Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models

Alexandrov, Natalia; Lewis, Robert; Gumbert, Clyde R.; Green, Lawrence L.; Newman, Perry A.

doi:10.2514/2.2877

Cited by 268 publications

(220 citation statements)

References 16 publications

(19 reference statements)

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“…The above description outlines the core of the trust-region approach to the use of surrogate models. More details can be found in Alexandrov et al [2], with a multi-fidelity implementation in Alexandrov et al [3].…”

Section: The Trust-region Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,869

954

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The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.

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Section: The Trust-region Methodsmentioning

confidence: 99%

“…Of note is the use of the augmented Lagrangian method for constrained optimization in a surrogate-based trust region search [3]. More simple to implement is the application of penalty functions [67].…”

Section: Constraintsmentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,869

954

View full text Add to dashboard Cite

show abstract

“…Hierarchical surrogates are derived from higher-fidelity models using approaches such as simplifying physics assumptions, coarser grids, alternative basis expansions, and looser residual tolerances. Examples in the literature include the use of simplified-physics models in design optimization [3,167], multigrid approaches to optimization of systems governed by differential equations [124,151], and mesh coarsening for solving a linear inverse problem [18].…”

Section: Parametric Model Reduction and Surrogate Modelingmentioning

confidence: 99%

“…3 Here, recall that we assumed (2.1) to be pointwise asymptotically stable so that (2.21) and (2.22) are well-defined.…”

Section: Error Measuresmentioning

confidence: 99%

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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“…However, there are cases in which target algorithm evaluations are overwhelmingly costly compared to the overall computational resources and time available for the parameter optimization process. Real-world applications of this nature can be found in the optimization of engineering designs in the aerospace and automotive industry (Alexandrov et al, 2001), in hydrological applications (Mayer et al, 2002), and in climate modeling. In those examples, the algorithms to be optimized control or model the behavior of complex systems, and evaluating their performance for a single parameter configuration can take hundreds of CPU hours.…”

Section: Interactive Exploration Of Parameter Spacementioning

confidence: 99%

Sequential Model-Based Parameter Optimization: an Experimental Investigation of Automated and Interactive Approaches

Hutter

Bartz-Beielstein

Hoos

et al. 2010

Experimental Methods for the Analysis of Optimization Algorithms

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This work experimentally investigates model-based approaches for optimizing the performance of parameterized randomized algorithms. Such approaches build a response surface model and use this model for finding good parameter settings of the given algorithm. We evaluated two methods from the literature that are based on Gaussian process models: sequential parameter optimization (SPO) (Bartz-Beielstein et al, 2005) and sequential Kriging optimization (SKO) (Huang et al, 2006). SPO performed better "out-of-the-box," whereas SKO was competitive when response values were log transformed. We then investigated key design decisions within the SPO paradigm, characterizing the performance consequences of each. Based on these findings, we propose a new version of SPO, dubbed SPO + , which extends SPO with a novel intensification procedure and a log-transformed objective function. In a domain for which performance results for other (model-free) parameter optimization approaches are available, we demonstrate that SPO + achieves state-of-the-art performance. Finally, we compare this automated parameter tuning approach to an interactive, manual process that makes use of classical regression techniques. This interactive approach is particularly useful when only a relatively small number of parameter configurations can be evaluated. Because it can relatively quickly draw attention to important parameters and parameter interactions, it can help experts gain insights into the parameter response of a given algorithm and identify reasonable parameter settings.

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Approximation and Model Management in Aerodynamic Optimization with Variable-Fidelity Models

Cited by 268 publications

References 16 publications

Recent advances in surrogate-based optimization

Recent advances in surrogate-based optimization

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

Sequential Model-Based Parameter Optimization: an Experimental Investigation of Automated and Interactive Approaches

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