Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The exponent of discrepancy is at most 1.4778…
Mathematics of Computation
A generalized discrepancy and quadrature error bound
Mathematics of Computation
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Computing Volume Properties Using Low-Discrepancy Sequences
Geometric Modelling
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy
Journal of Computational and Applied Mathematics
Deterministic design for neural network learning: an approach based on discrepancy
IEEE Transactions on Neural Networks
Constructing low star discrepancy point sets with genetic algorithms
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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Many fields rely on some stochastic sampling of a given complex space. Low-discrepancy sequences are methods aiming at producing samples with better space-filling properties than uniformly distributed random numbers, hence allowing a more efficient sampling of that space. State-of-the-art methods like nearly orthogonal Latin hypercubes and scrambled Halton sequences are configured by permutations of internal parameters, where permutations are commonly done randomly. This paper proposes the use of evolutionary algorithms to evolve these permutations, in order to optimize a discrepancy measure. Results show that an evolutionary method is able to generate low-discrepancy sequences of significantly better space-filling properties compared to sequences configured with purely random permutations.