 Second International Workshop on Advances in Simulation-Driven Optimization and Modeling (ASDOM 2013) August 9-11, 2013 Reykjavik University, Iceland
List of Speakers The list of confirmed speakers in alphabetical order:
A New Surrogate-Based Trust Region Optimization Approach with Application to RF Cavity Design for Linear Accelerator Hany L. Abdel-Malek Cairo University, Egypt Abstract: A novel surrogate-based trust region optimization approach is presented in this paper. The principle operation of the proposed approach relies on building and successively updating quadratic surrogate models of the objective function. These surrogate models are optimized instead of the objective function over trust regions. Truncated conjugate gradients are used to find the optimum point within each trust region. The approach constructs the initial quadratic surrogate model using few data points of order O(n), where n is the number of design variables. In each iteration, the algorithm updates the surrogate model using a weighted least squares fitting. The weights are assigned to give more emphasis to points close to the current center point. The accuracy and efficiency of the proposed algorithm are demonstrated by applying it on a set of classical bench-mark test problems. Also, the approach is employed to find the optimal design of RF cavity linear accelerator (LINAC). A comparison analysis with a recent optimization technique is also included. List of talks Main Page Surrogate-based Bayesian parameter estimation Robert J. Barthorpe University of Sheffield, UK Abstract: There is great interest in the structural dynamics community in applying Bayesian methods for estimating the parameters of numerical model from experimental data. This process is made tractable through applying sampling methods to build estimates of the parameter distributions. Markov Chain Monte Carlo (MCMC) techniques are predominant among these approaches. A principle drawback of MCMC approaches is that they require a very large number of model runs in order to build the parameter estimates. This can prove prohibitive for computationally expensive FE models and leads naturally to the adoption of surrogate-based methods. The background to MCMC and surrogate modelling are introduced, and an application of parameter estimation using surrogates for a numerical structural dynamics model is presented. List of talks Main Page Tackling High-dimensionality Problems in Data Mining by Using Metaheuristic Algorithms Simon Fong University of MaCau, China Abstract: Modern Bio-inspired computing and metaheuristics algorithms (BiCam) such as PSO, Fireflies, Ants, Bats and Bees algorithms etc. start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems. The research momentum is picking up recently as optimal solutions for combinatorial optimization are possible to be sought by Metaheuristics. The research introduced in this talk is about a new BiCam algorithm which can out-perform most of the current ones, as well as modifying from some important modern BiCam algorithms for applying in data mining applications; so as to produce optimal solutions in the most efficient way. The benefits offered by BiCam algorithms complement very well the limitations of data mining because data mining models usually face multidimensional combinatorial problems which are typically NP-hard, with very large search space including about finding global optima and overcoming local optima. Data mining models are well known to be prone to suffer from the curse of dimensionality, which also makes them infeasible for exhaustive search or complex analytical methods. Three case studies will be given in this talk: possible integration of BiCam algorithms into some classical data mining algorithms — namely (1) Data Clustering; (2) Feature Selection in Classification, and (3) Highly Non-linear Regression. At the end of the talk, related open-source codes will be provided, for fellow researchers to test out the integrated bio-inspired optimization and data mining algorithms on application problems of your own choice. List of talks Main Page Application of Surrogate Modeling for Circuit Yield and Lifetime Enhancement Paul D. Franzon North Carolina State University, USA Abstract: “Model based design” refers to using surrogate models for circuit and system design purposes. This talk will describe model based design in two applications: (1) increasing the yield and reliability of analog and RF circuits, and (2) thermal drive design of mobile CPUs. Recent focus in this work has been on handling high dimensionality and the extension of Surrogate based modeling to new application areas. List of talks Main Page Advanced Modeling of Coupled-Resonator Filters Olexandr Glubokov Reykjavik University, Iceland Abstract: This presentation is aimed at introducing a novel and efficient methodology for creating fast and accurate surrogate models of coupled-resonators microwave filters. Instead of approximating S-parameters of a filter directly, the discussed approach employs response surface modelling of its coupling matrix coefficients which show considerably smoother dependence on filter dimensions than S-parameters. As a result, the proposed technique allows obtaining accurate surrogates with substantially smaller number of training samples than required by conventional techniques. The new modelling procedure is illustrated using a substrate-integrated waveguide filter and compared with a standard approach. List of talks Main Page Nonlinear Observer Design using Local Model Networks Christoph Hametner Vienna University of Technology Abstract: In nonlinear