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Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design

Paul Saves, Nathalie Bartoli, Youssef Diouane, Thierry Lefebvre, Joseph Morlier, Christophe David, Eric Nguyen Van, Sébastien Defoort

TL;DR

This paper tackles the challenge of optimizing engineering designs with mixed continuous, integer, and categorical variables in aircraft design. It introduces a Bayesian optimization framework that combines continuous relaxation with an adaptive partial least squares (KPLS) kernel to drastically reduce the number of hyperparameters in the Gaussian process surrogate. The method uses a WB2s acquisition and UTB constraint handling to navigate expensive simulations, and an adaptive mechanism based on Wold's criterion selects the number of PLS components during optimization. The approach is validated on analytical benchmarks and real FAST-OAD aircraft-design problems CERAS and DRAGON, showing substantial performance gains over genetic algorithms and robustness in high-dimensional settings. The results demonstrate practical applicability for rapid concept-level aircraft design with mixed variable types.

Abstract

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.

Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design

TL;DR

This paper tackles the challenge of optimizing engineering designs with mixed continuous, integer, and categorical variables in aircraft design. It introduces a Bayesian optimization framework that combines continuous relaxation with an adaptive partial least squares (KPLS) kernel to drastically reduce the number of hyperparameters in the Gaussian process surrogate. The method uses a WB2s acquisition and UTB constraint handling to navigate expensive simulations, and an adaptive mechanism based on Wold's criterion selects the number of PLS components during optimization. The approach is validated on analytical benchmarks and real FAST-OAD aircraft-design problems CERAS and DRAGON, showing substantial performance gains over genetic algorithms and robustness in high-dimensional settings. The results demonstrate practical applicability for rapid concept-level aircraft design with mixed variable types.

Abstract

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and categorical variables might arise during the optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization but most existing approaches severely increase the number of the hyperparameters related to the surrogate model. In this paper, we address this issue by constructing surrogate models using less hyperparameters. The reduction process is based on the partial least squares method. An adaptive procedure for choosing the number of hyperparameters is proposed. The performance of the proposed approach is confirmed on analytical tests as well as two real applications related to aircraft design. A significant improvement is obtained compared to genetic algorithms.

Paper Structure

This paper contains 13 sections, 6 equations, 13 figures, 7 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Continuous constrained Bayesian optimization
  3. Mixed categorical constrained Bayesian optimization
  4. Results and discussion
  5. Implementation choices
  6. Benchmark test cases including unconstrained and constrained optimization problems
  7. Unconstrained optimization
  8. Constrained optimization
  9. Overall benchmark results
  10. Aircraft design test cases
  11. "CERAS" configuration
  12. "DRAGON" configuration
  13. Conclusion and perspectives

Figures (13)

  • Figure 1: "Branin 5" obtained optimization results. The Boxplots are generated, after 50 iterations, using the 20 best points.
  • Figure 2: "Set 1" obtained optimization results.
  • Figure 3: "Branin 3" optimization results.
  • Figure 4: "Branin 4" optimization results.
  • Figure 5: "Branin 4" PLS number of components.
  • ...and 8 more figures