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114
TrustRegion Proper Orthogonal Decomposition for Flow Control
 Institute for Computer
, 2000
"... . The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial di#erential equations, e.g. fluid flows. It can also be used to develop reduced order control models. The essential is the computation of POD basis functions that r ..."
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Cited by 25 (2 self)
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. The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial di#erential equations, e.g. fluid flows. It can also be used to develop reduced order control models. The essential is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where the suitable reduced order model is derived successively and give global convergence results. Keywords: proper orthogonal decomposition, flow control, reduced order modeling, trust region methods, global convergence 1. Introduction. We present a robust reduced order method for the control of complex timedependent physical processes governed by partial di#erential equations (PDE). Such a control problem often is hard to solve because of the high order system that describes the state (a large number of (finite element) basis elements for every point in the time d...
Managing Approximate Models in Evolutionary Aerodynamic Design Optimization
 In Proceedings of IEEE Congress on Evolutionary Computation
, 2001
"... Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors ..."
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Cited by 23 (4 self)
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Approximate models have to be used in evolutionary optimization when the original fitness function is computationally very expensive. Unfortunately, the convergence property of the evolutionary algorithm is unclear when an approximate model is used for fitness evaluation because approximation errors are involved in the model. What is worse, the approximate model may introduce false optima that lead the evolutionary algorithm to a wrong solution. To address this problem, individual and generation based evolution control are introduced to ensure that the evolutionary algorithm using approximate fitness functions will converge correctly. A framework for managing approximate models in generationbased evolution control is proposed. This framework is well suited for parallel evolutionary optimization in which evaluation of the fitness function is timeconsuming. Simulations on two benchmark problems and one example of aerodynamic design optimization demonstrate that the proposed algorithm is able to achieve a correct solution as well as a significantly reduced computation time. 1
Evolutionary Search of Approximated NDimensional Landscapes
 International Journal of Knowledgebased Intelligent Engineering Systems
, 2000
"... Finding the global optimum on a large, multimodal, complex, and discontinuous (or nondifferentiable) landscape is usually very hard, even using the evolutionary approach. However, some of these complex landscapes can be approximated and smoothened without changing the nature of the problem, i.e., wi ..."
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Cited by 21 (2 self)
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Finding the global optimum on a large, multimodal, complex, and discontinuous (or nondifferentiable) landscape is usually very hard, even using the evolutionary approach. However, some of these complex landscapes can be approximated and smoothened without changing the nature of the problem, i.e., without modifying the global optimum and its location. The approximated and smoothened landscape is often much easier to search than the original one. In this paper, we propose a new algorithm using landscape approximation and hybrid evolutionary and local search. We also list several algorithm design principles. Following the basic algorithm, an example algorithm is given from our previous work of the combination of landscape approximation and local search (LALS). Furthermore, we develop a novel evolutionary algorithm with ndimensional approximation (EANA), which shares the same rules as the basic algorithm, but remedies some of the drawbacks found in the LALS. Comparisons with evo...
Optimization Using Surrogate Objectives on a Helicopter Test Example
 RICE UNIVERSITY
, 1998
"... This paper presents results for a 31 variable helicopter rotor design example. Results are given for several numerical methods. This is a brief description of a portion of the Boeing/IBM/Rice University collaboration whose purpose is to develop effective numerical methods for managing the use of app ..."
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Cited by 21 (7 self)
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This paper presents results for a 31 variable helicopter rotor design example. Results are given for several numerical methods. This is a brief description of a portion of the Boeing/IBM/Rice University collaboration whose purpose is to develop effective numerical methods for managing the use of approximation concepts or response surface methodology in design optimization.
Multidisciplinary Design Optimization Techniques: Implications and Opportunities for Fluid Dynamics Research
 JAROSLAW SOBIESZCZANSKISOBIESKI AND RAPHAEL T. HAFTKA ā€¯MULTIDISCIPLINARY AEROSPACE DESIGN OPTIMIZATION: SURVEY OF RECENT DEVELOPMENTS,ā€¯ 34TH AIAA AEROSPACE SCIENCES MEETING AND EXHIBIT
, 1999
"... A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the de ..."
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Cited by 20 (0 self)
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A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.
Constructing Variable Fidelity Response Surface Approximations In The Usable Feasible Region
, 2000
"... The use of Response Surface Approximation (RSA) within an approximate optimization framework for the design of complex systems has increased as designers are challenged to develop better designs in reduced times. Traditionally, statistical sampling techniques (i. e., experimental design) have been u ..."
