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

By T. Robinson, Michael S. Eldred, Karen E. Willcox, Robert Haimes. 2008

284 citations recorded by the source corpus.

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 variable-parameterization 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.

Subfields: Computational Theory and Mathematics, Global and Planetary Change, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Global and Planetary Change

In Statistics and Probability

Citations in the corpus

A Stochastic Collocation Algorithm with Multifidelity Models (2014, methodology): “It has also recently become popular to utilize low-fidelity and reduced-order models in local searches of parameter space for optimal placement of new design points [7, 21, 22].”
Metamodeling in Multidisciplinary Design Optimization: How Far Have We Really Come? (2014, methodology): “mapping has been also developed and compared with the previously implemented techniques [163].”
Review of multi-fidelity models (2016, background): “Reference Dimensionality [57] 2D/3D Eu, [82] 1D/3D RANS+TM, [85] 2D/3D URANS, [108] 2D/3D, [147] 1D/2D RANS, [158] 1D/2D Li, [178] 1D/3D RANS, [190] 1D/3D RANS, [207] 1D,2D/3D RANS Coarse/Reﬁned [5] Eu, [25] RANS, [34] Eu, [35] Eu, [36] Li/Eu, [83] RANS, [89] MPF, [92] MHD, [99] Eu, [100], Eu[103] E”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “The work [180] develops a trust-region multifidelity approach for combining low- and high-fidelity models that are defined over different design spaces.”
Multiobjective Aerodynamic Optimization by Variable-Fidelity Models and Response Surface Surrogates (2016, methodology): “Various methods and algorithms are available, from conventional gradient-based algorithms [7], including those using inexpensive adjoint sensitivities [8,9], to the increasingly popular surrogate-based optimization (SBO) techniques [10–15] that offer an efficient global optimization and a substantia”
Review of surrogate modeling in water resources (2012, methodology): “Another mapping approach has been proposed based on proper orthogonal decomposition (also called principal component analysis) and compared against space mapping in a trust-region optimization framework [Robinson, 2007; Robinson et al., 2006].”