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Title: BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs

Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. Additionally, to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.
Authors:
 [1] ;  [2] ; ORCiD logo [1]
  1. Univ. of California, Davis, CA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Report Number(s):
SAND-2016-12289J
Journal ID: ISSN 0167-6377; PII: S0167637716302152
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Operations Research Letters
Additional Journal Information:
Journal Volume: 45; Journal Issue: 1; Journal ID: ISSN 0167-6377
Publisher:
Elsevier
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; stochastic programming; progressive hedging; branch and bound
OSTI Identifier:
1340699
Alternate Identifier(s):
OSTI ID: 1411451

Barnett, Jason, Watson, Jean -Paul, and Woodruff, David L. BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs. United States: N. p., Web. doi:10.1016/j.orl.2016.11.006.
Barnett, Jason, Watson, Jean -Paul, & Woodruff, David L. BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs. United States. doi:10.1016/j.orl.2016.11.006.
Barnett, Jason, Watson, Jean -Paul, and Woodruff, David L. 2016. "BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs". United States. doi:10.1016/j.orl.2016.11.006. https://www.osti.gov/servlets/purl/1340699.
@article{osti_1340699,
title = {BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs},
author = {Barnett, Jason and Watson, Jean -Paul and Woodruff, David L.},
abstractNote = {Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. Additionally, to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.},
doi = {10.1016/j.orl.2016.11.006},
journal = {Operations Research Letters},
number = 1,
volume = 45,
place = {United States},
year = {2016},
month = {11}
}