Scalable branching on dual decomposition of stochastic mixed-integer programming problems
Abstract
In this work, we present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.
- Authors:
-
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1883196
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Mathematical Programming Computation
- Additional Journal Information:
- Journal Volume: 14; Journal Issue: 1; Journal ID: ISSN 1867-2949
- Publisher:
- Mathematical Optimization Society, Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; branch-and-bound; dual decomposition; parallel computing; stochastic mixed-integer programming
Citation Formats
Kim, Kibaek, and Dandurand, Brian. Scalable branching on dual decomposition of stochastic mixed-integer programming problems. United States: N. p., 2022.
Web. doi:10.1007/s12532-021-00212-y.
Kim, Kibaek, & Dandurand, Brian. Scalable branching on dual decomposition of stochastic mixed-integer programming problems. United States. https://doi.org/10.1007/s12532-021-00212-y
Kim, Kibaek, and Dandurand, Brian. Tue .
"Scalable branching on dual decomposition of stochastic mixed-integer programming problems". United States. https://doi.org/10.1007/s12532-021-00212-y. https://www.osti.gov/servlets/purl/1883196.
@article{osti_1883196,
title = {Scalable branching on dual decomposition of stochastic mixed-integer programming problems},
author = {Kim, Kibaek and Dandurand, Brian},
abstractNote = {In this work, we present a scalable branching method for the dual decomposition of stochastic mixed-integer programming. Our new branching method is based on the branching method proposed by Caroe and Schultz that creates branching disjunctions on first-stage variables only. We propose improvements to the process for creating branching disjunctions, including (1) branching on the optimal solutions of the Dantzig-Wolfe reformulation of the restricted master problem and (2) using a more comprehensive (yet simple) measure for the dispersions associated with subproblem solution infeasibility. We prove that the proposed branching process leads to an algorithm that terminates finitely, and we provide conditions under which globally optimal solutions can be identified after termination. We have implemented our new branching method, as well as the Caroe-Schultz method and a branch-and-price method, in the open-source software package DSP. Using SIPLIB test instances, we present extensive numerical results to demonstrate that the proposed branching method significantly reduces the number of node subproblems and solution times.},
doi = {10.1007/s12532-021-00212-y},
journal = {Mathematical Programming Computation},
number = 1,
volume = 14,
place = {United States},
year = {Tue Jan 04 00:00:00 EST 2022},
month = {Tue Jan 04 00:00:00 EST 2022}
}
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