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Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

Bouhlel, Mohamed Amine and Bartoli, Nathalie and Regis, Rommel and Ostmane, Abdelkader and Morlier, Joseph Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method. (2018) Engineering Optimization, 50 (12). 2038-2053. ISSN 0305-215X

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Official URL: https://doi.org/10.1080/0305215X.2017.1419344

Abstract

In many engineering optimization problems, the number of function evaluations is often very limited because of the computational cost to run one high-fidelity numerical simulation. Using a classic optimization algorithm, such as a derivative-based algorithm or an evolutionary algorithm, directly on a computational model is not suitable in this case. A common approach to addressing this challenge is to use black-box surrogate modeling techniques. The most popular surrogate-based optimization algorithm is the Efficient Global Optimization (EGO) algorithm, which is an iterative sampling algorithm that adds one (or many) point(s) per iteration. This algorithm is often based on an infill sampling criterion, called expected im- provement, which represents a trade-off between promising and uncertain areas. Many studies have shown the efficiency of EGO, particularly when the number of input variables is relatively low. However, its performanceon high-dimensional problems is still poor since the Kriging models used are time-consuming to build. To deal with this issue, this paper introduces a surrogate-based optimization method that is suited to high-dimensional problems. The method first uses the “locating the regional extreme” criterion, which incorporates minimizing the surrogate model while also maximizing the expected improvement criterion. Then, it replaces the Kriging models by the KPLS(+K) models (Kriging combined with the partial least squares method), which are more suitable for high-dimensional problems. Finally, the proposed approach is validated by a comparison with alternative methods existing in the literature on some analytical functions and on 12-dimensional and 50-dimensional instances of the benchmark automotive problem “MOPTA08”.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Ecole nationale supérieure des Mines d'Albi-Carmaux - IMT Mines Albi (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Other partners > Saint Joseph's University (USA)
Other partners > Société nationale d'étude et de constructions de moteurs d'avion - SNECMA (FRANCE)
Other partners > University of Michigan - U-M (USA)
Laboratory name:
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Deposited By: Joseph Morlier
Deposited On:22 Mar 2018 08:46

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