Adaptive Dimensionality Reduction for Fast Sequential Optimization With Gaussian Processes

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Seyede Fatemeh Ghoreishi ◽  
Samuel Friedman ◽  
Douglas L. Allaire
Keyword(s):  
Global Optimization ◽  
Computational Models ◽  
Black Box ◽  
Optimization Techniques ◽  
Sequential Optimization ◽  
Benchmark Problems ◽  
Box Models ◽  
Gradient Based ◽  
Bayesian Global Optimization ◽  
Knowledge Gradient

Available computational models for many engineering design applications are both expensive and and of a black-box nature. This renders traditional optimization techniques difficult to apply, including gradient-based optimization and expensive heuristic approaches. For such situations, Bayesian global optimization approaches, that both explore and exploit a true function while building a metamodel of it, are applied. These methods often rely on a set of alternative candidate designs over which a querying policy is designed to search. For even modestly high-dimensional problems, such an alternative set approach can be computationally intractable, due to the reliance on excessive exploration of the design space. To overcome this, we have developed a framework for the optimization of expensive black-box models, which is based on active subspace exploitation and a two-step knowledge gradient policy. We demonstrate our approach on three benchmark problems and a practical aerostructural wing design problem, where our method performs well against traditional direct application of Bayesian global optimization techniques.

Expensive Black-Box Model Optimization via a Gold Rush Policy

2018 ◽  
Author(s):  
Benson Isaac ◽  
Douglas Allaire
Keyword(s):  
Global Optimization ◽  
Structural Information ◽  
Optimization Methods ◽  
Gold Rush ◽  
Black Box ◽  
Optimization Techniques ◽  
Benchmark Problems ◽  
Expensive Function ◽  
Box Models ◽  
Bayesian Global Optimization

The optimization of expensive black-box models is a challenging task owing to the lack of analytic gradient information and structural information about the underlying function, and also due to the sheer computational expense. A common approach to tackling such problems is the implementation of Bayesian global optimization techniques. However, these techniques often rely on surrogate modeling strategies that endow the approximation of the underlying expensive function with nonexistent features. Further, these techniques tend to push new queries away from previously queried design points, making it difficult to locate an optimum point that rests near a previous model evaluation. To overcome these issues, we propose a gold rush policy that relies on purely local information to identify the next best design alternative to query. The method employs a surrogate constructed pointwise, that adds no additional features to the approximation. The result is a policy that performs well in comparison to state of the art Bayesian global optimization methods on several benchmark problems. The policy is also demonstrated on a constrained optimization problem using a penalty method.

Expensive Black-Box Model Optimization Via a Gold Rush Policy

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Benson Isaac ◽  
Douglas Allaire
Keyword(s):  
Global Optimization ◽  
Structural Information ◽  
Optimization Methods ◽  
Gold Rush ◽  
Black Box ◽  
Optimization Techniques ◽  
Benchmark Problems ◽  
Expensive Function ◽  
Box Models ◽  
Bayesian Global Optimization

The optimization of black-box models is a challenging task owing to the lack of analytic gradient information and structural information about the underlying function, and also due often to significant run times. A common approach to tackling such problems is the implementation of Bayesian global optimization techniques. However, these techniques often rely on surrogate modeling strategies that endow the approximation of the underlying expensive function with nonexistent features. Further, these techniques tend to push new queries away from previously queried design points, making it difficult to locate an optimum point that rests near a previous model evaluation. To overcome these issues, we propose a gold rush (GR) policy that relies on purely local information to identify the next best design alternative to query. The method employs a surrogate constructed pointwise, that adds no additional features to the approximation. The result is a policy that performs well in comparison to state of the art Bayesian global optimization methods on several benchmark problems. The policy is also demonstrated on a constrained optimization problem using a penalty method.

Optimization of Micro-Textured Surfaces for Turbine Vane Impingement Cooling

2013 ◽  
Author(s):  
Justin Jacobs ◽  
Joe Tripp ◽  
David Underwood ◽  
Corinne Lengsfeld
Keyword(s):  
Computational Models ◽  
Leading Edge ◽  
Optimization Techniques ◽  
Internal Cooling ◽  
Textured Surfaces ◽  
Independent Manner ◽  
Current Effort ◽  
Impingement Cooling ◽  
Turbine Vane ◽  
Gradient Based

Gas turbine engines are challenged to operate at higher efficiencies, leading to turbine inlet temperatures that exceed turbine material limits. Increased internal cooling efficiency enables higher temperature operation, reduces cooling air injection into the core flow, and mitigates performance penalties from thermal mixing and total pressure loss. Micro Cooling Concepts has developed a turbine vane cooling concept that provides enhanced internal impingement cooling effectiveness via the use of micro-textured impingement surfaces (i.e., grooves and fins). The current effort employs computational models, in conjunction with optimization techniques, to explore the optimal design of these micro-textured surfaces. A computational fluid dynamics model of the vane leading edge was utilized to compute the flow in the vane interior and the temperature distribution in the vane material. A gradient-based optimization routine, implemented in Matlab, varied geometric parameters in an independent manner to minimize the maximum metal temperature in the vane material volume. Four separate design spaces were explored: grooves and fins (both shrouded and unshrouded). It was determined that the shrouded fins and fin design outperformed all others. The maximum external convective free stream temperature obtained was 2600 K while the maximum internal vane temperature remained below 1219 K.

