo EGO, baseando-se em metamodelos combinados através da aproximação por mínimos quadrados (metamodelos combinados LS). Através dos metamodelos combinados LS é possível estimar a incerteza da aproximação usando qualquer tipo de metamodelagem (e não somente do tipo kriging), permitindo estimar a função de expectativa de melhora para a função objetivo. Nos experimentos computacionais anteriores em problemas de otimização sem restrições, a abordagem LSEGO mostrou-se como uma alternativa viável para conduzir otimização eficiente global usando metamodelos combinados, sem se restringir a somente um ponto adicional por ciclo de otimização iterativa. Na presente tese o algoritmo LSEGO foi extendido de modo a tratar também problemas de otimização com restrições. Os resultados de testes numéricos com problemas analíticos e de referência e também em um estudo de caso de engenharia em escala industrial mostraram-se bastante promissores e competitivos em relação aos trabalhos similares encontrados na literaturaAbstract: In this work we review and compile the results of our previous research in the fields of ensemble of metamodels and efficient global optimization (EGO). Recently we implemented LSEGO that is an approach to drive EGO algorithms, based on LS (least squares) ensemble of metamodels. By means of LS ensemble of metamodels, it is possible to estimate the uncertainty of the prediction by using any kind of model (not only kriging) and provide an estimate for the expected improvement function. In previous numerical experiments with unconstrained optimization problems, LSEGO approach has shown to be a feasible alternative to drive efficient global optimization by using multiple or ensemble of metamodels, not restricted to kriging approximation or single infill point per optimization cycles. In the present work we extended the previous LSEGO algorithm to handle constrained optimization problems as well. Some numerical experiments were performed with analytical benchmark functions and also for industry scale engineering problems with competitive resultsDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânic