Regularized infill criteria for multi-objective Bayesian optimization with application to aircraft design

TL;DR

This work extends the SEGOMOE framework to constrained multi-objective Bayesian optimization by introducing regularized infill criteria that stabilize enrichment in high-dimensional, ill-posed settings. The approach builds separate GP surrogates for each objective, uses a multi-objective acquisition function within the approximate feasible region, and then constructs an approximate Pareto front via a constrained solver on the GP surrogates, aided by regularization inspired by WB2. Empirical results on twelve benchmark problems and a CERAS-based aircraft-design case show that regularized infill improves convergence (lower $IGD^{+}$) and dramatically reduces the number of function evaluations required to obtain high-quality Pareto fronts, with a reported reduction by roughly a factor of 20 relative to NSGA-II in the aircraft design study. These findings demonstrate significant gains in efficiency for constrained MOO in engineering design, enabling rapid exploration of trade-offs with substantial computational savings, and point toward future extensions to mixed-categorical variables and broader software integration.

Abstract

Bayesian optimization is an advanced tool to perform ecient global optimization It consists on enriching iteratively surrogate Kriging models of the objective and the constraints both supposed to be computationally expensive of the targeted optimization problem Nowadays efficient extensions of Bayesian optimization to solve expensive multiobjective problems are of high interest The proposed method in this paper extends the super efficient global optimization with mixture of experts SEGOMOE to solve constrained multiobjective problems To cope with the illposedness of the multiobjective inll criteria different enrichment procedures using regularization techniques are proposed The merit of the proposed approaches are shown on known multiobjective benchmark problems with and without constraints The proposed methods are then used to solve a biobjective application related to conceptual aircraft design with ve unknown design variables and three nonlinear inequality constraints The preliminary results show a reduction of the total cost in terms of function evaluations by a factor of 20 compared to the evolutionary algorithm NSGA-II.

Figures (13)

• Figure 1: The summary of SEGOMOE algorithm steps.
• Figure 2: Obtained convergence plots (i.e., ${IGD}^{+}$ values across iterations): a comparison of the acquisition functions $EHVI$, $PI$ and $MPI$ within SEGOMOE using ${IGD}^{+}$.
• Figure 3: A comparison of the obtained Pareto fronts obtained using $20d$ points.
• Figure 4: Obtained convergence plots (i.e., ${IGD}^{+}$ values across iterations): regularization effect on the $PI$ acquisition function within SEGOMOE.
• Figure 5: Obtained convergence plots (i.e., ${IGD}^{+}$ values across iterations): Regularization effect on the $MPI$ acquisition function within SEGOMOE.