Differential evolution for the optimization of low-discrepancy generalized Halton sequences

Abstract

Halton sequences are d-dimensional quasirandom sequences that fill the d-dimensional hyperspace in a uniform way. They can be used in a variety of applications such as multidimensional integration, uniform sampling, and, e.g., quasi-Monte Carlo simulations. Generalized Halton sequences improve the space-filling properties of original Halton sequences in higher dimensions by digit scrambling. In this work, an evolutionary optimization algorithm, the differential evolution, is used to optimize scrambling permutations of a cl-dimensional generalized Halton sequence so that the discrepancy of the generated point set is minimized.