Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms
Genetic and Evolutionary Computation Conference (GECCO), pp. 1330–1338
Abstract
The L∞ star discrepancy is a measure for the regularity of a finite set of points taken from [0, 1)d. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in numerical integration and several other applications. Unfortunately, computing the L∞ star discrepancy of a given point set is known to be a hard problem, with the best exact algorithms falling short for even moderate dimensions around 8. However, despite the difficulty of finding the global maximum that defines the L∞ star discrepancy of the set, local evaluations at selected points are inexpensive. This makes the problem tractable by black-box optimization approaches.
Authors 6
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Centre National de la Recherche Scientifique · Sorbonne Université · LIP6
Affiliation as printed
Sorbonne Université, CNRS, LIP6, Paris, France
RO - Recherche Opérationnelle (France)
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Diederick Vermetten Aachen
Affiliation as printed
LIACS, Leiden University, Leiden, Netherlands
LIACS - Leiden Institute of Advanced Computer Science [Leiden] ( Niels Bohrweg 1 2333 CA Leiden - Netherlands)
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Jacob de Nobel Aachen
Affiliation as printed
LIACS, Leiden University, Leiden, Netherlands
LIACS - Leiden Institute of Advanced Computer Science [Leiden] ( Niels Bohrweg 1 2333 CA Leiden - Netherlands)
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Affiliation as printed
University of Coimbra, CISUC, DEI, Coimbra, Portugal
UC - University of Coimbra [Portugal] (Portugal)
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Affiliation as printed
University of Coimbra, CISUC, DEI, Coimbra, Portugal
Universidade de Coimbra [Coimbra] (Palácio dos Grilos Rua da Ilha 3000-214 Coimbra - Portugal)
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Centre National de la Recherche Scientifique · Sorbonne Université · LIP6
Affiliation as printed
Sorbonne Université, CNRS, LIP6, Paris, France
RO - Recherche Opérationnelle (France)
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