The Cross-Entropy Method for Optimization

Botev, Zdravko I.; Kroese, Dirk P.; Rubinstein, Reuven Y.; L’Ecuyer, Pierre

doi:10.1016/b978-0-444-53859-8.00003-5

Cited by 157 publications

(101 citation statements)

References 38 publications

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“…The CE method has been successfully applied to many complicated integer non-linear programming and continuous multi-extremal optimization (see, for example, [20]). In this section we describe how the method can be used to determine pertinent (meaningful) Laguerre generators.…”

Section: Ce Methods For Inverting La-guerre Tessellationsmentioning

confidence: 99%

Inverting Laguerre Tessellations

Duan

Kroese

Brereton³

et al. 2014

The Computer Journal

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A Laguerre tessellation is a generalization of a Voronoi tessellation where the proximity between points is measured via a power distance rather than the Euclidean distance.Laguerre tessellations have found significant applications in materials science, providing improved modeling of (poly)crystalline microstructures and grain growth. There exist efficient algorithms to construct Laguerre tessellations from given sets of weighted generator points, similar to methods used for Voronoi tessellations. The purpose of this paper is to provide theory and methodology for the inverse construction; that is, to recover the weighted generator points from a given Laguerre tessellation. We show that, unlike the Voronoi case, the inverse problem is in general non-unique: different weighted generator points can create the same tessellation. To recover pertinent generator points we formulate the inversion problem as a multimodal optimization problem and apply the cross-entropy method to solve it.

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Section: Ce Methods For Inverting La-guerre Tessellationsmentioning

confidence: 99%

Inverting Laguerre Tessellations

Duan

Kroese

Brereton³

et al. 2014

The Computer Journal

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“…The corresponding RO implementations are often characterized by noisy objective functions due to the numerical noise associated with sampling-based failure probability estimates. Consequently, the solution to the RO problem often relies on the implementation of a global optimization algorithm (e.g., Genetic Algorithm [44], Crossentropy [7]), while the solution to the RBDO problem can be found through numerically more efficient nonlinear programming algorithms (e.g., [40]). A relatively straightforward solution to RO and RBDO problems is obtained by nesting a reliability algorithm within an optimization algorithm in a socalled 'double-loop' formulation.…”

Section: Short Literature Reviewmentioning

confidence: 99%

“…The CE method is a heuristic approach for estimating rare events and solving optimizations problems [14,7]. The method was initially developed as an adaptive importance sampling method for the estimation of rare-event probabilities by minimizing the cross-entropy or Kullback-Liebler divergence as a measure of distance between two distributions.…”

Section: Line Samplingmentioning

confidence: 99%

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Depina

Papaioannou²,

Straub³

et al. 2016

Struct Multidisc Optim

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An algorithm for risk-based optimization (RO) of engineering systems is proposed, which couples the Cross-entropy (CE) optimization method with the Line Sampling (LS) reliability method. The CE-LS algorithm relies on the CE method to optimize the total cost of a system that is composed of the design and operation cost (e.g., production cost) and the expected failure cost (i.e., failure risk). Guided by the random search of the CE method, the algorithm proceeds iteratively to update a set of random search distributions such that the optimal or near-optimal solution is likely to occur. The LS-based failure probability estimates are required to evaluate the failure risk. Throughout the optimization process, the coupling relies on a local weighted average approximation of the probability of failure to reduce the computational demands associated with RO. As the CE-LS algorithm proceeds to locate a region of design parameters with near-optimal solutions, the local weighted average approximation of the probability of failure is refined. The adaptive refinement procedure is repeatedly applied until convergence criteria with respect to both the optimization and the approximation of the failure probability are satisfied. The performance of the proposed optimization heuristic is examined empiri- cally on several RO problems, including the design of a monopile foundation for offshore wind turbines.

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“…The present paper is based on the stochastic search algorithm known as the cross-entropy method (CEM) whose efficiency has been observed in several works. The proposed algorithm given in Table 1 is derived from the one proposed for continuous optimization in [19] based on sampling with normal distributions.…”

Section: Selection Of the Svr Surrogate Model Parametersmentioning

confidence: 99%

“…, s max , is constructed in the standard space with training points which get closer to the failure domain F u with iteration s. The new training points at each iteration s are generated from the currently constructed SVR surrogate model G s by means of Monte Carlo Markov chains (MCMC). A new SVR surrogate is trained at each iterations s. Optimal values for its hyperparameters are accurately determined by minimization of an estimate of the leaveone-out (LOO) error proposed by Chang and Lin [18] using the cross-entropy (CE) method [19]. The approximation of the failure probability p f is evaluated from the SVR surrogate G smax trained at the final iteration.…”

Section: Introductionmentioning

confidence: 99%

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Bourinet¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Reliability assessment in the context of rare failure events still suffers from its computational cost despite some available methods widely accepted by researchers and engineers. Monte Carlo simulation methods even in their most efficient version such as subset simulation often require a large number of samples for an acceptable accuracy on the failure probability of interest. For low to moderately high dimensional problems and under the assumption of a rather smooth limit-state function, surrogate models a.k.a. metamodels or response surfaces represent interesting alternative solutions. This paper presents an adaptive method based on SVM surrogates used in regression. The SVM formulation hinges on the -insensitive loss function and a Gaussian RBF kernel. The key idea of the proposed method is to iteratively construct SVM surrogates which become more accurate as they get closer to the limit-state surface. Subset simulation is applied to the constructed SVM surrogates for assessing probabilities with respect to intermediate threshold values of the LSF and more importantly for generating new training points. The efficiency of the method is tested on several examples featuring various challenges: a parallel system, a highly curved limit-state surface at a single most probable failure point and a smooth high-dimensional limit-state surface with equal curvatures. The paper puts an emphasis on the key role of an optimal selection of SVM surrogate hyperparameters. This is achieved in the present work by minimizing an estimate of the leave-one-out error using the cross-entropy method.652

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The Cross-Entropy Method for Optimization

Cited by 157 publications

References 38 publications

Inverting Laguerre Tessellations

Inverting Laguerre Tessellations

Coupling the cross-entropy with the line sampling method for risk-based design optimization

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

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