A comparison of mixed-variables Bayesian optimization approaches

Autor: Jhouben Cuesta Ramirez, Rodolphe Le Riche, Olivier Roustant, Guillaume Perrin, Cédric Durantin, Alain Glière
Přispěvatelé: Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information (CEA-LETI), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), École des Mines de Saint-Étienne (Mines Saint-Étienne MSE), Institut Mines-Télécom [Paris] (IMT), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes (LIMOS), Ecole Nationale Supérieure des Mines de St Etienne-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Université Clermont Auvergne (UCA)-Université Clermont Auvergne (UCA), Institut Henri Fayol (FAYOL-ENSMSE), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Département Génie mathématique et industriel (FAYOL-ENSMSE), Ecole Nationale Supérieure des Mines de St Etienne-Institut Henri Fayol, Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA), Département Composants et Systèmes (COSYS), Université Gustave Eiffel, Centre d'Études de Limeil-Valenton (CEA-DAM), Direction des Applications Militaires (DAM), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Centre National de la Recherche Scientifique (CNRS)-Université Clermont Auvergne (UCA)-Institut national polytechnique Clermont Auvergne (INP Clermont Auvergne), Ecole Nationale Supérieure des Mines de St Etienne (ENSM ST-ETIENNE)-Institut Henri Fayol, Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Advanced Modeling and Simulation in Engineering Sciences
Advanced Modeling and Simulation in Engineering Sciences, 2022, ⟨10.21203/rs.3.rs-1050987/v1⟩
ISSN: 2213-7467
Popis: Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box simulation.General mixed and costly optimization problems are therefore of a great practical interest, yet their resolution remains in a large part an open scientific question. In this article, costly mixed problems are approached through Gaussian processes where the discrete variables are relaxed into continuous latent variables. The continuous space is more easily harvested by classical Bayesian optimization techniques than a mixed space would. Discrete variables are recovered either subsequently to the continuous optimization, or simultaneously with an additional continuous-discrete compatibility constraint that is handled with augmented Lagrangians. Several possible implementations of such Bayesian mixed optimizers are compared. In particular, the reformulation of the problem with continuous latent variables is put in competition with searches working directly in the mixed space. Among the algorithms involving latent variables and an augmented Lagrangian, a particular attention is devoted to the Lagrange multipliers for which a local and a global estimation techniques are studied. The comparisons are based on the repeated optimization of three analytical functions and a beam design problem.
Accepted for publication in Advanced Modeling and Simulation in Engineering Sciences, march 2022
Databáze: OpenAIRE
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