Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Abstract

Surrogate-based-optimization methods provide a means to achieve high-fidelity design optimization at reduced computational cost by using a high-fidelity model in combination with lower-fidelity models that are less expensive to evaluate.This paper presents a provably convergent trust-region model-management methodology for variableparameterization design models: that is, models for which the design parameters are defined over different spaces.Corrected space mapping is introduced as a method to map between the variable-parameterization design spaces.It is then used with a sequential-quadratic-programming-like trust-region method for two aerospace-related design optimization problems.Results for a wing design problem and a flapping-flight problem show that the method outperforms direct optimization in the high-fidelity space.On the wing design problem, the new method achieves 76% savings in high-fidelity function calls.On a bat-flight design problem, it achieves approximately 45% time savings, although it converges to a different local minimum than did the benchmark.