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A comparison of mixed-variables Bayesian optimization approaches
- Source :
- Advanced Modeling and Simulation in Engineering Sciences, Advanced Modeling and Simulation in Engineering Sciences, 2022, ⟨10.21203/rs.3.rs-1050987/v1⟩
- Publication Year :
- 2021
- Publisher :
- HAL CCSD, 2021.
-
Abstract
- 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.<br />Accepted for publication in Advanced Modeling and Simulation in Engineering Sciences, march 2022
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Applied Mathematics
Machine Learning (stat.ML)
Statistics - Applications
Statistics - Computation
[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Computer Science Applications
Machine Learning (cs.LG)
Machine Learning
Optimization and Control (math.OC)
Statistics - Machine Learning
Modeling and Simulation
Applications
Computation
FOS: Mathematics
Applications (stat.AP)
Engineering (miscellaneous)
Mathematics - Optimization and Control
Computation (stat.CO)
Subjects
Details
- Language :
- English
- ISSN :
- 22137467
- Database :
- OpenAIRE
- Journal :
- Advanced Modeling and Simulation in Engineering Sciences, Advanced Modeling and Simulation in Engineering Sciences, 2022, ⟨10.21203/rs.3.rs-1050987/v1⟩
- Accession number :
- edsair.doi.dedup.....b78d9c8a9bf6ff1eb6ce1868d215934c