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Evolutionary Optimization of Low-Discrepancy Sequences

François-Michel De Rainville 1 Christian Gagné 1 Olivier Teytaud 2, 3 Denis Laurendeau 4
2 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 : Low-discrepancy sequences provide a way to generate quasi-random numbers of high dimensionality with a very high level of uniformity. The nearly orthogonal Latin hypercube and the generalized Halton sequence are two pop- ular methods when it comes to generate low-discrepancy sequences. In this article, we propose to use evolutionary algorithms in order to nd optimized solutions to the combinatorial problem of con guring generators of these se- quences. Experimental results show that the optimized sequence generators behave at least as well as generators from the literature for the Halton sequence and signi cantly better for the nearly orthogonal Latin hypercube.
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François-Michel De Rainville, Christian Gagné, Olivier Teytaud, Denis Laurendeau. Evolutionary Optimization of Low-Discrepancy Sequences. ACM Transactions on Modeling and Computer Simulation, Association for Computing Machinery, 2012, 22 (2), pp.9:1-9:25. ⟨hal-00758158⟩

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