Variable-fidelity expected improvement method for efficient global optimization of expensive functions

2018 ◽  
Vol 58 (4) ◽  
pp. 1431-1451 ◽  
Author(s):  
Yu Zhang ◽  
Zhong-Hua Han ◽  
Ke-Shi Zhang
Keyword(s):  
Global Optimization ◽  
Expected Improvement ◽  
Efficient Global Optimization ◽  
Improvement Method ◽  
Variable Fidelity

Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

2011 ◽  
Author(s):  
Jack P. C. Kleijnen ◽  
Wim C. M. van Beers ◽  
Inneke Van Nieuwenhuyse
Keyword(s):  
Global Optimization ◽  
Expected Improvement ◽  
Efficient Global Optimization

scholarly journals Expected improvement in efficient global optimization through bootstrapped kriging

2011 ◽  
Vol 54 (1) ◽  
pp. 59-73 ◽  
Author(s):  
Jack P. C. Kleijnen ◽  
Wim van Beers ◽  
Inneke van Nieuwenhuyse
Keyword(s):  
Global Optimization ◽  
Expected Improvement ◽  
Efficient Global Optimization

Uncertainty Based Optimization Strategy for the Gappy-POD Multi-Fidelity Method

2020 ◽  
Author(s):  
Bernhard Poethke ◽  
Stefan Völker ◽  
Konrad Vogeler
Keyword(s):  
Global Optimization ◽  
Uncertainty Quantification ◽  
Industrial Test ◽  
Expected Improvement ◽  
Efficient Global Optimization ◽  
Test Case ◽  
Optimization Strategy ◽  
Constrained Problems ◽  
Design Variables ◽  
Gappy Pod

Abstract In the surrogate model-based optimization of turbine airfoils, often only the prediction values for objective and constraints are employed, without considering uncertainties in the prediction. This is also the case for multi-fidelity optimization strategies based on e.g. the Gappy-POD approach, in which results from analyses of different fidelities are incorporated. However, the consideration of uncertainties in global optimization has the advantage that a balanced coverage of the design space between unexplored regions and regions close to the current optimum takes place. This means that on the one hand regions are covered in which so far only a few sample points are present and thus a high degree of uncertainty exists (global exploration), and on the other hand regions with promising objective and constraint values are investigated (local exploitation). The genuine new contribution in this work is the quantification of the uncertainty of the multi-fidelity Gappy-POD method and an adapted optimization strategy based on it. The uncertainty quantification is based on the error of linear fitting of low-fidelity values to the POD basis and subsequent forward propagation to the high-fidelity values. The uncertainty quantification is validated for random airfoil designs in a design of experiment. Based on this, a global optimization strategy for constrained problems is presented, which is based on the well-known Efficient Global Optimization (EGO) strategy and the Feasible Expected Improvement criterion. This means that Kriging models are created for both the objective and the constraint values depending on the design variables that consider both the predictions and the uncertainties. This approach offers the advantage that existing and widely used programs or libraries can be used for multi-fidelity optimization that support the (single-fidelity) EGO algorithm. Finally, the method is demonstrated for an industrial test case. A comparison between a single-fidelity optimization and a multi-fidelity optimization is made, each with the EGO strategy. A coupling of 2D/3D simulations is used for multi-fidelity analyses. The proposed method achieves faster feasible members in the optimization, resulting in faster turn-around compared to the single-fidelity strategy.

scholarly journals Multi-Armed Bandit Regularized Expected Improvement for Efficient Global Optimization of Expensive Computer Experiments with Low Noise

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rajitha Meka ◽  
Adel Alaeddini ◽  
Chinonso Ovuegbe ◽  
Pranav Bhounsule ◽  
Peyman Najafirad ◽  
...  
Keyword(s):  
Global Optimization ◽  
Computer Experiments ◽  
Low Noise ◽  
Expected Improvement ◽  
Efficient Global Optimization

scholarly journals Accurate Multi-Objective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization

2019 ◽  
Author(s):  
Jon Paul Janet ◽  
Sahasrajit Ramesh ◽  
Chenru Duan ◽  
Heather Kulik
Keyword(s):  
Neural Network ◽  
Global Optimization ◽  
Transition Metal ◽  
Metal Complexes ◽  
Transition Metal Complexes ◽  
Density Functional ◽  
Data Availability ◽  
Expected Improvement ◽  
Efficient Global Optimization ◽  
Compound Libraries

<p>The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. Satisfaction of such constraints requires exploration of multi-million compound libraries over which even density-functional theory (DFT) screening is intractable. Machine learning (ML, e.g., artificial neural network, ANN, or Gaussian process, GP) models for this task are limited by training data availability and predictive uncertainty quantification (UQ). We overcome such limitations by using efficient global optimization (EGO) with the multi-dimensional expected improvement (EI) criterion. EGO balances exploitation of a trained model with acquisition of new DFT data at the Pareto front, the region of chemical space that contains the optimal trade-off between multiple design criteria. We demonstrate this approach for the simultaneous optimization of redox potential and solubility in candidate M(II)/M(III) redox couples for redox flow batteries from a space of 2.8M transition metal complexes designed for stability in practical RFB applications. We employ latent-distance-based UQ with a multi-task ANN to enable model generalization that surpasses that of a GP. With this approach, ANN prediction and EI scoring of the full 2.8M complex space is achieved in minutes. Starting from ca. 100 representative points, EGO improves both properties by 3-4 standard deviations in only five generations. Analysis of lookahead errors confirms rapid ANN model improvement during the EGO process, achieving suitable accuracy for predictive design in the space of transition metal complexes. The ANN-driven EI approach achieves at least 500-fold acceleration over random search, identifying a Pareto-optimal design in around five weeks instead of fifty years.<br></p>

Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

2010 ◽  
Author(s):  
Jack P. C. Kleijnen ◽  
Wim C. M. van Beers ◽  
Inneke Van Nieuwenhuyse
Keyword(s):  
Global Optimization ◽  
Expected Improvement ◽  
Efficient Global Optimization
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