A Lagrangian dual method for two-stage robust optimization with binary uncertainties
Abstract
This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.
- Authors:
-
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1969127
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Optimization and Engineering
- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 4; Journal ID: ISSN 1389-4420
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Lagrangian dual; binary uncertainty; robust optimization; two-stage problems
Citation Formats
Subramanyam, Anirudh. A Lagrangian dual method for two-stage robust optimization with binary uncertainties. United States: N. p., 2022.
Web. doi:10.1007/s11081-022-09710-x.
Subramanyam, Anirudh. A Lagrangian dual method for two-stage robust optimization with binary uncertainties. United States. https://doi.org/10.1007/s11081-022-09710-x
Subramanyam, Anirudh. Tue .
"A Lagrangian dual method for two-stage robust optimization with binary uncertainties". United States. https://doi.org/10.1007/s11081-022-09710-x. https://www.osti.gov/servlets/purl/1969127.
@article{osti_1969127,
title = {A Lagrangian dual method for two-stage robust optimization with binary uncertainties},
author = {Subramanyam, Anirudh},
abstractNote = {This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.},
doi = {10.1007/s11081-022-09710-x},
journal = {Optimization and Engineering},
number = 4,
volume = 23,
place = {United States},
year = {Tue Mar 29 00:00:00 EDT 2022},
month = {Tue Mar 29 00:00:00 EDT 2022}
}
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