Convergent Multifidelity Optimization using Bayesian Model Calibration
Andrew March, Karen E. Willcox · 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference · 2010
Multi delity optimization approaches seek to bring higherdelity analyses earlier into the design process by using performance estimates from lowerdelity models to accelerate convergence towards the optimum of a highdelity design problem. Current multi delity optimization methods generally fall into two broad categories: provably convergent methods that use either the highdelity gradient or a highdelity pattern-search, and heuristic model calibration approaches, such as interpolating highdelity data or adding a Kriging error model to a lowerdelity function. This paper presents a multi delity optimization method that combines these two ideas; our method iteratively calibrates lowerdelity information to the highdelity function, and is provably convergent to an optimum of the highdelity design problem. The algorithm developed minimizes a highdelity objective function subject to a highdelity constraint and other simple constraints. The algorithm never computes the gradient of a highdelity function; however, it demonstrates convergence using sensitivity information from the calibrated lowdelity models, which are constructed to have negligible error in a neighborhood around the solution. The method is demonstrated for aerodynamic shape optimization and shows an 80% reduction in the number of highdelity analyses compared with a singledelity sequential quadratic programming formulation and a similar number of highdelity analyses compared with a multi delity trust-region algorithm that estimates the highdelity gradient using nite di erences.