On bayesian methods for seeking the extremum

Mockus, Jonas

doi:10.1007/3-540-07165-2_55

Cited by 272 publications

(221 citation statements)

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“…Kriging does not only provide an estimate of the objective function everywhere, but also a normal distribution around that value that characterizes the uncertainty. The commonly used version of EGO employs the uncertainty by selecting as the next simulation the point that maximizes the expected improvement (EI) over the present best solution (an idea introduced earlier by Mockus et al 1978). The exploration part of the algorithm is enhanced by the fact that EI is actually a conditioned expected improvement, conditioned on improvement actually taking place.…”

Section: Surrogate-based Algorithmsmentioning

confidence: 99%

Parallel surrogate-assisted global optimization with expensive functions – a survey

Haftka

Villanueva

Chaudhuri

2016

Struct Multidisc Optim

209

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Surrogate assisted global optimization is gaining popularity. Similarly, modern advances in computing power increasingly rely on parallelization rather than faster processors. This paper examines some of the methods used to take advantage of parallelization in surrogate based global optimization. A key issue focused on in this review is how different algorithms balance exploration and exploitation. Most of the papers surveyed are adaptive samplers that employ Gaussian Process or Kriging surrogates. These allow sophisticated approaches for balancing exploration and exploitation and even allow to develop algorithms with calculable rate of convergence as function of the number of parallel processors. In addition to optimization based on adaptive sampling, surrogate assisted parallel evolutionary algorithms are also surveyed. Beyond a review of the present state of the art, the paper also argues that methods that provide easy parallelization, like multiple parallel runs, or methods that rely on population of designs for diversity deserve more attention.

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Section: Surrogate-based Algorithmsmentioning

confidence: 99%

Parallel surrogate-assisted global optimization with expensive functions – a survey

Haftka

Villanueva

Chaudhuri

2016

Struct Multidisc Optim

209

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“…Additional sample points are then selected by optimizing this criterion. The Expected Improvement (EI) infill criterion [18,23,5] effectively balances between enhancing the global accuracy of the surrogate model (exploration) and improving its accuracy near the current optimum (exploitation). Surrogate-based optimization with the expected improvement as infill criterion is also known as the Efficient Global Optimization (EGO) algorithm [18].…”

Section: Surrogate-based Optimizationmentioning

confidence: 99%

Inverse modelling of an aneurysm’s stiffness using surrogate-based optimization and fluid-structure interaction simulations

Degroote

Couckuyt

Vierendeels

et al. 2012

Struct Multidisc Optim

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Characterization of the mechanical properties of arterial tissues is highly relevant. In this work, we apply an inverse modelling approach to a model accounting for an aneurysm and the distal part of the circulation which can be modified using two independent stiffness parameters. For given values of these parameters, the position of the arterial wall as a function of time is calculated using a forward simulation which takes the fluid-structure interaction (FSI) into account. Using this forward simulation, the correct values of the stiffness parameters are obtained by minimizing a cost function, which is defined as the difference between the forward simulation and a measurement. The minimization is performed by means of surrogate-based optimization using a Kriging model combined with the expected improvement infill criterion. The results show that the stiffness parameters converge to the correct values, both for a zero-dimensional and for a three-dimensional model of the aneurysm.

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“…First, there are the expected improvement (EI; Mockus 1972) and maximum probability of improvement (MPI; Kushner 1964) policies, both of which were discussed in §1. In addition, there is the interval estimation (IE) policy (Kaelbling 1993), which combines exploration with exploitation by measuring the compound for which a particular linear combination of the posterior mean and posterior standard deviation is largest.…”

Section: Other Related Measurement Policiesmentioning

confidence: 99%

“…Then, as in Bayesian ranking and selection, these beliefs are used to decide at which points to evaluate this function, with the ultimate goal of finding the function's global maximum. There are two predominant methods for choosing measurements in BGO: maximal probability of improvement (MPI, also called P * ) (Kushner 1964, Stuckman 1988, Perevozchikov 1991 and expected improvement (EI) (Mockus 1972, Mockus et al 1978, Jones et al 1998). These two methods are most frequently applied when measurements are free from noise, but MPI was extended to the noisy case in Calvin and Zilinskas (2005), and EI was extended to the noisy case in Huang et al (2006).…”

mentioning

confidence: 99%

The Knowledge-Gradient Algorithm for Sequencing Experiments in Drug Discovery

Negoescu

Frazier

Powell

2011

INFORMS Journal on Computing

103

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W e present a new technique for adaptively choosing the sequence of molecular compounds to test in drug discovery. Beginning with a base compound, we consider the problem of searching for a chemical derivative of the molecule that best treats a given disease. The problem of choosing molecules to test to maximize the expected quality of the best compound discovered may be formulated mathematically as a ranking-andselection problem in which each molecule is an alternative. We apply a recently developed algorithm, known as the knowledge-gradient algorithm, that uses correlations in our Bayesian prior distribution between the performance of different alternatives (molecules) to dramatically reduce the number of molecular tests required, but it has heavy computational requirements that limit the number of possible alternatives to a few thousand. We develop computational improvements that allow the knowledge-gradient method to consider much larger sets of alternatives, and we demonstrate the method on a problem with 87,120 alternatives.

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On bayesian methods for seeking the extremum

Cited by 272 publications

References 0 publications

Parallel surrogate-assisted global optimization with expensive functions – a survey

Parallel surrogate-assisted global optimization with expensive functions – a survey

Inverse modelling of an aneurysm’s stiffness using surrogate-based optimization and fluid-structure interaction simulations

The Knowledge-Gradient Algorithm for Sequencing Experiments in Drug Discovery

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