Heuristic Approaches to Obtain Low-Discrepancy Point Sets via Subset Selection

06/27/2023

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by   Francois Clément, et al.

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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 we prove that the heuristic does not necessarily return an optimal solution, we obtain very promising results for all tested dimensions. For example, for moderate point set sizes 30 ≤ n ≤ 240 in dimension 6, we obtain point sets with L_∞ star discrepancy up to 35 sequence. Our heuristic works in all dimensions, the main limitation being the precision of the discrepancy calculation algorithms. We also provide a comparison with a recent energy functional introduced by Steinerberger [J. Complexity, 2019], showing that our heuristic performs better on all tested instances.