Upper Trust Bound Feasibility Criterion for Mixed Constrained Bayesian Optimization with Application to Aircraft Design
This work addresses mixed constrained optimization for expensive black-box problems like aircraft design, representing an incremental improvement over existing methods.
The paper tackled mixed constrained Bayesian optimization problems by adapting the super efficient global optimization algorithm with an upper trust bound for constraint handling and a refinement procedure for trade-off enhancement, showing good potential in numerical experiments and superiority over state-of-the-art solvers in an aircraft design application.
Bayesian optimization methods have been successfully applied to black box optimization problems that are expensive to evaluate. In this paper, we adapt the so-called super effcient global optimization algorithm to solve more accurately mixed constrained problems. The proposed approach handles constraints by means of upper trust bound, the latter encourages exploration of the feasible domain by combining the mean prediction and the associated uncertainty function given by the Gaussian processes. On top of that, a refinement procedure, based on a learning rate criterion, is introduced to enhance the exploitation and exploration trade-off. We show the good potential of the approach on a set of numerical experiments. Finally, we present an application to conceptual aircraft configuration upon which we show the superiority of the proposed approach compared to a set of the state-of-the-art black box optimization solvers. Keywords: Global Optimization, Mixed Constrained Optimization, Black box optimization, Bayesian Optimization, Gaussian Process.