scholarly journals A Relative Adequacy Framework for Multi-Model Management in Design Optimization

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Ahmed H. Bayoumy ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Computational Models ◽  
Computational Cost ◽  
Trust Region ◽  
Model Management ◽  
Flexible Beam ◽  
Flow Conditions ◽  
Management Framework ◽  
Derivative Free Optimization ◽  
Derivative Free

Abstract We consider the problem of selecting among different physics-based computational models of varying, and oftentimes not assessed, fidelity for evaluating the objective and constraint functions in numerical design optimization. Typically, higher-fidelity models are associated with higher computational cost. Therefore, it is desirable to employ them only when necessary. We introduce a relative adequacy framework that aims at determining whether lower-fidelity models (that are typically associated with lower computational cost) can be used in certain areas of the design space as the latter is being explored during the optimization process. We implement our approach by means of a trust-region management framework that utilizes the mesh adaptive direct search derivative-free optimization algorithm. We demonstrate the link between feasibility and fidelity and the key features of the proposed approach using two design optimization examples: a cantilever flexible beam subject to high accelerations and an airfoil in transonic flow conditions.

A Reference Error Formulation for Multi-Fidelity Design Optimization

2017 ◽  
Author(s):  
Ahmed H. Bayoumy ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Computational Models ◽  
Design Space ◽  
Computational Cost ◽  
Trust Region ◽  
Model Management ◽  
Flexible Beam ◽  
Management Framework ◽  
Numerical Design ◽  
Region Model

We consider the problem of selecting among different computational models of various fidelity for evaluating the objective and constraint functions in numerical design optimization. Typically, higher-fidelity models are associated with higher computational cost. Therefore, it is desirable to employ them only when necessary. We introduce a reference error formulation that aims at determining whether lower-fidelity models (that are computationally cheaper) can be used in certain areas of the design space as the latter is being explored during the optimization process. The proposed approach is implemented using an existing trust region model management framework. We demonstrate the link between feasibility and fidelity and the key features of the proposed approach using the design example of a cantilever flexible beam subject to high accelerations.

Problem Formulations for Simulation-Based Design Optimization Using Statistical Surrogates and Direct Search

2014 ◽  
Author(s):  
Bastien Talgorn ◽  
Sébastien Le Digabel ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Computational Models ◽  
Optimization Problems ◽  
Direct Search ◽  
Local Optima ◽  
Numerical Noise ◽  
Derivative Free Optimization ◽  
Simulation Based Design ◽  
Derivative Free ◽  
Simulation Based

Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. The remedy for all these issues is to use surrogate models in lieu of the computational models or simulations and derivative-free optimization algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivative-free optimization. We present different formulations for the surrogate problem considered at each search step of the Mesh Adaptive Direct Search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on two simulation-based multidisciplinary design optimization problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.

Statistical Surrogate Formulations for Simulation-Based Design Optimization

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Bastien Talgorn ◽  
Sébastien Le Digabel ◽  
Michael Kokkolaras
Keyword(s):  
Design Optimization ◽  
Computational Models ◽  
Direct Search ◽  
Benchmark Problems ◽  
Local Optima ◽  
Numerical Noise ◽  
Derivative Free Optimization ◽  
Simulation Based Design ◽  
Derivative Free ◽  
Simulation Based

Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima, and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and derivative-free optimization algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivative-free optimization. We present different formulations for the surrogate problem (SP) considered at each search step of the mesh adaptive direct search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on 20 analytical benchmark problems and two simulation-based multidisciplinary design optimization (MDO) problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.

