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27
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 19 (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
Adaptive Experimental Design For Construction Of Response Surface Approximations
, 2001
"... Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, wher ..."
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Cited by 19 (10 self)
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Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n²) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(n) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n²) update of the second order approximation to maintain accuracy. Results show
Reduced Sampling For Construction Of Quadratic Response Surface Approximations Using Adaptive Experimental Design
, 2002
"... Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitive when the complexity of the simulation codes is large. Increasingly, response surface approximations(RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimi ..."
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Cited by 12 (5 self)
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Applying nonlinear optimization strategies directly to complex multidisciplinary systems can be prohibitive when the complexity of the simulation codes is large. Increasingly, response surface approximations(RSAs), and specifically quadratic approximations, are being integrated with nonlinear optimizers in order to reduce the CPU time required for the optimization of complex multidisciplinary systems. RSAs provide a computationally inexpensive lower fidelity representation of the system performance. The curse of dimensionality is a major drawback in the implementation of these approximations as the amount of required data grows quadratically with the number of design variables.
Adaptive Response Surface Method  A Global Optimization Scheme for Computationintensive Design Problems
 JOURNAL OF ENGINEERING OPTIMIZATION
, 2001
"... For design problems involving computationintensive analysis or simulation processes, approximation models are usually introduced to reduce computation time. Most approximationbased optimization methods make stepbystep improvements to the approximation model by adjusting the limits of the design ..."
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Cited by 9 (2 self)
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For design problems involving computationintensive analysis or simulation processes, approximation models are usually introduced to reduce computation time. Most approximationbased optimization methods make stepbystep improvements to the approximation model by adjusting the limits of the design variables. In this work, a new approximationbased optimization method for computationintensive design problems — the adaptive response surface method (ARSM), is presented. The ARSM creates quadratic approximation models for the computationintensive design objective function in a gradually reduced design space. The ARSM was designed to avoid being trapped by local optimum and to identify the global design optimum with a modest number of objective function evaluations. Extensive tests on the ARSM as a global optimization scheme using benchmark problems, as well as an industrial design application of the method, are presented. Advantages and limitations of the approach are also discussed.
Formulations for SurrogateBased Optimization with DataFit, Multifidelity and ReducedOrder Models
 Proceedings of the 11 th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, No. 20067117 in AIAA Paper
, 2006
"... Surrogatebased optimization (SBO) methods have become established as effective techniques for engineering design problems through their ability to tame nonsmoothness and reduce computational expense. Possible surrogate modeling techniques include data fits (local, multipoint, or global), multifidel ..."
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Cited by 9 (2 self)
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Surrogatebased optimization (SBO) methods have become established as effective techniques for engineering design problems through their ability to tame nonsmoothness and reduce computational expense. Possible surrogate modeling techniques include data fits (local, multipoint, or global), multifidelity model hierarchies, and reducedorder models, and each of these types has unique features when employed within SBO. This paper explores a number of SBO algorithmic variations and their effect for different surrogate modeling cases. First, general facilities for constraint management are explored through approximate subproblem formulations (e.g., direct surrogate), constraint relaxation techniques (e.g., homotopy), merit function selections (e.g., augmented Lagrangian), and iterate acceptance logic selections (e.g., filter methods). Second, techniques specialized to particular surrogate types are described. Computational results are presented for sets of algebraic test problems and an engineering design application solved using the DAKOTA software. I.
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 8 (3 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
Decoupling the Design Sampling Region from the Trust Region in
, 2000
"... Response Surface Approximations (RSA's) are widely used in the design community to provide designers with an approximate representation of a system. The use of RSA's allow designers to query the system while avoiding the high computational costs associated with today's advanced simula ..."
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Cited by 6 (3 self)
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Response Surface Approximations (RSA's) are widely used in the design community to provide designers with an approximate representation of a system. The use of RSA's allow designers to query the system while avoiding the high computational costs associated with today's advanced simulation codes. Sequential Approximate Optimization (SAO) methodologies have proved to be effective in managing the optimization of multidisciplinary design problems. In SAO the sampling required to build the RSA's often takes place within the same bounds as imposed on the current optimization iterate. This assures a good representation of the system in the region where it will be optimized. However it may restrict the approximation from extrapolating beyond the design space, and therefore improve the convergence rate of the algorithm. In this research a decoupling of the sampling region from the trust region is proposed.
An Interior Point Sequential Approximate Optimization Methodology
, 2002
"... The use of optimization in a simulation based design environment has become a common trend in industry today. Computer simulation tools are common place in many engineering disciplines, providing the designers with tools to evaluate a design's performance without building a physical prototype. ..."
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Cited by 5 (4 self)
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The use of optimization in a simulation based design environment has become a common trend in industry today. Computer simulation tools are common place in many engineering disciplines, providing the designers with tools to evaluate a design's performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior point approach for trust region managed sequential approximate optimization. The interior point approach will insure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.
An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design
, 2004
"... ..."
Homotopy Curve Tracking In Approximate Interior Point Optimization
, 2003
"... The use of computer simulations has revolutionized the way engineers design and improve products and affects all design stages from concept to realization. As a consequence optimization has become an important tool for the engineer to realize better designs without the need of extensive prototype bu ..."
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Cited by 3 (1 self)
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The use of computer simulations has revolutionized the way engineers design and improve products and affects all design stages from concept to realization. As a consequence optimization has become an important tool for the engineer to realize better designs without the need of extensive prototype building. One of the algorithms that has shown an important ability to deal with this type of optimization is known as sequential approximate optimization. In sequential approximate optimization a series of local minimizations are performed over local response surface approximations of the system.