system identification, black-box and grey-box models are widely used since these methods require no or only little physical or formal information about the underlying process. In this context, local model networks (LMNs) are an established concept for a wide field of applications. The construction of LMNs is based on partitioning the operating space into a number of operating regimes and the global model output is then formed by a weighted combination of local models. Such a model then provides a basis for the development of systematic approaches to controller and observer design in view of powerful conventional control theory and techniques. In the present contribution, the design of a nonlinear observer for battery state of charge (SoC) estimation is described. An augmented state space representation of the LMN is derived and the nonlinear SoC observer design is described. In particular, the use of a fuzzy observer is beneficial in combination with LMNs since the local observers are time-invariant which greatly reduces the complexity of the global estimator. The proposed concepts are validated experimentally by means of a Lithium Ion power cell. List of talks Main Page Geometrical Design Centering Approach Exploiting Normed Distances and Space Mapping Interpolating Surrogates Abdel-Karim S.O. Hassan Cairo University, Egypt Abstract: In this paper, generalized space mapping (GSM) surrogates are integrated with the normed distances concept to develop a novel surrogate-based geometrical design centring technique for microwave circuit applications. The design centering problem is formulated as a max-min optimization problem using normed distances from a feasible point to the feasible region boundaries. The norm used in evaluating the distances is related to the probability distribution of the circuit parameters. The normed distances are evaluated by solving a nonlinear optimization problem. A convergent iterative boundary search technique is used to solve the nonlinear optimization problem concerning the normed distances. In the new approach of microwave design centering, a GSM surrogate is initially constructed based on the coarse model and then updated through space mapping (SM) iterations. In each SM iteration, a current SM feasible region approximation is available and the centring process using normed distances is implemented with this region approximation leading to a better design center. The new center point is validated by the fine model and is used to update the current GSM surrogate. The process is repeated to obtain the next center point. Practical circuit examples are given to show the effectiveness of the new design centring method. List of talks Main Page Bat Algorithm with Simulated Annealing and Gaussian Perturbations Xingshi He Xi'an Polytechnic University, China Abstract: Nature-inspired algorithms such as cuckoo search and bat algorithm have gained popularity due to their quick convergence properties. In this paper, we try to enhance the bat algorithm by introducing Gaussian perturbations and simulated annealing to produce a hybrid bat algorithm. The results suggest better convergence can be achieved, and the statistical testing of the simulations results shows that the proposed approach can be very efficient. List of talks Main Page Classification of 3-D Airborne Laser Scanning Data Ronald Hochreiter WU Vienna University of Economics and Business, Austria Abstract: Advances in laser technology and geospatial accuracy have led to a lasting shift in land surveying methodology. While in traditional field, land was being surveyed by taking orthographic images, todays state of the art involves airborne laser scanners. In a first step, airborne laser scanning only computed and recorded the altitude above ground for each laser echo. Modern scanners, however, are able to record the full wave's spectral information. This is especially useful, as different ground materials exhibit specific laser return signal modifications. However, today it is still very difficult to separate this signal from noise, i.e. trees in forest from watchtowers overgrown with vegetation. To this end, we present a manually annotated data set containing more than 4 million laser return echoes of a characteristic ravine landscape in central Europe. We demonstrate the varying classification achievements obtained by supervised and unsupervised approaches. List of talks Main Page Approximation of transport network equations Nils Hornung Fraunhofer-Institute for Algorithms and Scientific Computing SCAI, Germany Abstract: Radial basis function (RBF) interpolation is a simple but very effective and general method to approximate smooth mappings from a space of control parameters to a space of objectives. Within certain problem classes they allow for good approximation rates with uniformly distributed, but meshless samplings, e. g. if we consider objective functions constructed from solutions of elliptic partial differential equations (PDEs) from a diffusion process. Nonlinear transport problems on network graphs with first-order spatial derivatives, on the other hand, can present problems to general RBF approaches due to their innate structure, local nonlinearities and time-dependence. Such problems often arise in practical applications such as gas pipeline simulations, water distribution networks and even in oil reservoir simulation. In this presentation we first review a practical approach from model order reduction and apply it to an index-reduced class of differential algebraic equations. First numerical results in gas transport networks of pipes only are obtained, not considering more elaborate components. We then discuss possible extensions and their implications. As an outlook we present a brief literature survey of kernel construction methods and initial considerations how to make use of known invariances of the solutions of linear and also nonlinear transport-type first-order PDEs. List of talks Main Page Applications
