Bayesian optimization of variable-size design space problems

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a vari...

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Vydáno v:	Optimization and engineering Ročník 22; číslo 1; s. 387 - 447
Hlavní autoři:	Pelamatti, Julien, Brevault, Loïc, Balesdent, Mathieu, Talbi, El-Ghazali, Guerin, Yannick
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.03.2021 Springer Nature B.V Springer Verlag
Témata:	Bayesian analysis Budgets Complex systems Complex variables Continuity (mathematics) Control Covariance Design optimization Engineering Engineering Sciences Environmental Management Financial Engineering Kernel functions Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Physics Research Article Systems design Systems Theory Variables Mixed-variable optimization problems Bayesian optimization Variable-size design space optimization problems Discrete variables
ISSN:	1389-4420, 1573-2924
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Abstract	Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists of a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches.
AbstractList	Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists of a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches.
Author	Brevault, Loïc Balesdent, Mathieu Pelamatti, Julien Guerin, Yannick Talbi, El-Ghazali
Author_xml	– sequence: 1 givenname: Julien surname: Pelamatti fullname: Pelamatti, Julien email: julien.pelamatti@gmail.com organization: DTIS, ONERA, Université Paris Saclay, Centre National d’Études Spatiales, Direction des lanceurs – sequence: 2 givenname: Loïc surname: Brevault fullname: Brevault, Loïc organization: DTIS, ONERA, Université Paris Saclay – sequence: 3 givenname: Mathieu surname: Balesdent fullname: Balesdent, Mathieu organization: DTIS, ONERA, Université Paris Saclay – sequence: 4 givenname: El-Ghazali surname: Talbi fullname: Talbi, El-Ghazali organization: Inria Lille - Nord Europe – sequence: 5 givenname: Yannick surname: Guerin fullname: Guerin, Yannick organization: Centre National d’Études Spatiales, Direction des lanceurs
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Keywords	Mixed-variable optimization problems Bayesian optimization Variable-size design space optimization problems Discrete variables
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SubjectTerms	Bayesian analysis Budgets Complex systems Complex variables Continuity (mathematics) Control Covariance Design optimization Engineering Engineering Sciences Environmental Management Financial Engineering Kernel functions Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Physics Research Article Systems design Systems Theory Variables
Title	Bayesian optimization of variable-size design space problems
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