DDR13 - Generalized Halton Point Set - 7 dimensions

Generalized Halton point set in 7 dimensions optimized over the star discrepancy by an evolutionary algorithm as described in Doerr and De Rainville 2013.

Properties

Point sets obtained when minimizing the star discrepancy of point sets with fixed number of points. Italic values are approximated by running 50 times the TA algorithm described in Gnewuch et al. 2012 and available here, with 10 000 iterations each.

Dimensions Number of Points Star Discrepancy
7 30 0.21349
40 0.18683
49 0.16410
50 0.16366
60 0.14486
65 0.13613
70 0.13326
80 0.12017
90 0.11494
100 0.10917
110 0.10256
120 0.09497
130 0.09069
140 0.08822
145 0.08640
150 0.08202
160 0.08327
170 0.08190
180 0.07976
190 0.07541
200 0.07198
210 0.06909
220 0.06776
230 0.06748
240 0.06458
250 0.06380
343 0.05192
2401 0.01518

Downloads

The permutation vectors in the JSON file are values of a dictionary where the key is the number of points (as string). Points sets should be read row major; an entire row is a point and each column is one dimension for a point.

Cite As

C. Doerr, and F.-M. De Rainville. Constructing Low Star Discrepancy Point Sets with Genetic Algorithms, In Proceedings of the Genetic and Evolutionary Computation Conference, 2013.
ArXiv Version

References

M. Gnewuch, M. Wahlström, and C. Winzen. A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting. SIAM Journal on Numerical Analysis, 50:781-807, 2012.
Official Version
MPI Dep. Version


Quasi-random Sequences Repository © 2017
Powered by GetSimple