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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Bibliographic Details
Published in:Optimization and engineering Vol. 22; no. 1; pp. 387 - 447
Main Authors: Pelamatti, Julien, Brevault, Loïc, Balesdent, Mathieu, Talbi, El-Ghazali, Guerin, Yannick
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2021
Springer Nature B.V
Springer Verlag
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-020-09520-z