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Kriging-based black-box global optimization : analysis and new algorithms

Abstract : The Efficient Global Optimization (EGO) is regarded as the state-of-the-art algorithm for global optimization of costly black-box functions. Nevertheless, the method has some difficulties such as the ill-conditioning of the GP covariance matrix and the slow convergence to the global optimum. The choice of the parameters of the GP is critical as it controls the functional family of surrogates used by EGO. The effect of different parameters on the performance of EGO needs further investigation. Finally, it is not clear that the way the GP is learned from data points in EGO is the most appropriate in the context of optimization. This work deals with the analysis and the treatment of these different issues. Firstly, this dissertation contributes to a better theoretical and practical understanding of the impact of regularization strategies on GPs and presents a new regularization approach based on distribution-wise GP. Moreover, practical guidelines for choosing a regularization strategy in GP regression are given. Secondly, a new optimization algorithm is introduced that combines EGO and CMA-ES which is a global but converging search. The new algorithm, called EGO-CMA, uses EGO for early exploration and then CMA-ES for final convergence. EGO-CMA improves the performance of both EGO and CMA-ES. Thirdly, the effect of GP parameters on the EGO performance is carefully analyzed. This analysis allows a deeper understanding of the influence of these parameters on the EGO iterates. Finally, a new self-adaptive EGO is presented. With the self-adaptive EGO, we introduce a novel approach for learning parameters directly from their contribution to the optimization.
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Hossein Mohammadi. Kriging-based black-box global optimization : analysis and new algorithms. Other. Université de Lyon, 2016. English. ⟨NNT : 2016LYSEM005⟩. ⟨tel-01332549v2⟩

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