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44
A Comparison of Two Methods for Fitting High Dimensional Response Surfaces
 Proc. of International Symposium on Inverse Problems, Design and Optimization
"... In this paper we compare two methodologies to interpolate linear as well as highly nonlinear functions in multidimensional spaces having up to 500 dimensions. Two methodologies are compared: the Radial Basis Function (RBF) and the Wavelet based Neural Network (WNN). The accuracy, robustness, effici ..."
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In this paper we compare two methodologies to interpolate linear as well as highly nonlinear functions in multidimensional spaces having up to 500 dimensions. Two methodologies are compared: the Radial Basis Function (RBF) and the Wavelet based Neural Network (WNN). The accuracy, robustness, efficiency, transparency and conceptual simplicity are discussed. Based on the extensive testing performed on 13 test functions, the RBF approach seems easy to implement computationally and results are better interpolation for higher dimensional spaces than the WNN, requiring lesser computing time.
A Study on Metamodeling Techniques, Ensembles, and MultiSurrogates in Evolutionary Computation ABSTRACT
"... SurrogateAssisted Memetic Algorithm(SAMA) is a hybrid evolutionary algorithm, particularly a memetic algorithm that employs surrogate models in the optimization search. Since most of the objective function evaluations in SAMA are approximated, the search performance of SAMA is likely to be affected ..."
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SurrogateAssisted Memetic Algorithm(SAMA) is a hybrid evolutionary algorithm, particularly a memetic algorithm that employs surrogate models in the optimization search. Since most of the objective function evaluations in SAMA are approximated, the search performance of SAMA is likely to be affected by the characteristics of the models used. In this paper, we study the search performance of using different metamodeling techniques, ensembles, and multisurrogates in SAMA. In particular, we consider the SAMATRF, a SAMA model management framework that incorporates a trust region scheme for interleaving use of exact objective function with computationally cheap local metamodels during local searches. Four different metamodels, namely Gaussian Process (GP), Radial Basis Function (RBF), Polynomial Regression (PR), and Extreme Learning Machine
A modebased metamodel for the frequency response functions of uncertain structural systems
, 2008
"... Frequency response functions (FRFs) play an important role in the assessment of the structural response of linear systems subjected to dynamic forces. In this work a metamodel is presented to approximate the eigenfrequencies and mode shapes to describe the FRFs. The metamodel is supposed to provid ..."
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Frequency response functions (FRFs) play an important role in the assessment of the structural response of linear systems subjected to dynamic forces. In this work a metamodel is presented to approximate the eigenfrequencies and mode shapes to describe the FRFs. The metamodel is supposed to provide a computationally fast solution for the eigenvalue problem, which needs to be solved for each set of random structural input parameters. The provided relations can be helpful in the design stage to control the dynamic response within certain frequency bands. Moreover, the metamodel can be used for optimization and reliability assessments based on Monte Carlo sampling procedures. Numerical examples show the application of the method focusing mainly on the variability of the FRFs w.r.t. the number of random variables involved to model the mechanical system. The accuracy of the metamodel to approximate FRFs is assessed by a comparison with the solution by Finite Element (FE) analyses.
Flexible Approximation Model Approach for BiLevel
 Integrated System Synthesis,” AIAA20044545, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference
"... BiLevel Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimi ..."
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BiLevel Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.
Using Radial Basis Function Neural Networks to Calibrate Water Quality Model
 International Journal of Intelligent Systems and Technologies
, 2008
"... Abstract—Modern managements of water distribution system (WDS) need water quality models that are able to accurately predict the dynamics of water quality variations within the distribution system environment. Before water quality models can be applied to solve system problems, they should be calibr ..."
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Abstract—Modern managements of water distribution system (WDS) need water quality models that are able to accurately predict the dynamics of water quality variations within the distribution system environment. Before water quality models can be applied to solve system problems, they should be calibrated. Although former researchers use GA solver to calibrate relative parameters, it is difficult to apply on the largescale or mediumscale real system for long computational time. In this paper a new method is designed which combines both macro and detailed model to optimize the water quality parameters. This new combinational algorithm uses radial basis function (RBF) metamodeling as a surrogate to be optimized for the purpose of decreasing the times of timeconsuming water quality simulation and can realize rapidly the calibration of pipe wall reaction coefficients of chlorine model of largescaled WDS. After two cases study this method is testified to be more efficient and promising, and deserve to generalize in the future. Keywords—Metamodeling, model calibration, radial basis function, water distribution system, water quality model. I.
