Algorithm 659

Bratley, Paul; Fox, Bennett L.

doi:10.1145/42288.214372

Cited by 713 publications

(251 citation statements)

References 9 publications

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“…There exist other kinds of schemes however, that only consider uniformity, and therefore, are usually deterministic. From among those strategies, we applied the methods Sobol Set (ss) [1] and Good Lattice Points (glp) [16], which are able to provide a set of points well distributed in the decision space.…”

Section: Initialisation Strategies For Differential Evolutionmentioning

confidence: 99%

“…Consequently, it was also considered for the lsgo competition organised during cec'15. 1 The set is composed of 15 functions ( f 1 -f 15 ) with different features: fully-separable functions (category 1: f 1 -f 3 ), partially additively separable functions (category 2: f 4 -f 11 ), overlapping functions (category 3: f 12 -f 14 ), and a non-separable function (category 4: f 15 ). Following the indications given for the different editions of the lsgo competition, in the current work, the number of decision variables D was fixed to 1000 for all the aforementioned functions, with the exception of problems f 13 and f 14 , where D was fixed to 905 decision variables due to overlapping subcomponents.…”

Section: Problem Setmentioning

confidence: 99%

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On the comparison of initialisation strategies in differential evolution for large scale optimisation

et al. 2017

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Differential Evolution (de) has shown to be a promising global optimisation solver for continuous problems, even for those with a large dimensionality. Different previous works have studied the effects that a population initialisation strategy has on the performance of de when solving large scale continuous problems, and several contradictions have appeared with respect to the benefits that a particular initialisation scheme might provide. Some works have claimed that by applying a particular approach to a given problem, the performance of de is going to be better than using others. In other cases however, researchers have stated that the overall performance of de is not going to be affected by the use of a particular initialisation method. In this work, we study a wide range of well-known initialisation techniques for de. Taking into account the best and worst results, statistically significant differences among considered initialisation strategies appeared. Thus, with the aim of increasing the probability of appearance of high-quality results and/or reducing the probability of appearance of low-quality ones, a suitable initialisation strategy, which depends on the large scale problem being solved, should be selected.

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Section: Initialisation Strategies For Differential Evolutionmentioning

confidence: 99%

Section: Problem Setmentioning

confidence: 99%

On the comparison of initialisation strategies in differential evolution for large scale optimisation

et al. 2017

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“…For instance, if d = 1, the ith point of P n before the shift is (ia mod n)/n. The points of a Sobol' net are usually enumerated by order of their Gray code, because this is a bit faster than enumerating them in their natural order (see, e.g., Antonov and Saleev, 1979;Bratley and Fox, 1988;L'Ecuyer, 2004b). Enumerating the points of P n by their Gray code is equivalent to applying a permutation to the second and further coordinates of the points of P n , i.e., it performs an additional scrambling for these coordinates.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains

L’Ecuyer

Lécot

Tuffin

2008

Operations Research

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Abstract. We introduce and study a randomized quasi-Monte Carlo method for estimating the state distribution at each step of a Markov chain. The number of steps in the chain can be random and unbounded. The method simulates n copies of the chain in parallel, using a (d + 1)-dimensional highly-uniform point set of cardinality n, randomized independently at each step, where d is the number of uniform random numbers required at each transition of the Markov chain. This technique is effective in particular to obtain a low-variance unbiased estimator of the expected total cost up to some random stopping time, when state-dependent costs are paid at each step. It is generally more effective when the state space has a natural order related to the cost function.We provide numerical illustrations where the variance reduction with respect to standard Monte Carlo is substantial. The variance can be reduced by factors of several thousands in some cases. We prove bounds on the convergence rate of the worst-case error and variance for special situations. In line with what is typically observed in randomized quasi-Monte Carlo contexts, our empirical results indicate much better convergence than what these bounds guarantee.

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“…[15], [5] for an overview of this line of research. We perform comparative tests for OLH and Sobol sequences (which are of the low discrepancy type) generated by the free software which is discribed in [4] and which is available from Netlib (www.netlib.org). These tests are presented in section 4.1 and 4.4.…”

Section: Projection Propertiesmentioning

confidence: 99%

“…For the generation of Sobol sequences, which are based on completely different ideas, we refer to [4] and the references therein. In section 2.6 we collect some remarks on the algorithm we use for the tests.…”

Section: Description Of Algorithmsmentioning

confidence: 99%

A study on algorithms for optimization of Latin hypercubes

Liefvendahl

Stocki

2006

Journal of Statistical Planning and Inference

182

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A crucial component in the statistical simulation of a computationally expensive model is a good design of experiments. In this paper we compare the efficiency of the columnwise-pairwise (CP) and genetic algorithms for the optimization of Latin hypercubes (LH) for the purpose of sampling in statistical investigations. The performed experiments indicate, among other results, that CP methods are most efficient for small and medium size LH while an adopted genetic algorithm performs better for large LH.Two optimality criteria suggested in the literature are evaluated with respect to statistical properties and efficiency. The obtained results lead us to favor a criterion based on the physical analogy of minimization of forces between charged particles suggested in [1] over a 'maximin distance' criterion from [9].

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Algorithm 659

Abstract: We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol' generator.

Cited by 713 publications

References 9 publications

On the comparison of initialisation strategies in differential evolution for large scale optimisation

On the comparison of initialisation strategies in differential evolution for large scale optimisation

A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains

A study on algorithms for optimization of Latin hypercubes

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