of adjoint based shape optimization to the design of low drag airplane
wings, including wings to support natural laminar flow Antony Jameson Stanford University, USA Abstract: The aerodynamic efficiency of an airplane can be significantly improved if wings supporting natural laminar flow can be designed. A basic requirement for achieving natural laminar flow is for the flow to maintain a favorable pressure gradient up to the desired transition location. A tool that can be used to design a wing with such desirable characteristic needs the capabilities of inverse design, transition prediction, and automatic shape optimization. In this talk, an adjoint based shape optimization method with transition prediction that can be used to design natural laminar flow wings is discussed. In particular, the formulation and advantage of aerodynamic shape optimization using control theory will be addressed. This is followed by discussion on the extension of the current formulation to include transition prediction. Using this method, a state of the art wing has been designed that can support extensive natural laminar flow over a very wide range of operation conditions. Other applications include drag minimization to achieve shock-free airfoils and design optimization of a deswept wing. List of talks Main Page Shape-preserving response prediction for engineering design modeling and optimization Slawomir Koziel Reykjavik University, Iceland Abstract: Contemporary engineering design relies heavily on computer simulations. The structures and systems considered in many engineering disciplines are far too complex to be described accurately using simple theoretical models; using simulations is often the only way to adequately assess the performance of the design. Unfortunately, high-fidelity simulations are computationally expensive so that their use in an automated design process based on conventional optimization algorithms is often prohibitive. Despite the availability of faster computers and more efficient simulation software: growing demand for improved accuracy and the need to evaluate larger and larger systems effectively diminishes the benefits of this increase in computing power. One of the most promising ways of alleviating these problems are surrogate-based optimization (SBO) techniques which are capable of reducing the number of expensive objective function evaluations in a simulation-driven design process. In SBO, the direct optimization of the expensive model is replaced by iterative updating and re-optimization of its cheap surrogate model. Among proven SBO techniques, the methods exploiting physics-based low-fidelity models are probably the most efficient. This is because the knowledge about the system of interest embedded in the low-fidelity model allows constructing the surrogate model that has good generalization capability at a cost of just a few evaluations of the original model. In this talk, we review one of the most recent techniques of this kind, the so-called shape-preserving response prediction (SPRP). We discuss the formulation of SPRP, its limitations and generalizations, and, most importantly, demonstrate its applications to solve design problems in various engineering areas, including microwave engineering, antenna design, and aerodynamic shape optimization. Applications of SPRP for surrogate modeling are also presented. List of talks Main Page Simulation Optimization for Logistics Models Jörg Lässig University of Applied Sciences Zittau/Goerlitz, Germany Abstract: The efficient control of logistics systems is a complex task. Although analytical models allow to estimate the effect of certain policies, they necessitate the introduction of simplifying assumptions. Therefore, their scope is limited. To surmount these restrictions, Simulation Optimization is often a promising approach. This idea is illustrated for a very general class of multi-location inventory models with lateral transshipments (MLIMT). Such models have become increasingly important in a globalized economic setting. We discuss their characteristics and introduce different approaches to optimize them. Experimental studies show the applicability of this approach. The presented research is joint work with Christian Hochmuth, Chemnitz University of Technology. List of talks Main Page Multi-level CFD-based Aerodynamic Shape Optimization Leifur Leifsson Reykjavik University, Iceland Abstract: A robust and computationally efficient airfoil shape optimization algorithm using high-fidelity computational fluid dynamic (CFD) models is described. The technique exploits a set of CFD models of increasing discretization density that are sequentially optimized with the optimal design of the “coarser” model being the initial design for the “finer” one. The final design is refined using a response surface approximation model constructed from the coarse-discretization CFD-simulation data and corrected using single high-fidelity evaluation. The presented technique is easy to implement. Operation of our algorithm is demonstrated using several test cases of transonic airfoils. List of talks Main Page Surrogate-based design of antenna arrays Stanislav Ogurtsov Reykjavik University, Iceland Abstract: In this talk, we consider surrogate-based