Article

Quasi-Monte Carlo strategies for stochastic optimization

Authors:

Tito Homem-de-MelloAuthors Info & Claims

WSC '06: Proceedings of the 38th conference on Winter simulation

Pages 774 - 782

Published: 03 December 2006 Publication History

Abstract

In this paper we discuss the issue of solving stochastic optimization problems using sampling methods. Numerical results have shown that using variance reduction techniques from statistics can result in significant improvements over Monte Carlo sampling in terms of the number of samples needed for convergence of the optimal objective value and optimal solution to a stochastic optimization problem. Among these techniques are stratified sampling and Quasi-Monte Carlo sampling. However, for problems in high dimension, it may be computationally inefficient to calculate Quasi-Monte Carlo point sets in the full dimension. Rather, we wish to identify which dimensions are most important to the convergence and implement a Quasi-Monte Carlo sampling scheme with padding, where the important dimensions are sampled via Quasi-Monte Carlo sampling and the remaining dimensions with Monte Carlo sampling. We then incorporate this sampling scheme into an external sampling algorithm (ES-QMCP) to solve stochastic optimization problems.

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Cited By

Heitsch HLeövey HRömisch W(2016)Are Quasi-Monte Carlo algorithms efficient for two-stage stochastic programs?Computational Optimization and Applications10.1007/s10589-016-9843-z65:3(567-603)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10589-016-9843-z
Stockbridge RBayraksan G(2016)Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programmingComputational Optimization and Applications10.1007/s10589-015-9814-964:2(407-431)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1007/s10589-015-9814-9
Stockbridge RBayraksan G(2013)A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programmingMathematical Programming: Series A and B10.1007/s10107-012-0563-6142:1-2(107-131)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1007/s10107-012-0563-6

Quasi-Monte Carlo strategies for stochastic optimization
1. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms

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Information

Published In

cover image ACM Conferences

WSC '06: Proceedings of the 38th conference on Winter simulation

December 2006

2429 pages

ISBN:1424405017

Editors:
L. Felipe Perrone
Bucknell University
,
Barry G. Lawson
University of Richmond
,
Jason Liu
Colorado School of Mines
,
Frederick P. Wieland
Sensis Corporation
,
General Chair:
David Nicol
University of Illinois, Urbana-Champaign
,
Program Chair:
Richard Fujimoto
College of Computing, Georgia Tech

Sponsors

IIE: Institute of Industrial Engineers
ASA: American Statistical Association
IEICE ESS: Institute of Electronics, Information and Communication Engineers, Engineering Sciences Society
IEEE-CS\DATC: The IEEE Computer Society
SIGSIM: ACM Special Interest Group on Simulation and Modeling
NIST: National Institute of Standards and Technology
(SCS): The Society for Modeling and Simulation International
INFORMS-CS: Institute for Operations Research and the Management Sciences-College on Simulation

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Winter Simulation Conference

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Published: 03 December 2006

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IIE
ASA
IEICE ESS
IEEE-CS\DATC
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NIST
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INFORMS-CS

WSC06: Winter Simulation Conference 2006

December 3 - 6, 2006

California, Monterey

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WSC '06 Paper Acceptance Rate 177 of 252 submissions, 70%;

Overall Acceptance Rate 3,413 of 5,075 submissions, 67%

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Cited By

Heitsch HLeövey HRömisch W(2016)Are Quasi-Monte Carlo algorithms efficient for two-stage stochastic programs?Computational Optimization and Applications10.1007/s10589-016-9843-z65:3(567-603)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10589-016-9843-z
Stockbridge RBayraksan G(2016)Variance reduction in Monte Carlo sampling-based optimality gap estimators for two-stage stochastic linear programmingComputational Optimization and Applications10.1007/s10589-015-9814-964:2(407-431)Online publication date: 1-Jun-2016
https://dl.acm.org/doi/10.1007/s10589-015-9814-9
Stockbridge RBayraksan G(2013)A probability metrics approach for reducing the bias of optimality gap estimators in two-stage stochastic linear programmingMathematical Programming: Series A and B10.1007/s10107-012-0563-6142:1-2(107-131)Online publication date: 1-Dec-2013
https://dl.acm.org/doi/10.1007/s10107-012-0563-6

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