Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Abstract

Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm-super efficient global optimization coupled with mixture of experts (SEGOMOE)can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.

Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

“…We extend the EGO algorithm to work with multiple fidelities. In practice as the SEGOMOE framework proposed by Bartoli et al [11,12,13] is capable of handling both unconstrained and constrained problems and this with or without MOE, we choose to note in this paper the unconstrained version of SEGOMOE without MOE as EGO. The multi-fidelity is defined as MFEGO.…”

“…In 2002, EGO was extended to constrained problems with the development of SEGO [10]). More recently SEGO was coupled to MOE (mixture of experts) methodology in order to solve high dimensional variables and constrained optimization problems such as wing shape aerodynamic optimization in the SEGOMOE framework [11][12][13]. SEGOMOE will be used in this work as a reference for surrogate based constrained optimizer with a single high fidelity (HF).…”

On the Use of Upper Trust Bounds in Constrained Bayesian Optimization Infill Criteria

“…The latter ones are called design variables and their number increases with the number of disciplines. In this way, the resulting MDO problem is a large-scale constrained optimization problem min The models used to represent the different disciplines [3] are often very accurate, meaning that a large number of design variables has to be managed during the optimization process. Moreover, the models can be very time consuming to evaluate and do not always provide the gradient of the objective and constraints functions.…”

“…Bayesian Optimization (BO) [4] methods are proposed to solve expensive time consuming problems [3,[5][6][7][8][9][10]. The BO procedure uses only few objective function evaluations to solve the regarded optimization problems by means of Gaussian process (GP) models [11].…”

“…Currently, most of the BO methods are not adapted to handle large-scale constrained optimization problems, particularly this is due to the difficulty of estimating accurately the feasible domain. A possible solution was proposed in [3] where one uses the super efficient global optimization (SEGO) framework [12] and handles separately the objective and constraints functions in the optimization procedure using a dedicated criterion. The latter constraints criterion, although is practical, does not take into account the accuracy level of the constraints surrogate models during the estimation of the feasible domain.…”