Optimizing Low-Discrepancy Sequences with an Evolutionary Algorithm

Abstract : Many elds rely on some stochastic sampling of a given com- plex space. Low-discrepancy sequences are methods aim- ing at producing samples with better space-lling properties than uniformly distributed random numbers, hence allow- ing a more ecient sampling of that space. State-of-the-art methods like nearly orthogonal Latin hypercubes and scram- bled Halton sequences are congured by permutations of in- ternal parameters, where permutations are commonly done randomly. This paper proposes the use of evolutionary al- gorithms to evolve these permutations, in order to optimize a discrepancy measure. Results show that an evolution- ary method is able to generate low-discrepancy sequences of signicantly better space-lling properties compared to sequences congured with purely random permutations.