Ensemble of surrogates
31 Jan 2007-Structural and Multidisciplinary Optimization (Springer-Verlag)-Vol. 33, Iss: 3, pp 199-216
TL;DR: The utility of an ensemble of surrogate models is extended to identify regions of possible high errors at locations where predictions of surrogates widely differ, and provide a more robust approximation approach.
Abstract: The custom in surrogate-based modeling of complex engineering problems is to fit one or more surrogate models and select the one surrogate model that performs best. In this paper, we extend the utility of an ensemble of surrogates to (1) identify regions of possible high errors at locations where predictions of surrogates widely differ, and (2) provide a more robust approximation approach. We explore the possibility of using the best surrogate or a weighted average surrogate model instead of individual surrogate models. The weights associated with each surrogate model are determined based on the errors in surrogates. We demonstrate the advantages of an ensemble of surrogates using analytical problems and one engineering problem. We show that for a single problem the choice of test surrogate can depend on the design of experiments.
Citations
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TL;DR: The present state of the art of constructing surrogate models and their use in optimization strategies is reviewed and extensive use of pictorial examples are made to give guidance as to each method's strengths and weaknesses.
1,919 citations
TL;DR: This paper provides a concise overview of the history and recent developments in surrogate-assisted evolutionary computation and suggests a few future trends in this research area.
Abstract: Surrogate-assisted, or meta-model based evolutionary computation uses efficient computational models, often known as surrogates or meta-models, for approximating the fitness function in evolutionary algorithms. Research on surrogate-assisted evolutionary computation began over a decade ago and has received considerably increasing interest in recent years. Very interestingly, surrogate-assisted evolutionary computation has found successful applications not only in solving computationally expensive single- or multi-objective optimization problems, but also in addressing dynamic optimization problems, constrained optimization problems and multi-modal optimization problems. This paper provides a concise overview of the history and recent developments in surrogate-assisted evolutionary computation and suggests a few future trends in this research area.
1,072 citations
Cites background from "Ensemble of surrogates"
...The benefit of using multiple surrogates has also been shown empirically in many papers [54,55,52]....
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TL;DR: This paper compares Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriged model, permitting the comparison of different forms of a k Riging model.
Abstract: The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.
833 citations
TL;DR: In many situations across computational science and engineering, multiple computational models are available that describe a system of interest as discussed by the authors, and these different models have varying evaluation costs, i.e.
Abstract: In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs...
678 citations
TL;DR: Two of the frequently used surrogates, radial basis functions, and Kriging are tested on a variety of test problems and guidelines for the choice of appropriate surrogate model are discussed.
421 citations
References
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Book•
29 Aug 1995TL;DR: Using a practical approach, this book discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques.
Abstract: From the Publisher:
Using a practical approach, it discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques. Features numerous authentic application examples and problems. Illustrates how computers can be a useful aid in problem solving. Includes a disk containing computer programs for a response surface methodology simulation exercise and concerning mixtures.
10,104 citations
TL;DR: The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.
2,152 citations
TL;DR: This paper surveys their existing application in engineering design, and addresses the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes, along with recommendations for the appropriate use of statistical approximation techniques in given situations.
Abstract: The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of today’s engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper, we review several of these techniques, including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning and kriging. We survey their existing application in engineering design, and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations, and how common pitfalls can be avoided.
1,886 citations
TL;DR: This paper systematically compare four popular metamodelling techniques – polynomial regression, multivariate adaptive regression splines, radial basis functions, and kriging – based on multiple performance criteria using fourteen test problems representing different classes of problems.
Abstract: Despite advances in computer capacity, the enormous computational cost of running complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in place of the actual simulation models. In this paper, we systematically compare four popular metamodelling techniques – polynomial regression, multivariate adaptive regression splines, radial basis functions, and kriging – based on multiple performance criteria using fourteen test problems representing different classes of problems. Our objective in this study is to investigate the advantages and disadvantages of these four metamodelling techniques using multiple criteria and multiple test problems rather than a single measure of merit and a single test problem.
1,567 citations
TL;DR: A survey of recent publications in the field of aerospace where interest in MDO has been particularly intense is presented, focused on the interaction of the structures discipline with other disciplines.
Abstract: The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focused on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design- oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors'' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.
1,049 citations