Improved Trust Region Model Management for Approximate Optimization

1998 ◽  
Author(s):  
Brett A. Wujek ◽  
John E. Renaud
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Low Cost ◽  
Approximation Error ◽  
Trust Region ◽  
Model Management ◽  
Multidisciplinary Design ◽  
Test Problems ◽  
Approximation Techniques ◽  
Approximate Optimization

Abstract Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate optimization strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karush Kuhn Tucker solution a move limit management strategy is required. In this paper, issues of move-limit management are reviewed and a new adaptive strategy for move limit management is developed. With its basis in the provably convergent trust region methodology, the TRAM (Trust region Ratio Approximation Method) strategy utilizes available gradient information and employs a backtracking process using various two-point approximation techniques to provide a flexible move-limit adjustment factor. The new strategy is successfully implemented in application to a suite of multidisciplinary design optimization test problems. These implementation studies highlight the ability of the TRAM strategy to control the amount of approximation error and efficiently manage the convergence to a Karush Kuhn Tucker solution.

scholarly journals Trust region model management in multidisciplinary design optimization

2000 ◽  
Vol 124 (1-2) ◽  
pp. 139-154 ◽  
Author(s):  
José F. Rodrı́guez ◽  
John E. Renaud ◽  
Brett A. Wujek ◽  
Ravindra V. Tappeta
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Trust Region ◽  
Model Management ◽  
Multidisciplinary Design ◽  
Region Model

A Note on Wedge Trust Region Radius Update

2011 ◽  
Vol 52-54 ◽  
pp. 926-931
Author(s):  
Qing Hua Zhou ◽  
Feng Xia Xu ◽  
Yan Geng ◽  
Ya Rui Zhang
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Region Method ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Updating Rule

Wedge trust region method based on traditional trust region is designed for derivative free optimization problems. This method adds a constraint to the trust region problem, which is called “wedge method”. The problem is that the updating strategy of wedge trust region radius is somewhat simple. In this paper, we develop and combine a new radius updating rule with this method. For most test problems, the number of function evaluations is reduced significantly. The experiments demonstrate the effectiveness of the improvement through our algorithm.

Rapid design optimization of antennas using variable-fidelity EM models and adjoint sensitivities

2016 ◽  
Vol 33 (7) ◽  
pp. 2007-2018 ◽  
Author(s):  
Slawomir Koziel ◽  
Adrian Bekasiewicz
Keyword(s):  
Design Optimization ◽  
Optimization Technique ◽  
Computational Cost ◽  
Trust Region ◽  
Simulation Models ◽  
Direct Optimization ◽  
Content Type ◽  
Variable Fidelity ◽  
Em Simulation ◽  
Conventional Methods

Purpose Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues. Design/methodology/approach The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach. Findings Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods. Research limitations/implications The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes. Originality/value Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

Variable-fidelity shape optimization of dual-rotor wind turbines

2018 ◽  
Vol 35 (7) ◽  
pp. 2514-2542
Author(s):  
Andrew Thelen ◽  
Leifur Leifsson ◽  
Anupam Sharma ◽  
Slawomir Koziel
Keyword(s):  
Design Optimization ◽  
Wind Turbines ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Fast Variable ◽  
Efficient Design ◽  
Content Type ◽  
Optimization Framework ◽  
Derivative Free ◽  
Variable Fidelity

Purpose Dual-rotor wind turbines (DRWTs) are a novel type of wind turbines that can capture more power than their single-rotor counterparts. Because their surrounding flow fields are complex, evaluating a DRWT design requires accurate predictive simulations, which incur high computational costs. Currently, there does not exist a design optimization framework for DRWTs. Since the design optimization of DRWTs requires numerous model evaluations, the purpose of this paper is to identify computationally efficient design approaches. Design/methodology/approach Several algorithms are compared for the design optimization of DRWTs. The algorithms vary widely in approaches and include a direct derivative-free method, as well as three surrogate-based optimization methods, two approximation-based approaches and one variable-fidelity approach with coarse discretization low-fidelity models. Findings The proposed variable-fidelity method required significantly lower computational cost than the derivative-free and approximation-based methods. Large computational savings come from using the time-consuming high-fidelity simulations sparingly and performing the majority of the design space search using the fast variable-fidelity models. Originality/value Due the complex simulations and the large number of designable parameters, the design of DRWTs require the use of numerical optimization algorithms. This work presents a novel and efficient design optimization framework for DRWTs using computationally intensive simulations and variable-fidelity optimization techniques.

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