In design optimization of complex systems, the surrogate model approach relying on progressively enriched Design of Experiments (DOE) avoids efficiency problems encountered when embedding simulation codes within optimization loops. However, an efficient a priori sampling of the design space rapidly becomes costly when using High-Fidelity (HF) simulators, especially in high dimension. On the other hand, in applications such as aeronautical design, multiple simulation tools are frequently available for the same problem, generally with a degree of precision inversely proportional to the CPU cost. Thus, the concept of multi-fidelity proposes to merge different levels of fidelity within a single model with controlled variance. Based on recent Reduced-Order Modeling (ROM) techniques, an alternative approach allows to pursue the objective of mastering the simulation budget by replacing costly models with their approximate full-field counterparts, providing additional insight to scalar surrogates built directly from the Quantities of Interest (QoI). Both approaches: multi-fidelity and ROM, may be combined, allowing for additional flexibility in choosing the degree of fidelity required in different zones of the design space. This paper reviews the strategies that seek to improve surrogate-based optimization efficiency, including ROM, multi-fidelity metamodeling, and DOE enrichment strategies.

This article addresses the problem of constrained derivative-free optimization in a multi-fidelity (or variable-complexity) framework using Bayesian optimization techniques. It is assumed that the objective and constraints involved in the optimization problem can be evaluated using either an accurate but time-consuming computer program or a fast lower-fidelity one. In this setting, the aim is to solve the optimization problem using as few calls to the high-fidelity program as possible. To this end, it is proposed to use Gaussian process models with trend functions built from the projection of low-fidelity solutions on a reduced-order basis synthesized from scarce high-fidelity snapshots. A study on the ability of such models to accurately represent the objective and the constraints and a comparison of two improvement-based infill strategies are performed on a representative benchmark test case.