Optimization of computer simulation models with rare events

Rubinstein, Reuven Y.

doi:10.1016/s0377-2217(96)00385-2

Cited by 579 publications

(340 citation statements)

References 23 publications

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“…We refer the reader to the A79, page 2 of 8 papers of Rubinstein (1997), Rubinstein (1999), and Kroese & Rubinstein (2006) for their very complete discussion of the technique and the series of papers of our group (Monteiro et al 2010;Monteiro & Dias 2011;Dias et al 2012;and Oliveira et al 2013) for an application of the method to the determine fundamental parameters of open clusters. The main goal of the CE continuous multi-extremal optimization method is to find a set of parameters for which the model provides the best description of the data as per maximum likelihood definition.…”

Section: The Cross-entropy Algorithm For the Parameters Estimationmentioning

confidence: 99%

Proper motions of the optically visible open clusters based on the UCAC4 catalog

Dias

Monteiro

Caetano

et al. 2014

A&A

179

207

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We present a catalog of mean proper motions and membership probabilities of individual stars for optically visible open clusters, which have been determined using data from the UCAC4 catalog in a homogeneous way. The mean proper motion of the cluster and the membership probabilities of the stars in the region of each cluster were determined by applying the statistical method in a modified fashion. In this study, we applied a global optimization procedure to fit the observed distribution of proper motions with two overlapping normal bivariate frequency functions, which also take the individual proper motion errors into account. For 724 clusters, this is the first determination of proper motion, and for the whole sample, we present results with a much larger number of identified astrometric member stars. Furthermore, it was possible to estimate the mean radial velocity of 364 clusters (102 unpublished so far) with the stellar membership using published radial velocity catalogs. These results provide an increase of 30% and 19% in the sample of open clusters with a determined mean absolute proper motion and mean radial velocity, respectively.

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Section: The Cross-entropy Algorithm For the Parameters Estimationmentioning

confidence: 99%

Proper motions of the optically visible open clusters based on the UCAC4 catalog

Dias

Monteiro

Caetano

et al. 2014

A&A

179

207

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“…The approach was introduced by R.Y. Rubinstein in [41,42], extending his earlier work on variance minimization methods for rare-event probability estimation [40].…”

Section: Introductionmentioning

confidence: 99%

“…The approach was introduced by R.Y. Rubinstein in [41,42], extending his earlier work on variance minimization methods for rare-event probability estimation [40].The CE method can be applied to two types of problem:, where X is a random variable or vector taking values in some set X and H is function on X . An important special case is the estimation of a probability = P(S(X) γ), where S is another function on X .…”

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confidence: 99%

A Tutorial on the Cross-Entropy Method

et al. 2005

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Abstract:The cross-entropy method is a recent versatile Monte Carlo technique. This article provides a brief introduction to the cross-entropy method and discusses how it can be used for rare-event probability estimation and for solving combinatorial, continuous, constrained and noisy optimization problems. A comprehensive list of references on cross-entropy methods and applications is included.Keywords: cross-entropy, Kullback-Leibler divergence, rare events, importance sampling, stochastic search.The cross-entropy (CE) method is a recent generic Monte Carlo technique for solving complicated simulation and optimization problems. The approach was introduced by R.Y. Rubinstein in [41,42], extending his earlier work on variance minimization methods for rare-event probability estimation [40].The CE method can be applied to two types of problem:, where X is a random variable or vector taking values in some set X and H is function on X . An important special case is the estimation of a probability = P(S(X) γ), where S is another function on X .2. Optimization: Optimize (that is, maximize or minimize) S(x) over all x ∈ X , where S is some objective function on X . S can be either a known or a noisy function. In the latter case the objective function needs to be estimated, e.g., via simulation.In the estimation setting, the CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback-Leibler divergence as a measure of closeness between two sampling distributions, as is explained further in Section 1. In the optimization setting, the optimization problem is first translated into a rare-event estimation problem, and then the CE method for estimation is used as an adaptive algorithm to locate the optimum, as is explained further in Section 2.An easy tutorial on the CE method is given in [15]. A more comprehensive treatment can be found in [45]; see also [46, Chapter 8]. The CE method homepage can be found at www.cemethod.org .The CE method has been successfully applied to a diverse range of estimation and optimization problems, including buffer allocation [1], queueing models of telecommunication systems [14,16], optimal control of HIV/AIDS spread [48,49], signal detection [30], combinatorial auctions [9], DNA sequence alignment [24,38], scheduling and vehicle routing [3,8,11,20,23,53], neural and reinforcement learning [31,32,34,52,54], project management [12], rare-event simulation with light-and heavy-tail distributions [2,10,21,28], clustering analysis [4,5,29]. Applications to classical combinatorial optimization problems including the max-cut, traveling salesman, and Hamiltonian cycle 1

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“…The ce methods generally aim to estimate rare event probabilities and the eda methods derive from genetic algorithms, and aim to solve optimization problems [2,13,19]. Important choices in the implementation of these methods include methods of initialisation, choice of distributions, selection method and parameters, and constraint handling.…”

Section: Introductionmentioning

confidence: 99%

TAM-EDA: Multivariate t Distribution, Archive and Mutation Based Estimation of Distribution Algorithm

Gao¹,

Wood

2014

ANZIAMJ

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We present a novel estimation of a distribution algorithm (eda), tam-eda, which uses a multivariate t distribution model, an archive population and a mutation operation to escape local minima, avoid premature convergence and utilize a record of the best solutions. Earlier edas used multivariate normal distributions to model low-cost regions of the search space. The multivariate t distribution has heavier tails and so is more likely to maintain diversity, while still allowing convergence to occur. The current population of potential solutions has limited ability to represent all the best regions of the search space explored so far. The archive allows storage of a larger population of promising solutions, which are then used in model building. However, the eda Contents C721model and archive may still become stuck at suboptimal solutions, so to combat this we introduce a decomposition mutation operation which retains most of the attributes of a current solution but attempts large changes in others. A comparison with generic eda, genetic algorithms and the Nelder-Mead method shows that tam-eda is an effective optimization algorithm for a range of test problems.

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Optimization of computer simulation models with rare events

Cited by 579 publications

References 23 publications

Proper motions of the optically visible open clusters based on the UCAC4 catalog

Proper motions of the optically visible open clusters based on the UCAC4 catalog

A Tutorial on the Cross-Entropy Method

TAM-EDA: Multivariate t Distribution, Archive and Mutation Based Estimation of Distribution Algorithm

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