design of planar antenna arrays. Reliable designs of planar arrays are challenging due to the time consuming high-fidelity electromagnetic (EM) simulations necessary to evaluate both radiation and reflection responses of the realistic array model . In addition, antenna array designs involve large numbers of design variables, including dimensions of elements, location of feeds, spacings, excitation amplitudes and/or phases, finite dimensions of substrates and grounds. Models based on the single element radiation response combined with the analytical array factor do not produce accurate radiation responses in the directions off the main beam and fail to account for inter element coupling. Therefore, a use of full-wave EM models for the entire array is necessary. Such models, however, are computationally expensive when accurate, and conducting array design through simulation-driven optimization might be prohibitively expensive in terms of the CPU time. To alleviate this difficulty and speed up the design optimization process we exploit the surrogate-based optimization (SBO) approach. Array design normally comprises two major steps: adjusting of the radiation response, e.g., directivity pattern, and adjusting the reflection response. The use of surrogate models can be beneficial at both of these two steps. We consider two specific design cases: (i) 5x5 array of microstrip antennas using a low-fidelity coarse-discretization model of the entire array exploited in through the design process, and (ii) 7x7 array of microstrip antennas using two surrogate models, one based on the single element radiation response combined with the analytical array factor and the other based on the coarse-discretization model of the entire array. List of talks Main Page Multi-objective programming: adaptive surrogate based approach with Chebyshev scalarization Alexey Pospelov Datadvance, IITP RAS, Russia Abstract: Optimizing computationally expensive models we usually have to submit to strict limitations on amount of evaluations of models. These limitations become especially pressing in multi-objective optimization. A prominent approach to deal with such situations is surrogate-based optimization, where cheap synthetic models are used to approximate expensive models. In this talk we present a new surrogate-based multi-objective optimization algorithm based on a generalization of probability of improvement method. The key component of the proposed algorithm is adaptive Chebyshev scalarization. Scalarization itself has a mixed reputation. Main obvious advantage of scalarization is possibility to apply a single-objective optimization techniques. This advantage is usually considered outweighed by numerous problems such as non-uniform frontier discovery and necessity in repeating solving of optimization problems, both of each may dramatically increase number of evaluation required to find an adequate approximation of Pareto frontier. Within the framework of the proposed algorithm we suggest a way around both of these impediment. Uniformity of frontier discovery can be significantly improved by adaptive selection of scalarization parameters. In the algorithm incrementally growing knowledge about Pareto frontier during optimization is used to select scalarization parameters to direct search into the most promising areas. Surrogate models help us to tie together usually independent scalarized subtasks. All expensive evaluations made during solution of prior subtasks are used to build more and more precise models thus making subsequent subtasks incrementally easier. List of talks Main Page Approaches to Constrained Aerodynamic Design of Wings Arthur Rizzi KTH Royal Institute of Technology, Sweden Abstract: The inverse design and shape optimization methods for transonic airfoil and wing shape design are discussed with examples presented of a hybrid method on test cases defined for an AIAA Special Session on Aerodynamic Design Optimization. List of talks Main Page The Knowledge Based 3-Step Modelling Strategy Murat Simsek Istanbul Technical University, Turkey Abstract: Artificial Neural Networks (ANNs) provide an efficient strategy to solve engineering modeling and optimization problems where only input-output data are available. Complex modeling problems are required more computational effort and time consuming process during modeling. The knowledge based modeling can be preferred to reduce complexity of the modeling problem, therefore more accurate and less time consuming solutions can be obtained. The knowledge based artificial neural networks are used by incorporating the existing knowledge such as empirical formulas, equivalent circuit models and semi-analytical equations in neural network structures. Existing knowledge which is known as a coarse model decreases complexity of engineering problem; hence less data can be sufficient to constitute relationship between input and output of modeling problem. 