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Tsinghua Science and Technology 2021, 26(4): 417-425 https://doi.org/10.26599/TST.2020.9010006
Open Access | Issue | Published: 04 January 2021

A Multilevel Splitting Algorithm for Quick Sampling

Show Author's Information Liping Wang( ),  Wenhui Fan
Department of Automation, Tsinghua University, Beijing 100084, China.
Keywords:
rare event simulation, splitting method, elite set, adaptive differential evolution, local searching
Cite this article:
Wang L, Fan W. A Multilevel Splitting Algorithm for Quick Sampling. Tsinghua Science and Technology, 2021, 26(4): 417-425. https://doi.org/10.26599/TST.2020.9010006
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Abstract Full text About this article

To reduce intermediate levels of splitting process and enhance sampling accuracy, a multilevel splitting algorithm for quick sampling is proposed in this paper. Firstly, the selected area of the elite set is expanded to maintain the diversity of the samples. Secondly, the combined use of an adaptive difference evolution algorithm and a local searching algorithm is proposed for the splitting procedure. Finally, a suite of benchmark functions are used for performance testing. The results indicate that the convergence rate and stability of this algorithm are superior to those of the classical importance splitting algorithm and an adaptive multilevel splitting algorithm.


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About this article

A Multilevel Splitting Algorithm for Quick Sampling

Show Author's information Liping Wang( ), Wenhui Fan
Department of Automation, Tsinghua University, Beijing 100084, China.

Abstract

To reduce intermediate levels of splitting process and enhance sampling accuracy, a multilevel splitting algorithm for quick sampling is proposed in this paper. Firstly, the selected area of the elite set is expanded to maintain the diversity of the samples. Secondly, the combined use of an adaptive difference evolution algorithm and a local searching algorithm is proposed for the splitting procedure. Finally, a suite of benchmark functions are used for performance testing. The results indicate that the convergence rate and stability of this algorithm are superior to those of the classical importance splitting algorithm and an adaptive multilevel splitting algorithm.

Keywords: rare event simulation, splitting method, elite set, adaptive differential evolution, local searching

References(10)

[1]
H. Kahn and T. E. Harris, Estimation of particle transmission by random sampling, National Bureau of Standards Applied Mathematics Series, vol. 12, pp. 27-30, 1951.
Google Scholar
[2]
Z. I. Botev, An algorithm for rare-event probability estimation using the product rule of probability theory, https://www.researchgate.net/publication/43492609, 2008.
[3]
W. S. Wadman, M. S. Squillante, and S. Ghosh, Accelerating splitting algorithms for power grid reliability estimation, in Proc. 2016 Winter Simulation Conf., Washington, DC, USA, 2016, pp. 1757-1768.
[4]
H. Louvin, E. Dumonteil, T. Lelièvre, M. Rousset, and C. M. Diop, Adaptive multilevel splitting for Monte Carlo particle transport, EPJ Web of Conferences, vol. 153, p. 06006, 2017.
Google Scholar
[5]
L. P. Wang and W. H. Fan, A multi-level splitting algorithm based on differential evolution, Int. J. Model. Simul. Sci. Comput., vol. 9, no. 2, p. 1850021, 2018.
Google Scholar
[6]
J. Morio, R. Pastel, and F. Le Gland, An overview of importance splitting for rare event simulation, Eur. J. Phys., vol. 31, no. 5, pp. 1295-1303, 2010.
Google Scholar
[7]
C. E. Bréhier and T. Lelièvre, On a new class of score functions to estimate tail probabilities of some stochastic processes with adaptive multilevel splitting, Chaos, vol. 29, no. 3, p. 033126, 2019.
Google Scholar
[8]
D. Aristoff, T. Lelièvre, C. G. Mayne, and I. Teo, Adaptive multilevel splitting in molecular dynamics simulations, ESAIM: Proceedings and Surveys, vol. 48, pp. 215-225, 2015.
Google Scholar
[9]
X. S. Suo, X. Q. Yu, and H. S. Li, Subset simulation for multi-objective optimization, Appl. Math. Model., vol. 44, pp. 425-445, 2017.
Google Scholar
[10]
P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger, and S. Tiwari, Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization. Singapore: Nanyang Technological University, 2005.
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Publication history

Received: 29 September 2019
Revised: 14 January 2020
Accepted: 09 February 2020
Published: 04 January 2021
Issue date: August 2021

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© The author(s) 2021

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The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).

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