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93
Flexibility and Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations
, 2002
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Efficient Pareto frontier exploration using surrogate approximations
 Optimization and Engineering
, 2001
"... Abstract. In this paper we present an efficient and effective method of using surrogate approximations to explore the design space and capture the Pareto frontier during multiobjective optimization. The method employs design of experiments and metamodeling techniques (e.g., response surfaces and kri ..."
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Cited by 16 (2 self)
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Abstract. In this paper we present an efficient and effective method of using surrogate approximations to explore the design space and capture the Pareto frontier during multiobjective optimization. The method employs design of experiments and metamodeling techniques (e.g., response surfaces and kriging models) to sample the design space, construct global approximations from the sample data, and quickly explore the design space to obtain the Pareto frontier without specifying weights for the objectives or using any optimization. To demonstrate the method, two mathematical example problems are presented. The results indicate that the proposed method is effective at capturing convex and concave Pareto frontiers even when discontinuities are present. After validating the method on the two mathematical examples, a design application involving the multiobjective optimization of a piezoelectric bimorph grasper is presented. The method facilitates multiobjective optimization by enabling us to efficiently and effectively obtain the Pareto frontier and identify candidate designs for the given design requirements.
The Value of Using Imprecise Probabilities in Engineering Design
 ASME 2005 DETC DTM
, 2005
"... Imprecision, imprecise probabilities, epistemic uncertainty, aleatory uncertainty, engineering ..."
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Cited by 14 (8 self)
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Imprecision, imprecise probabilities, epistemic uncertainty, aleatory uncertainty, engineering
Computationally inexpensive metamodel assessment strategies
 AIAA Journal
, 2002
"... In many scienti � c and engineering domains, it is common to analyze and simulate complex physical systems using mathematical models. Although computing resources continue to increase in power and speed, computer simulation and analysis codes continue to grow in complexity and remain computationally ..."
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Cited by 14 (1 self)
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In many scienti � c and engineering domains, it is common to analyze and simulate complex physical systems using mathematical models. Although computing resources continue to increase in power and speed, computer simulation and analysis codes continue to grow in complexity and remain computationally expensive, limiting their use in design and optimization. Consequently, many researchers have developed different metamodeling strategies to create inexpensive approximations of computationally expensive computer simulations. These approximations introduce a new element of uncertainty during design optimization, and there is a need to develop ef � cient methods to assess metamodel validity. We investigate computationally inexpensive assessment methods for metamodel validation based on leavekout cross validation and develop guidelines for selecting k for different types of metamodels. Based on the results from two sets of test problems, k = 1 is recommended for leavekout cross validation of loworder polynomial and radial basis function metamodels, whereas k = 0:1N or N is recommended for kriging metamodels, where N is the number of sample points used to construct the metamodel. Nomenclature N = number of sample points x = design (input) variable y = actual output (response) value Oyi = predicted output (response) value from metamodel I.
Spacemapping optimization with adaptive surrogate model
 IEEE TRANS. MICROWAVE THEORY TECH
, 2007
"... The proper choice of mapping used in spacemapping optimization algorithms is typically problem dependent. The number of parameters of the spacemapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over ..."
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Cited by 11 (10 self)
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The proper choice of mapping used in spacemapping optimization algorithms is typically problem dependent. The number of parameters of the spacemapping surrogate model must be adjusted so that the model is flexible enough to reflect the features of the fine model, but at the same time is not over flexible. Its extrapolation capability should allow the prediction of the fine model response in the neighborhood of the current iteration point. A wrong choice of spacemapping type may lead to poor performance of the spacemapping optimization algorithm. In this paper, we consider a spacemapping optimization algorithm with an adaptive surrogate model. This allows us to adjust the type of spacemapping surrogate model used in a given iteration based on the approximation/extrapolation capability of the model. The technique does not require any additional fine model evaluations.
Robust Optimization for Unconstrained Simulationbased Problems
"... In engineering design, an optimized solution often turns out to be suboptimal, when errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse ..."
