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Journal Articles Journal of Complexity Year : 2024

Heuristic approaches to obtain low-discrepancy point sets via subset selection

Abstract

Building upon the exact methods presented in our earlier work [J. Complexity, 2022], we introduce a heuristic approach for the star discrepancy subset selection problem. The heuristic gradually improves the current-best subset by replacing one of its elements at a time. While the heuristic does not necessarily return an optimal solution, we obtain very promising results for all tested dimensions. For example, for moderate sizes $30 \leq n \leq 240$, we obtain point sets in dimension 6 with $L_{\infty}$ star discrepancy up to 35\% better than that of the first $n$ points of the Sobol' sequence. Our heuristic works in all dimensions, the main limitation being the precision of the discrepancy calculation algorithms. We provide a comparison with a recent energy functional introduced by Steinerberger [J. Complexity, 2019], showing that our heuristic performs better on all tested instances. Finally, our results and complementary experiments also give further empirical information on inverse star discrepancy conjectures.
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Dates and versions

hal-04580559 , version 1 (20-05-2024)

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François Clément, Carola Doerr, Luís Paquete. Heuristic approaches to obtain low-discrepancy point sets via subset selection. Journal of Complexity, 2024, 83, pp.101852. ⟨10.1016/j.jco.2024.101852⟩. ⟨hal-04580559⟩
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