3-step modeling strategy based on knowledge based techniques is presented to develop a new efficient modeling instead of conventional artificial neural networks. In this strategy, required knowledge is created in the first step using ANNs and output of the first step is used in the second step as a coarse model. Therefore each model shows better performance than former. This strategy provides not only more accurate results but also time efficiency especially in complex modeling problems. In this strategy, conventional ANN, prior knowledge input and prior knowledge input with difference techniques are utilized not only to improve modeling accuracy but also to reduce time consumption during modeling. The advantages of using 3-step modeling are demonstrated on modeling problems comparing with conventional ANNs. List of talks Main Page Surrogate-Based Methods for Parameter Identification in Climate Models Thomas Slawig Christian Albrechts University, Germany Abstract: We present the application of the Surrogate-based Optimization method on parameter identification problems in 3-D marine ecosystem models. The latter are used for modeling the carbon cycle in global climate simulations. The simulation of a stable annual cycle in the coupled system of ocean circulation and marine ecosystem is computationally very costly. These high computational costs are multiplied when simulation-based parameter optimization or model calibration runs are necessary. Each optimization run may need several hundreds of function evaluations. As a consequence, methods to reduce the computational effort in both simulation and optimization runs are highly desirable. One of these methods is Surrogate-based Optimization. In this method, the original and computationally expensive fine model is replaced by a so-called surrogate, which is created from a less accurate but computationally cheaper coarse model with a additional correction approach to increase its accuracy. Surrogate-based Optimization has been widely and successfully used in engineering applications. Here, we apply the approach on parameter optimization for a three-dimensional marine ecosystem model. In order to obtain a stable annual cycle of the ocean circulation and the ecosystem, the model is spun-up via the Transport Matrix Approach. The low-fidelity model consists of a reduced number of spin-up iterations (several decades instead of millennia used for the original model). A multiplicative correction operator is exploited to extrapolate the less accurate low-fidelity model onto the original one. We validate the optimization method by twin-experiments that use synthetic observations generated by the original model. Moreover we evaluate the method by using real measurement data that typically are spatially and temporally sparse. Here, we study also hybrid strategies that use different levels of accuracy for the coarse model in different optimization steps. List of talks Main Page Requirements for Incorporating Surrogate Models as Native Models in Circuit Simulators Michael Steer North Carolina State University, USA Abstract: This paper explores the computational trade-offs in implementing various surrogate modeling techniques in transient and steady-state nonlinear circuit simulators. Particular technologies analyzed are surrogate models using polynomial models, Kriging methods, neural networks, and machine-learning. Particular attention is given to the space-mapping class of surrogate models and the requirements for high dynamic range simulation. List of talks Main Page Wikipedia Conceptual Knowledge for Interactive Information Retrieval Julian Szymanski Gdansk University of Technology, Poland Abstract: Current methods of information retrieval from text repositories are mostly based on keywords. In our research we build an algorithm allows to narrow the set of search results to the most relevant ones enabling interaction with the user. We present the prove of concept of our system and application of the algorithm for a repository of Wikipedia articles. Using conceptual knowledge possessed form the Wikipedia categories the system allows to refine the set of results according to the user preferences. Additionally it offers alternative user interface that instead of ranked list of results aggregates them into thematic groups. We used for that purpose clustering algorithm that has been based on analysis of the distance densities between documents. The clustering algorithm using the conceptual knowledge allows to form high quality thematic groups within the results retrieved with keywords which significantly increases readability of the search. Evaluation of the proposed approach indicates it can be used as an effective tool for improving information retrieval based on keywords. In our further work we plan to build large scale text classifier for Wikipedia categories that should allow to apply the proposed method for refining the results of typical search engines. List of talks Main Page Stochastic Modelling to Generate Alternatives Using a Nature-Inspired Simulation-Optimization Algorithm Julian Scott Yeomans York University, Canada Abstract: In solving many practical mathematical programming applications, it is generally preferable to formulate several quantifiably good alternatives that provide multiple, disparate approaches to the problem. This is because decision-making typically involves complex problems that are riddled with incompatible performance objectives and possess competing design requirements which are very difficult – if not impossible – to quantify and capture at the time that the supporting decision models are constructed. By generating a set of maximally different solutions, it is hoped that some of the dissimilar alternatives can provide very different perspectives that may serve to satisfy the unmodelled objectives. This maximally different solution creation approach is referred to as modelling to generate-alternatives (MGA). This study provides a nature-inspired simulation-optimization MGA algorithm that can efficiently create multiple solution alternatives to problems containing stochastic uncertainties that satisfy required system performance criteria and yet are maximally different within the decision space. The efficacy of this stochastic MGA approach is