Evolutionary Wavelet Neural Network for Large Scale Function Estimation
 in Optimization”, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper AIAA20066955
, 2006
"... This paper describes a new method for constructing wavelet neural network in order to improve the accuracy of prediction for multidimensional function spaces. An algorithm is developed using the concept of evolutionary search in wavelet neural network. It helps in decreasing the computational effor ..."
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This paper describes a new method for constructing wavelet neural network in order to improve the accuracy of prediction for multidimensional function spaces. An algorithm is developed using the concept of evolutionary search in wavelet neural network. It helps in decreasing the computational effort needed for building the wavelet neural network. Several modifications to wavelet neural network are also suggested for improving its performance in predicting nonlinear function spaces. These algorithms were tested using diverse test functions. These networks can be effectively used as nonlinear system estimators for large scale optimization problems. I.
ASAGA: An Adaptive SurrogateAssisted Genetic Algorithm
"... Genetic algorithms (GAs) used in complex optimization domains usually need to perform a large number of fitness function evaluations in order to get nearoptimal solutions. In real world application domains such as the engineering design problems, such evaluations might be extremely expensive comput ..."
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Genetic algorithms (GAs) used in complex optimization domains usually need to perform a large number of fitness function evaluations in order to get nearoptimal solutions. In real world application domains such as the engineering design problems, such evaluations might be extremely expensive computationally. It is therefore common to estimate or approximate the fitness using certain methods. A popular method is to construct a so called surrogate or metamodel to approximate the original fitness function, which can simulate the behavior of the original fitness function but can be evaluated much faster. It is usually difficult to determine which approximate model should be used and/or what the frequency of usage should be. The answer also varies depending on the individual problem. To solve this problem, an adaptive fitness approximation GA (ASAGA) is presented. ASAGA adaptively chooses the appropriate model type; adaptively adjusts the model complexity and the frequency of model usage according to time spent and model accuracy. ASAGA also introduces a stochastic penalty function method to handle constraints. Experiments show that ASAGA outperforms nonadaptive surrogateassisted GAs with statistical significance.
SelfAdaptive SurrogateAssisted Covariance Matrix Adaptation Evolution Strategy
 In GECCO ’2012 Proceedings
, 2012
"... This paper presents a novel mechanism to adapt surrogateassisted populationbased algorithms. This mechanism is applied to ACMES, a recently proposed surrogateassisted variant of CMAES. The resulting algorithm, s ∗ ACMES, adjusts online the lifelength of the current surrogate model (the number o ..."
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This paper presents a novel mechanism to adapt surrogateassisted populationbased algorithms. This mechanism is applied to ACMES, a recently proposed surrogateassisted variant of CMAES. The resulting algorithm, s ∗ ACMES, adjusts online the lifelength of the current surrogate model (the number of CMAES generations before learning a new surrogate) and the surrogate hyperparameters. Both heuristics significantly improve the quality of the surrogate model, yielding a significant speedup of s ∗ ACMES compared to the ACMES and CMAES baselines. The empirical validation of s ∗ ACMES on the BBOB2012 noiseless testbed demonstrates the efficiency and the scalability w.r.t the problem dimension and the population size of the proposed approach, that reaches new best results on some of the benchmark problems.
MetaModels of the Eigensolution of Uncertain Structures
, 2008
"... The measurement of frequency response functions (FRFs) on nominally identical items reveals usually a considerable scatter induced by some inherent variabilities. In this paper a stochastic parametric approach is suggested in order to analyze the variability of the FRFs, where random as well as unce ..."
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The measurement of frequency response functions (FRFs) on nominally identical items reveals usually a considerable scatter induced by some inherent variabilities. In this paper a stochastic parametric approach is suggested in order to analyze the variability of the FRFs, where random as well as uncertain structural properties are modeled as a function of independent random variables with prescribed probability distributions. This work focuses on the establishment of a functional relation (metamodel) between the random variables and the modal properties to be utilized for assessing the variability of the FRFs. The proposed procedure aims to extract a close approximation of the modal properties from the set modal solutions obtained by Monte Carlo and FE analyses, of which the sample size should be as small as possible for computational efficiency. An adaptive sampling procedure has been developed for this purpose which allows a balancing between efficiency and accuracy. The concept of modal superposition is then used for calculating the FRFs. The main advantage is the fast approximate evaluation of the FRF in order to identify critical domains of the random input parameter space within some particular frequency bands. This information is
Abstract Review of Metamodeling Techniques in Support of Engineering Design Optimization
"... Computationintensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximat ..."
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Computationintensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. The metamodels are initially developed as “surrogates ” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the stateoftheart metamodelbased techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.