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Cited by 8 (3 self)
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In engineering design, an optimized solution often turns out to be suboptimal, when errors are encountered. While the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method, which is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations such as large PDE solvers, response surface, and kriging metamodels. Moreover, this technique can be employed for most realworld problems, because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiplescattering of aperiodically arranged dielectrics, relevant to nanophotonic design. The corresponding objective function is highly nonconvex and resides in a 100dimensional design space. Starting from an “optimized ” design, we report a robust solution with a significantly lower worst case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.
Accelerated Microwave Design Optimization With Tuning Space Mapping
, 2009
"... We introduce a tuning spacemapping technology for microwave design optimization. The general tuning spacemapping algorithm is formulated, which is based on a socalled tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant upd ..."
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Cited by 8 (8 self)
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We introduce a tuning spacemapping technology for microwave design optimization. The general tuning spacemapping algorithm is formulated, which is based on a socalled tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant updates of the design variables. The tuning model is developed in a fast circuittheory based simulator and typically includes the fine model data at the current design in the form of the properly formatted scattering parameter values. It also contains a set of tuning parameters, which are used to optimize the model so that it satisfies the design specification. The calibration process may involve analytical formulas that establish the dependence of the design variables on the tuning parameters. If the formulas are not known, the calibration process can be performed using an auxiliary spacemapping surrogate model. Although the tuning space mapping can be considered to be a specialized case of the standard spacemapping approach, it can offer even better performance because it enables engineers to exploit their experience within the context of efficient space mapping. Our approach is demonstrated using several microwave design optimization problems.
A nonstationary covariancebased Kriging method for metamodelling in engineering design
"... Metamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with nonlinear behaviour. However, the ass ..."
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Cited by 5 (0 self)
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Metamodels are widely used to facilitate the analysis and optimization of engineering systems that involve computationally expensive simulations. Kriging is a metamodelling technique that is well known for its ability to build surrogate models of responses with nonlinear behaviour. However, the assumption of a stationary covariance structure underlying Kriging does not hold in situations where the level of smoothness of a response varies significantly. Although nonstationary Gaussian process models have been studied for years in statistics and geostatistics communities, this has largely been for physical experimental data in relatively low dimensions. In this paper, the nonstationary covariance structure is incorporated into Kriging modelling for computer simulations. To represent the nonstationary covariance structure, we adopt a nonlinear mapping approach based on parameterized density functions. To avoid overparameterizing for the high dimension problems typical of engineering design, we propose a modified version of the nonlinear map approach, with a sparser, yet flexible, parameterization. The effectiveness of the proposed method is demonstrated through both mathematical and engineering examples. The robustness of the method is verified by testing multiple functions under various sampling settings. We also demonstrate
BUILDING SURROGATE MODELS BASED ON DETAILED AND APPROXIMATE SIMULATIONS
"... Preliminary design of a complex system often involves exploring a broad design space. This may require repeated use of computationally expensive simulations. To ease the computational burden, surrogate models are built to provide rapid approximations of more expensive models. However, the surrogate ..."
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Cited by 4 (2 self)
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Preliminary design of a complex system often involves exploring a broad design space. This may require repeated use of computationally expensive simulations. To ease the computational burden, surrogate models are built to provide rapid approximations of more expensive models. However, the surrogate models themselves are often expensive to build because they are based on repeated experiments with computationally expensive simulations. An alternative approach is to replace the detailed simulations with simplified approximate simulations, thereby sacrificing accuracy for reduced computational time. Naturally, surrogate models built from these approximate simulations will also be imprecise. A strategy is needed for improving the precision of surrogate models based on approximate simulations without significantly increasing computational time. In this paper, a new approach is taken to integrate data from approximate and detailed simulations to build a surrogate model that describes the relationship between output and input parameters. Experimental results from approximate simulations form the bulk of the data, 1 Professor and Corresponding Author
Evolutionary model type selection for global surrogate modeling
 2054 SURROGATE MODELING AND ADAPTIVE SAMPLING TOOLBOX FOR COMPUTER BASED DESIGN
"... Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualizati ..."
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Cited by 4 (2 self)
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Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist (Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm (heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type.