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Cited by 18 (9 self)
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The use of Response Surface Approximation (RSA) within an approximate optimization framework for the design of complex systems has increased as designers are challenged to develop better designs in reduced times. Traditionally, statistical sampling techniques (i. e., experimental design) have been used for constructing RSA's. These statistical sampling techniques are designed to be space filling, so that the response surface approximations are predictive across the range of the design sample space. When used in sequential approximate optimization strategies, a portion of the samples can be in the infeasible and/or ascent regions of the design space. These samples can bias the resulting RSA and make it less predictive in the usable feasible region where the optimization takes place. In the response surface based concurrent subsace optimization approach the design sampling strategy for RSA construction is optimization based. This optimization based sampling has proved to be effective due to the fact it samples in the linearized usable feasible region. In the present research, an experimental design strategy for projecting data points in the linearized usable feasible region is developed for constructing RSA's. The technique is implemented in a Sequential Approximate Optimization framework and tested in application to two multidisciplinary design optimization (MDO) test problems. Results show that the proposed technique pro
SurrogateAssisted Evolutionary Optimization Frameworks for HighFidelity Engineering Design Problems
 In Knowledge Incorporation in Evolutionary Computation
, 2004
"... Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where high ..."
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Cited by 16 (4 self)
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Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where highfidelity analysis models are used, each function evaluation may require a Computational Structural Mechanics (CSM), Computational Fluid Dynamics (CFD) or Computational ElectroMagnetics (CEM) simulation costing minutes to hours of supercomputer time. Since EAs typically require thousands of function evaluations to locate a near optimal solution, the use of EAs often becomes computationally prohibitive for this class of problems. In this paper, we present frameworks that employ surrogate models for solving computationally expensive optimization problems on a limited computational budget. In particular, the key factors responsible for the success of these frameworks are discussed. Experimental results obtained on benchmark test functions and realworld complex design problems are presented.
Generalized pattern searches with derivative information
 Mathematical Programming, Series B
"... Abstract: A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specific ..."
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Cited by 15 (8 self)
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Abstract: A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS poll step. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for poll steps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the poll step to a single function evaluation. We prove that using these less expensive poll steps does not weaken the known convergence properties of the method, all of which depend only on the poll step. Key words: Pattern search algorithm, linearly constrained optimization, surrogatebased optimization, nonsmooth optimization, gradientbased optimization. 1
Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework
 Optimization and Engineering
, 2004
"... Shape optimization is applied to timedependent trailingedge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a nongradient based pattern search method chosen for its e#ciency and rigorous convergence properties. Using SMF, d ..."
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Cited by 15 (4 self)
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Shape optimization is applied to timedependent trailingedge flow in order to minimize aerodynamic noise. Optimization is performed using the surrogate management framework (SMF), a nongradient based pattern search method chosen for its e#ciency and rigorous convergence properties. Using SMF, design space exploration is performed not with the expensive actual function but with an inexpensive surrogate function. The use of a polling step in the SMF guarantees that the algorithm generates a convergent subsequence of mesh points, each iterate of which is a local minimizer of the cost function on a mesh in the parameter space. Results are presented for an unsteady laminar flow past an acoustically compact airfoil. Constraints on lift and drag are handled within SMF by applying the filter pattern search method of Audet and Dennis, within which a penalty function is used to form and optimize a surrogate function.
A Framework for Managing Models in Nonlinear Optimization of Computationally Expensive Functions
, 1998
"... One of the most significant problems in the application of standard optimization methods to realworld engineering design problems is that the computation of the objective function often takes so much computer time (sometimes hours) that traditional optimization techniques are not practical. A sol ..."
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Cited by 14 (3 self)
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One of the most significant problems in the application of standard optimization methods to realworld engineering design problems is that the computation of the objective function often takes so much computer time (sometimes hours) that traditional optimization techniques are not practical. A solution that has long been used in this situation has been to approximate the objective function with something much cheaper to compute, called a "model" (or surrogate), and optimize the model instead of the actual objective function. This simple approach succeeds some of the time, but sometimes it fails because there is not sufficient a priori knowledge to build an adequate model. One way to address this problem is to build the model with whatever a priori knowledge is available, and during the optimization process sample the true objective at selected points and use the results to monitor the progress of the optimization and to adapt the model in the region of interest. We call this approach "model management". This thesis will build on the fundamental ideas and theory of pattern search optimization methods to develop a rigorous methodology for model management. A general framework for model management algorithms will iv be presented along with a convergence analysis. A software implementation of the framework, which allows for the reuse of existing modeling and optimization software, has been developed and results for several test problems will be presented. The model management methodology and potential applications in aerospace engineering are the subject of an ongoing collaboration between researchers at Boeing, IBM, Rice and College of William & Mary.