Abstract
Many practical applications such as multidimensional integration and quasi–Monte Carlo simulations rely on a uniform sampling of high–dimensional spaces. Halton sequences are d–dimensional quasirandom sequences that fill the d–dimensional hyperspace uniformly and can be generated with low computational costs. Generalized (scrambled) Halton sequences improve the properties of plain Halton sequences in higher dimensions by digit scrambling. Discrete nature–inspired optimization methods have been used to search for scrambling permutations of d–dimensional generalized Halton sequences that minimized the discrepancy of the generated point sets in the past. In this work, a continuous nature–inspired optimization method, the differential evolution, is used to optimize generalized Halton sequences.
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Acknowledgement
This work was supported from ERDF in project “A Research Platform focused on Industry 4.0 and Robotics in Ostrava”, reg. no. CZ.02.1.01/0.0/0.0/17_049/ 0008425, by the Technology Agency of the Czech Republic in the frame of the project no. TN01000024 “National Competence Center – Cybernetics and Artificial Intelligence”, and by the projects SP2019/135 and SP2019/141 of the Student Grant System, VSB – Technical University of Ostrava.
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Krömer, P., Platoš, J., Snášel, V. (2020). Optimization of Generalized Halton Sequences by Differential Evolution. In: Matsatsinis, N., Marinakis, Y., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 2019. Lecture Notes in Computer Science(), vol 11968. Springer, Cham. https://doi.org/10.1007/978-3-030-38629-0_30
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