scholarly journals Gradient-Based Cuckoo Search for Global Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Seif-Eddeen K. Fateen ◽  
Adrián Bonilla-Petriciolet
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Cuckoo Search ◽  
Optimization Methods ◽  
Benchmark Problems ◽  
Stochastic Global Optimization ◽  
Original Algorithm ◽  
Gradient Based

One of the major advantages of stochastic global optimization methods is the lack of the need of the gradient of the objective function. However, in some cases, this gradient is readily available and can be used to improve the numerical performance of stochastic optimization methods specially the quality and precision of global optimal solution. In this study, we proposed a gradient-based modification to the cuckoo search algorithm, which is a nature-inspired swarm-based stochastic global optimization method. We introduced the gradient-based cuckoo search (GBCS) and evaluated its performance vis-à-vis the original algorithm in solving twenty-four benchmark functions. The use of GBCS improved reliability and effectiveness of the algorithm in all but four of the tested benchmark problems. GBCS proved to be a strong candidate for solving difficult optimization problems, for which the gradient of the objective function is readily available.

scholarly journals Implementation of Black Box Models for Internal Ballistics Optimization Using an Artificial Neural Network

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Chen ◽  
JingYin Li ◽  
ShuangXi Li ◽  
YunXiang You
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Rotational Speed ◽  
Black Box ◽  
Optimization Techniques ◽  
Low Energy ◽  
Internal Ballistics ◽  
Box Models ◽  
Artificial Neural ◽  
Black Box Models

The process of UUV delivery is a typical nonlinear transient dynamic phenomenon, which is generally described by the internal ballistic model. Evaluation of optimal internal ballistics parameters is a key step for promoting ballistic weapon performance under given launch constraints. Hence, accurate and efficient optimization techniques are required in ballistics technology. In this study, an artificial neural network (ANN) is used to simplify the process of regression analysis. To this end, an internal ballistics model is built in this study as a black box for a classic underwater launching system, such as a torpedo launcher, based on ANN parameter identification. The established black box models are mainly employed to calculate the velocity of a ballistic body and the torque of a launching pump. Typical internal ballistics test data are adopted as samples for training the ANN. Comparative results demonstrate that the developed black box models can accurately reflect changes in internal ballistics parameters according to rotational speed variations. Therefore, the proposed approach can be fruitfully applied to the task of internal ballistics optimization. The optimization of internal ballistics precision control, optimal control of the launching pump, and optimal low-energy launch control were, respectively, realized in conjunction with the established model using the SHERPA search algorithm. The results demonstrate that the optimized internal ballistics rotational speed curve can achieve the optimization objectives of low-energy launch and peak power while meeting the requirements of optimization constraints.

scholarly journals A method for convex black-box integer global optimization

2021 ◽  
Author(s):  
Jeffrey Larson ◽  
Sven Leyffer ◽  
Prashant Palkar ◽  
Stefan M. Wild
Keyword(s):  
Global Optimization ◽  
Black Box

scholarly journals Branch and Bound Algorithm Based on Prediction Error of Metamodel for Computational Electromagnetics

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6749
Author(s):  
Reda El Bechari ◽  
Stéphane Brisset ◽  
Stéphane Clénet ◽  
Frédéric Guyomarch ◽  
Jean Claude Mipo
Keyword(s):  
Branch And Bound ◽  
Prediction Error ◽  
Global Solutions ◽  
Black Box ◽  
High Fidelity ◽  
Electromagnetic Devices ◽  
Box Models ◽  
Element Simulation ◽  
The Cost ◽  
Black Box Models

Metamodels proved to be a very efficient strategy for optimizing expensive black-box models, e.g., Finite Element simulation for electromagnetic devices. It enables the reduction of the computational burden for optimization purposes. However, the conventional approach of using metamodels presents limitations such as the cost of metamodel fitting and infill criteria problem-solving. This paper proposes a new algorithm that combines metamodels with a branch and bound (B&B) strategy. However, the efficiency of the B&B algorithm relies on the estimation of the bounds; therefore, we investigated the prediction error given by metamodels to predict the bounds. This combination leads to high fidelity global solutions. We propose a comparison protocol to assess the approach’s performances with respect to those of other algorithms of different categories. Then, two electromagnetic optimization benchmarks are treated. This paper gives practical insights into algorithms that can be used when optimizing electromagnetic devices.

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