Expected improvement in efficient global optimization through bootstrapped kriging

Kleijnen, J.P.C.; Beers, W.C.M. van; Nieuwenhuyse, Inneke Van

doi:10.1007/s10898-011-9741-y

Cited by 92 publications

(16 citation statements)

References 29 publications

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“…Knowles (2006), Ponweiser et al (2008), Zhang et al (2010) and Couckuyt, Deschrijver, and Dhaene (2014) developed extensions of EGO and the EI criterion to handle expensive multiobjective optimization. Kleijnen, van Beers, and van Nieuwenhuyse (2012) developed an improved variant of EGO that uses an unbiased boostrap estimator of the variance of the Kriging predictor. Marzat, Walter, and Piet-Lahanier (2013) combined EGO with a relaxation procedure to develop an algorithm for continuous minimax optimization of black-box functions.…”

Section: Related Workmentioning

confidence: 99%

Trust regions in Kriging-based optimization with expected improvement

Regis

2015

Engineering Optimization

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The Kriging-based Efficient Global Optimization (EGO) method works well on many expensive blackbox optimization problems. However, it does not seem to perform well on problems with steep and narrow global minimum basins and on high-dimensional problems. This article develops a new Krigingbased optimization method called TRIKE (Trust Region Implementation in Kriging-based optimization with Expected improvement) that implements a trust-region-like approach where each iterate is obtained by maximizing an Expected Improvement (EI) function within some trust region. This trust region is adjusted depending on the ratio of the actual improvement to the EI. This article also develops the Kriging-based CYCLONE (CYClic Local search in OptimizatioN using Expected improvement) method that uses a cyclic pattern to determine the search regions where the EI is maximized. TRIKE and CYCLONE are compared with EGO on 28 test problems with up to 32 dimensions and on a 36-dimensional groundwater bioremediation application in appendices supplied as an online supplement available at http://dx.. The results show that both algorithms yield substantial improvements over EGO and they are competitive with a radial basis function method.

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Section: Related Workmentioning

confidence: 99%

Trust regions in Kriging-based optimization with expected improvement

Regis

2015

Engineering Optimization

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“…The seminal paper by Jones et al [102] which introduced the EGO algorithm for simulations with deterministic output, uses Kriging to interpolate between function values, and chooses future samples based on an expected improvement metric [140]. Examples of analogs to this for simulation optimization are provided in [93,118].…”

Section: Response Surface Methodologymentioning

confidence: 99%

Simulation optimization: a review of algorithms and applications

et al. 2015

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Simulation optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation-discrete or continuous decisions, expensive or cheap simulations, single or multiple outputs, homogeneous or heterogeneous noise-various algorithms have been proposed in the literature. As one can imagine, there exist several competing algorithms for each of these classes of problems. This document emphasizes the difficulties in SO as compared to algebraic model-based mathematical programming, makes reference to state-of-the-art algorithms in the field, examines and contrasts the different approaches used, reviews some of the diverse applications that have been tackled by these methods, and speculates on future directions in the field.Keywords Simulation optimization · Optimization via simulation · Derivative-free optimization This is an updated version of the paper that appeared in 4OR, 12(4), 301-333 (2014).

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“…An acquisition function is adopted to evaluate the system performance. There are different methods to formulate an acquisition function such as probability of improvement, 11 expected improvement 12 and upper confidence bound (UCB). 13 In this paper, we use UCB to evaluate the system performance based on the mean and variance.…”

Section: Proposed Solutionmentioning

confidence: 99%

Controller parameter optimization for complex industrial system with uncertainties

Chen

Bowels

Zhang³

et al. 2019

Measurement and Control

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Proportional–integral–derivative control system has been widely used in industrial applications. For complex systems, tuning controller parameters to satisfy the process requirements is very challenging. Different methods have been proposed to solve the problem. However these methods suffer several problems, such as dealing with system complexity, minimizing tuning effort and balancing different performance indices including rise time, settling time, steady-state error and overshoot. In this paper, we develop an automatic controller parameter optimization method based on Gaussian process regression Bayesian optimization algorithm. A non-parametric model is constructed using Gaussian process regression. By combining Gaussian process regression with Bayesian optimization algorithm, potential candidate can be predicted and applied to guide the optimization process. Both experiments and simulation were performed to demonstrate the effectiveness of the proposed method.

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Expected improvement in efficient global optimization through bootstrapped kriging

Cited by 92 publications

References 29 publications

Trust regions in Kriging-based optimization with expected improvement

Trust regions in Kriging-based optimization with expected improvement

Simulation optimization: a review of algorithms and applications

Controller parameter optimization for complex industrial system with uncertainties

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