Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs
Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs
We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very relaxed approximation with assumptions that do not generally hold. Computational results demonstrate on average over a 43% improvement in the bounds. As a byproduct, we provide an exact reformulation of the floor function in optimization models.
Bonferroni inequalities, Chance-constrained optimization, Floor function, Linearization, Stochastic optimization, Union bounds
327-336
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
March 2021
Singh, Bismark
9d3fc6cb-f55e-4562-9d5f-42f9a3ddd9a1
Singh, Bismark
(2021)
Tighter reformulations using classical Dawson and Sankoff bounds for approximating two-stage chance-constrained programs.
Optimization Letters, 15 (2), .
(doi:10.1007/s11590-020-01592-1).
Abstract
We extend and improve recent results given by Singh and Watson on using classical bounds on the union of sets in a chance-constrained optimization problem. Specifically, we revisit the so-called Dawson and Sankoff bound that provided one of the best approximations of a chance constraint in the previous analysis. Next, we show that our work is a generalization of the previous work, and in fact the inequality employed previously is a very relaxed approximation with assumptions that do not generally hold. Computational results demonstrate on average over a 43% improvement in the bounds. As a byproduct, we provide an exact reformulation of the floor function in optimization models.
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Accepted/In Press date: 13 May 2020
e-pub ahead of print date: 25 May 2020
Published date: March 2021
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Publisher Copyright:
© 2020, The Author(s).
Keywords:
Bonferroni inequalities, Chance-constrained optimization, Floor function, Linearization, Stochastic optimization, Union bounds
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Local EPrints ID: 472278
URI: http://eprints.soton.ac.uk/id/eprint/472278
ISSN: 1862-4472
PURE UUID: be983317-a1a4-4cb0-b20a-d82ad75ef921
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Date deposited: 30 Nov 2022 17:45
Last modified: 17 Mar 2024 04:16
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Author:
Bismark Singh
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