🤖 AI Summary
Bayesian optimization (BO) methods for computationally expensive, nonlinearly constrained multi-objective optimization problems—such as aircraft conceptual design—often suffer from ill-conditioning in multi-objective acquisition functions, leading to unstable surrogate updates and poor convergence.
Method: This paper extends the SEGOMOE framework by introducing a novel regularization mechanism directly into the multi-objective acquisition function, synergistically integrating Kriging surrogates, a Mixture-of-Experts (MoE) architecture, and an enhanced SEGO algorithm.
Contribution/Results: The proposed approach systematically alleviates the trade-off between ill-conditioning and convergence in constrained multi-objective BO. Empirical evaluation on aircraft design tasks demonstrates that it achieves high-quality Pareto fronts using only 5% of the function evaluations required by NSGA-II, significantly improving the efficiency of identifying high-fidelity, low-cost compromise solutions.
📝 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.