Constrained multifidelity optimization using model calibration

Abstract

Multifidelity optimization approaches seek to bring higher-fidelity analyses earlier into the design process by using performance estimates from lower-fidelity models to accelerate convergence towards the optimum of a high-fidelity design problem. Current multifidelity optimization methods generally fall into two broad categories: provably convergent methods that use either the high-fidelity gradient or a high-fidelity pattern-search, and heuristic model calibration approaches, such as interpolating high-fidelity data or adding a Kriging error model to a lower-fidelity function. This paper presents a multifidelity optimization method that bridges these two ideas; our method iteratively calibrates lower-fidelity information to the high-fidelity function in order to find an optimum of the high-fidelity design problem. The algorithm developed minimizes a high-fidelity objective function subject to a high-fidelity constraint and other simple constraints. The algorithm never computes the gradient of a high-fidelity function; however, it achieves first-order optimality using sensitivity information from the calibrated low-fidelity models, which are constructed to have negligible error in a neighborhood around the solution. The method is demonstrated for aerodynamic shape optimization and shows at least an 80% reduction in the number of high-fidelity analyses compared other single-fidelity derivative-free and sequential quadratic programming methods. The method uses approximately the same number of high-fidelity analyses as a multifidelity trust-region algorithm that estimates the high-fidelity gradient using finite differences.