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

Journal Article · · Operations Research Letters
 [1];  [2]; ORCiD logo [1]
  1. Univ. of California, Davis, CA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1340699
Alternate ID(s):
OSTI ID: 1411451
Report Number(s):
SAND-2016-12289J; PII: S0167637716302152
Journal Information:
Operations Research Letters, Vol. 45, Issue 1; ISSN 0167-6377
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

References (14)

Dual decomposition in stochastic integer programming journal February 1999
Progressive hedging-based metaheuristics for stochastic network design journal August 2011
Scenario grouping in a progressive hedging-based meta-heuristic for stochastic network design journal March 2014
BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems journal April 2009
Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method journal March 2008
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs journal April 2016
Pyomo: modeling and solving mathematical programs in Python journal August 2011
Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic journal November 2006
Using scenario trees and progressive hedging for stochastic inventory routing problems journal March 2008
Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra journal December 2002
Scenarios and Policy Aggregation in Optimization Under Uncertainty journal February 1991
Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs journal November 2010
Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems journal July 2010
PySP: modeling and solving stochastic programs in Python journal March 2012

Cited By (1)

A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs journal June 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
stochastic programming
progressive hedging
branch and bound