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3rd issmo/aiaa internet conference on approximations in optimization

作者： Sóbester, A Leary, SJ Keane, AJ Univ Southampton Sch Engn Sci CEDG Southampton SO17 1BJ Hants England

Approximation methods are often used to construct surrogate models, which can replace expensive computer simulations for the purposes of optimization. One of the most important aspects of such optimization techniques is the choice of model updating strategy. In this paper we employ parallel updates by searching an expected improvement surface generated from a radial basis function model. We look at optimization based on standard and gradient-enhanced models. Given N-p processors, the best N-p local maxima of the expected improvement surface are highlighted and further runs are performed on these designs. To test these ideas, simple analytic functions and a finite element model of a simple structure are analysed and various approaches compared.

关键词： gradient-enhanced approximations parallel optimization radial basis functions

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Global-local structural optimization using response surfaces of local optimization margins

Global-local structural optimization using response surfaces...

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3rd issmo/aiaa internet conference on approximations in optimization

作者： Liu, B Haftka, RT Watson, LT Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32611 USA Virginia Polytech Inst & State Univ Dept Comp Sci Blacksburg VA 24061 USA Virginia Polytech Inst & State Univ Dept Math Blacksburg VA 24061 USA

A general decomposition method developed by Haftka and Watson is applied to global-local structural optimization problems. First, a large number of component optimizations for maximization of margins are performed. Response surface approximations (RSAs) for maximum margins of component optimization are constructed. At the system-level optimization, the RSAs of maximum margins are used as surrogates for the components. One advantage of the decomposition approach is that it allows much of the search for a global optimum to be conducted in low dimensions for each component separately. Minimization of a portal frame weight with eight local optima is used to demonstrate the approach.

关键词： constraint margins decomposition local/global structural optimization response surfaces

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Global-local structural optimization using response surfaces of local optimization margins

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2004年第5期27卷 352-359页

关键词： constraint margins decomposition local/global structural optimization response surfaces

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A parallel updating scheme for approximating and optimizing high fidelity computer simulations

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2004年第5期27卷 371-383页

作者： Sóbester, A Leary, SJ Keane, AJ Univ Southampton Sch Engn Sci CEDG Southampton SO17 1BJ Hants England

关键词： gradient-enhanced approximations parallel optimization radial basis functions

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Multipoint cubic surrogate function for sequential approximate optimization

Multipoint cubic surrogate function for sequential approxima...

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3rd issmo/aiaa internet conference on approximations in optimization

作者： Canfield, RA USAF Inst Technol Dept Aeronaut & Astronaut Engn ENY Wright Patterson AFB OH 45433 USA

Multipoint cubic approximations are investigated as surrogate functions for nonlinear objective and constraint functions in the context of sequential approximate optimization. The proposed surrogate functions match actual function and gradient values, including the current expansion point, thus satisfying the zero and first-order necessary conditions for global convergence to a local minimum of the original problem. Function and gradient information accumulated from multiple design points during the iteration history is used in estimating a reduced Hessian matrix and selected cubic terms in a design subspace appropriate for problems with many design variables. The resulting approximate response surface promises to accelerate convergence to an optimal design within the framework of a trust region algorithm. The hope is to realize computational savings in solving large numerical optimization problems. Numerical examples demonstrate the effectiveness of the new multipoint surrogate function in reducing errors over large changes in design variables.

关键词： multipoint approximation optimization response surface surrogate function

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Multipoint cubic surrogate function for sequential approximate optimization

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2004年第5期27卷 326-336页

作者： Canfield, RA USAF Inst Technol Dept Aeronaut & Astronaut Engn ENY Wright Patterson AFB OH 45433 USA

关键词： multipoint approximation optimization response surface surrogate function

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Crashworthiness optimization of helicopter subfloor based on decomposition and global approximation

Crashworthiness optimization of helicopter subfloor based on...

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3rd issmo/aiaa internet conference on approximations in optimization

作者： Lanzi, L Bisagni, C Ricci, S Politecn Milan Dipartimento Ingn Aerospaziale I-20156 Milan Italy

This work deals with the development of an optimization procedure under crashworthiness requirements applied to a typical helicopter subfloor. The difficulties due to the nonlinear design space and structural behaviour are overcome by developing an optimization procedure based on decomposition, where the structure to be optimized is converted into a set of smaller and linked substructures. To evaluate the response of each substructure, global approximation strategies, based on neural networks, are used. Size variables (dimensions, thickness) and geometrical variables (element number and position) are considered in order to maximize the global crashworthiness performance. The energy absorbed per unit mass by the subfloor is chosen as objective function and acceleration constraints are considered. Genetic algorithms are used to find the optimal configuration. The optimization allowed an increase in the crush force efficiency of 12% and a decrease in the subfloor mass of 4%. A significant CPU time saving was also obtained.

关键词： crashworthiness optimization global approximation neural networks problem decomposition

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Crashworthiness optimization of helicopter subfloor based on decomposition and global approximation

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2004年第5期27卷 401-410页

作者： Lanzi, L Bisagni, C Ricci, S Politecn Milan Dipartimento Ingn Aerospaziale I-20156 Milan Italy

关键词： crashworthiness optimization global approximation neural networks problem decomposition

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An interior-point sequential approximate optimization methodology

An interior-point sequential approximate optimization method...

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3rd issmo/aiaa internet conference on approximations in optimization

作者： Pérez, VM Renaud, JE Watson, LT Univ Notre Dame Dept Aerosp & Mech Engn Notre Dame IN 46556 USA Virginia Polytech Inst & State Univ Dept Math & Comp Sci Blacksburg VA 24061 USA

The use of optimization in a simulation-based design environment has become a common trend in industry today. Computer simulation tools are commonplace 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 ensure 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.

关键词： interior-point methods multidisciplinary optimization sequential approximate optimization trust region methods

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Reliability-based design optimization using probabilistic sufficiency factor

Reliability-based design optimization using probabilistic su...

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3rd issmo/aiaa internet conference on approximations in optimization

作者： Qu, X Haftka, RT Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32611 USA

A probabilistic sufficiency factor approach is proposed that combines safety factor and probability of failure. The probabilistic sufficiency factor approach represents a factor of safety relative to a target probability of failure. It provides a measure of safety that can be used more readily than the probability of failure or the safety index by designers to estimate the required weight increase to reach a target safety level. The probabilistic sufficiency factor can be calculated from the results of Monte Carlo simulation with little extra computation. The paper presents the use of probabilistic sufficiency factor with a design response surface approximation, which fits it as a function of design variables. It is shown that the design response surface approximation for the probabilistic sufficiency factor is more accurate than that for the probability of failure or for the safety index. Unlike the probability of failure or the safety index, the probabilistic sufficiency factor does not suffer from accuracy problems in regions of low probability of failure when calculated by Monte Carlo simulation. The use of the probabilistic sufficiency factor accelerates the convergence of reliability-based design optimization.

关键词： Monte Carlo simulation probabilistic sufciency factor reliability-based design optimization response surface approximation

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