Multi-objective Bayesian Optimization With Mixed-categorical Design Variables for Expensive-to-evaluate Aeronautical Applications

TL;DR

This paper addresses expensive, multi-objective aeronautical design optimization with mixed continuous, integer, and categorical variables. It introduces two frameworks: JPAD Optimizer for surrogate-based optimization and SEGOMOE for Bayesian optimization with mixtures of experts, where SEGOMOE employs continuous relaxation and Partial Least Squares to manage high dimensionality, along with Gaussian-process surrogates and a regularized acquisition $α^{reg}_{f}(x)$ to drive infill; a post-processing NSGA-II step constructs the predicted Pareto front from the enriched data. The authors validate the methods on three realistic AGILE 4.0 cases, achieving favorable Pareto fronts with relatively few expensive evaluations and demonstrating diverse trade-offs between performance, cost, and manufacturing/supply-chain considerations. The work advances practical mixed-variable, multi-objective optimization for large-scale aeronautical design and points to future directions in hierarchical/mixed discrete kernels and system-of-systems optimization under the COLOSSUS program.

Abstract

This work aims at developing new methodologies to optimize computational costly complex systems (e.g., aeronautical engineering systems). The proposed surrogate-based method (often called Bayesian optimization) uses adaptive sampling to promote a trade-off between exploration and exploitation. Our in-house implementation, called SEGOMOE, handles a high number of design variables (continuous, discrete or categorical) and nonlinearities by combining mixtures of experts for the objective and/or the constraints. Additionally, the method handles multi-objective optimization settings, as it allows the construction of accurate Pareto fronts with a minimal number of function evaluations. Different infill criteria have been implemented to handle multiple objectives with or without constraints. The effectiveness of the proposed method was tested on practical aeronautical applications within the context of the European Project AGILE 4.0 and demonstrated favorable results. A first example concerns a retrofitting problem where a comparison between two optimizers have been made. A second example introduces hierarchical variables to deal with architecture system in order to design an aircraft family. The third example increases drastically the number of categorical variables as it combines aircraft design, supply chain and manufacturing process. In this article, we show, on three different realistic problems, various aspects of our optimization codes thanks to the diversity of the treated aircraft problems.

Figures (11)

• Figure 1: Hypervolume Improvement: the hypervolume indicator of the non-dominated set (green points) corresponds to the area dominated by it, up to $R$ (reference point in black). The gray rectangle is the hypervolume improvement brought by the new added point in magenta.
• Figure 2: XDSM DOE MDA for Airframe upgrade design.
• Figure 3: XDSM optimization for airframe upgrade design.
• Figure 4: Reference regional jet aircraft.
• Figure 5: Different PF using four objectives: 108 DOE points for JPAD (orange dot), 15 points (blue circle) on the final PF combining JPAD (red cross) and SEGOMOE (green cross) databases.