demonstrated. List of talks Main Page Aerodynamic Shape Optimization Using Space Mapping Yonatan Tesfahunegn Reykjavik University, Iceland Abstract: Aerodynamic shape optimization is of primary importance in the design of engineering systems and devices such as aircraft, turbomachinery, ships and propellers, and automotives. In this presentation, a computationally efficient optimization methodology for aerodynamic design using high-fidelity computational fluid dynamic (CFD) models is described. Direct optimization of an expensive high-fidelity CFD model is replaced by an iterative updating and re-optimization of a cheap surrogate model. The surrogate is constructed using the low-fidelity model which is based on the same governing fluid flow equations as the high-fidelity model, but uses coarser mesh resolution and relaxed convergence criteria. The low-fidelity model undergoes suitable corrections to become a reliable representation of the high-fidelity one so that it can be subsequently used to find an approximate optimum design of the latter. The corrections are implemented using space mapping. Our method is applied to constrained airfoil and wing design optimization in transonic flow. List of talks Main Page Gaussian Process NARX Models for Nonlinear System Identification Keith Worden University of Sheffield, UK Abstract: One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. Although the NARMAX model is most often given a polynomial form, this is not a restriction of the method and other formulations have been proposed based on multi-layer perceptron neural networks or radial basis function networks for example. All of these forms of the NARMAX model allow the computation of Higher-order Frequency Response Functions (HFRFs) which encode the model in the frequency domain and allow a direct interpretation of how frequencies interact in the nonlinear system under study. In a recent paper, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression. The advantage of the GP-NARX was that confidence intervals are a natural part of the prediction process. The objective of the current paper is to provide the theory for the HFRFS corresponding to GP-NARX and provide a means of converting the prediction bounds in the time domain into bounds on the HFRFs. Examples will be given based on simulated data and on ocean wave data. List of talks Main Page Multiobjective Firefly Algorithm for Engineering Designs Xin-She Yang Middlesex University, UK Abstract: Most design problems in engineering and industry are multiobjective, and thus require multiobjective approaches. Recent trends tend to use bio-inspired algorithms to tackle multiobjective optimization. In this talk, we will use multiobjective firefly algorithm (MOFA) to solve a few case studies for design optimization and discuss efficient ways to deal with Pareto fronts. We also discuss some challenging issues and topics further research. List of talks Main Page Neural network based parametric EM modeling and optimization Qi-Jun Zhang Carleton University, Canada Abstract: This talk presents fast parametric modeling of microwave components where the EM behavior of the component can be evaluated quickly while the values of physical/geometrical parameters are repetitively changed. A recently developed method combines neural networks and transfer functions, where the neural network maps the geometrical/physical variables of the component to the coefficients of the transfer function. In this way, the transfer function is extended from a function of frequency only to a function of frequency and physical/geometrical variables. The neural network mapping is trained through accurate EM data. Our recently developed algorithm guarantees the continuity of the coefficients of the transfer function over large variations in physical/geometrical parameters. Compared to a brute-force approach, our method allows better accuracy in challenging modeling applications involving wide frequency range and large geometrical variations. Parametric models for antenna and microwave filter examples developed from EM training data will be demonstrated showing fast model evaluation with near EM accuracy while physical and geometrical parameters are repetitively changed. List of talks Main Page Surrogate-based aerodynamic optimization via gradient-enhanced kriging and hierachical kriging Han Zhong-hua Northwestern Polytechnical University, China Abstract: Surrogate-based optimization received increasing interest for aerodynamic design, where high-fidelity thus expensive computational fluid dynamics (CFD) is employed. Traditionally, the expensive CFD solver of single fidelity (such as Reynolds-averaged Navier-Stokes flow solver) is coupled with a surrogate-based optimizer to get the optimum aerodynamic shape. In this study, the auxiliary, cheaper information, such as the gradient information obtained by adjoint method and the information obtained from the lower-fidelity CFD, is used and exercised to improve the quality and efficiency of the traditional surrogate-based optimization. The key idea is to use so-called gradient-enhanced kriging and hierarchical kriging, in which gradient information or lower-fidelity functional value is incorporated to build a more accurate kriging surrogate model. A number of tests on analytical functions, inverse design and drag minimization of transonic airfoils have been carried out. It is shown that the new methods feature better optimal results and faster convergence, for both local and global optimization problems. List of talks Main Page Main Page |
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