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Optimizing Low-Discrepancy Sequences with an Evolutionary Algorithm

François-Michel De Rainville 1 Christian Gagné 1 Olivier Teytaud 2, 3, 4 Denis Laurendeau 1
2 TANC - Algorithmic number theory for cryptology
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
4 TAO - Machine Learning and Optimisation
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique
Abstract : Many elds rely on some stochastic sampling of a given com- plex space. Low-discrepancy sequences are methods aim- ing at producing samples with better space-lling properties than uniformly distributed random numbers, hence allow- ing a more ecient sampling of that space. State-of-the-art methods like nearly orthogonal Latin hypercubes and scram- bled Halton sequences are congured by permutations of in- ternal parameters, where permutations are commonly done randomly. This paper proposes the use of evolutionary al- gorithms to evolve these permutations, in order to optimize a discrepancy measure. Results show that an evolution- ary method is able to generate low-discrepancy sequences of signicantly better space-lling properties compared to sequences congured with purely random permutations.
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Submitted on : Thursday, May 21, 2009 - 10:15:49 PM
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François-Michel De Rainville, Christian Gagné, Olivier Teytaud, Denis Laurendeau. Optimizing Low-Discrepancy Sequences with an Evolutionary Algorithm. Genetic and Evolutionary Computation Conference, 2009, Montréal, Canada. 8 p. ⟨inria-00386475⟩

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