Investigation on parallel algorithms in efficient global optimization based on multiple points infill criterion and domain decomposition

Li, Zheng; Ruan, Shilun; Gu, Junfeng; Wang, Xinyu; Shen, Changyu

doi:10.1007/s00158-016-1441-2

Cited by 31 publications

(14 citation statements)

References 30 publications

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“…The LS-SVM binary classifier is finally extended to a probabilistic classification, relating h in (17) to the probability of the class C + , denoted P(C + |x). A comparison of several probability models for the LS-SVM classification is provided in [36].…”

Section: Classification Methodsmentioning

confidence: 99%

“…To do this, a first optimization problem is solved for the parameters (γ,λ ) (line 3). Then, the system (16) is solved, at line 4, to determine (α n ,b) in (17). Finally, the coefficients A and B in (20) are computed by Newton's method [38].…”

Section: Ego-ls-svm Methods 231 Extended Merit Functionsmentioning

confidence: 99%

“…In all these problems, a statistical criterion accounting for the Expected Improvement (EI) [16], usually referred to as merit function, is used to select a new (or multiple [17]) design point, at which the objective function should be evaluated. This new evaluation is used to improve the accuracy of the surrogate.…”

Section: Introductionmentioning

confidence: 99%

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A classification approach to efficient global optimization in presence of non-computable domains

Sacher

Duvigneau

Maître

et al. 2018

Struct Multidisc Optim

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Gaussian-Process based optimization methods have become very popular in recent years for the global optimization of complex systems with high computational costs. These methods rely on the sequential construction of a statistical surrogate model, using a training set of computed objective function values, which is refined according to a prescribed infilling strategy. However, this sequential optimization procedure can stop prematurely if the objective function cannot be computed at a proposed point. Such a situation can occur when the search space encompasses design points corresponding to an unphysical configuration, an ill-posed problem, or a non-computable problem due to the limitation of numerical solvers. To avoid such a premature stop in the optimization procedure, we propose to use a classification model to learn non-computable areas and to adapt the infilling strategy accordingly. Specifically, the proposed method splits the training set into two subsets composed of computable and non-computable points. A surrogate model for the objective function is built using the training set of computable points, only, whereas a probabilistic classification model is built using the union of the computable and non-computable training sets. The classifier is then incorporated in the surrogate-based optimization procedure to avoid proposing new points in the noncomputable domain while improving the classification uncertainty if needed. The method has the advantage to automatically adapt both the surrogate of the objective function and the classifier during the iterative optimization process. Therefore, non-computable areas do not need to be a priori known. The proposed method is applied to several analytical problems presenting different types of difficulty, and to the optimization of a fully nonlinear fluid-structure interaction system. The latter problem concerns the drag minimization of a flexible hydrofoil with cavitation constraints. The efficiency of the proposed method compared favorably to a reference evolutionary algorithm, except for situations where the feasible domain is a small portion of the design space.

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Section: Classification Methodsmentioning

confidence: 99%

Section: Ego-ls-svm Methods 231 Extended Merit Functionsmentioning

confidence: 99%

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A classification approach to efficient global optimization in presence of non-computable domains

Sacher

Duvigneau

Maître

et al. 2018

Struct Multidisc Optim

View full text Add to dashboard Cite

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“…They compared several approaches, and concluded that a multi-objective treatment of the objective and constraints (also known as the filter method) works best. Zhu et al (2015) extended Kriging Believer to robust design with expensive constraints Li et al (2016) proposed a method of adding multiple points by combining maximization of EI and minimization of mutual information between the points to be added.…”

Section: Ego -Expected Improvementmentioning

confidence: 99%

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

Haftka

Villanueva

Chaudhuri

2016

Struct Multidisc Optim

204

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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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“…The weak point of the multiple additional sampling EI is it requires more experiments or the expensive data than the single additional sampling [17] because it can use less data to predict a function with the surrogate model. The target to increase the efficiency of the multiple additional sampling points by EGO is to increase the accuracy of the surrogate model.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Multi-Additional Sampling for Multi-Fidelity Efficient Global Optimization

et al. 2020

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Powerful computer-aided design tools are presently vital for engineering product development. Efficient global optimization (EGO) is one of the most popular methods for design of a high computational cost problem. The original EGO is proposed for only one additional sample point. In this work, parallel computing is applied to the original EGO process via a multi-additional sampling technique. The weak point of the multi-additional sampling is it has slower convergence rate when compared with the original EGO. This paper applies the multi-fidelity technique to the multi-additional EGO process to see the effect of the number of multi-additional sampling points and the converge rate. A co-kriging method and a hybrid RBF/Kriging surrogate model are selected for the surrogate model in the EGO process to show the advantage of the multi-additional EGO process compared with the single-fidelity Kriging surrogate model. In the experiment, single-additional sampling points and two to four number of multi-additional sampling per iteration are tested with symmetry and asymmetry mathematical test functions. The results show the hybrid RBF/Kriging surrogate model can obtain the similar optimal points when using the multi-additional sampling EGO.

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Investigation on parallel algorithms in efficient global optimization based on multiple points infill criterion and domain decomposition

Cited by 31 publications

References 30 publications

A classification approach to efficient global optimization in presence of non-computable domains

A classification approach to efficient global optimization in presence of non-computable domains

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

The Effect of Multi-Additional Sampling for Multi-Fidelity Efficient Global Optimization

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