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

Barnett, Jason; Watson, Jean -Paul; Woodruff, David L.

doi:10.1016/j.orl.2016.11.006

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

Journal Article · Sun Nov 27 00:00:00 EST 2016 · Operations Research Letters

DOI:https://doi.org/10.1016/j.orl.2016.11.006· OSTI ID:1340699

Barnett, Jason ^[1]; Watson, Jean -Paul ^[2]; ^[1]

Univ. of California, Davis, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

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 Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

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, Journal Name: Operations Research Letters Journal Issue: 1 Vol. 45; ISSN 0167-6377

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (14)

Progressive hedging-based metaheuristics for stochastic network design Crainic, Teodor Gabriel; Fu, Xiaorui; Gendreau, Michel Networks, Vol. 58, Issue 2 https://doi.org/10.1002/net.20456	journal	August 2011
Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra Ruszczy?ski, Andrzej Mathematical Programming, Vol. 93, Issue 2 https://doi.org/10.1007/s10107-002-0337-7	journal	December 2002
Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M. Mathematical Programming, Vol. 157, Issue 1 https://doi.org/10.1007/s10107-016-1000-z	journal	April 2016
Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems Watson, Jean-Paul; Woodruff, David L. Computational Management Science, Vol. 8, Issue 4 https://doi.org/10.1007/s10287-010-0125-4	journal	July 2010
Using scenario trees and progressive hedging for stochastic inventory routing problems Hvattum, Lars Magnus; Løkketangen, Arne Journal of Heuristics, Vol. 15, Issue 6 https://doi.org/10.1007/s10732-008-9076-0	journal	March 2008
Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method Fan, Yueyue; Liu, Changzheng Networks and Spatial Economics, Vol. 10, Issue 2 https://doi.org/10.1007/s11067-008-9062-y	journal	March 2008
BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems Escudero, Laureano F.; Garín, Araceli; Merino, María TOP, Vol. 17, Issue 1 https://doi.org/10.1007/s11750-009-0083-6	journal	April 2009
Pyomo: modeling and solving mathematical programs in Python Hart, William E.; Watson, Jean-Paul; Woodruff, David L. Mathematical Programming Computation, Vol. 3, Issue 3 https://doi.org/10.1007/s12532-011-0026-8	journal	August 2011
PySP: modeling and solving stochastic programs in Python Watson, Jean-Paul; Woodruff, David L.; Hart, William E. Mathematical Programming Computation, Vol. 4, Issue 2 https://doi.org/10.1007/s12532-012-0036-1	journal	March 2012
Dual decomposition in stochastic integer programming Carøe, Claus C.; Schultz, Rüdiger Operations Research Letters, Vol. 24, Issue 1-2 https://doi.org/10.1016/S0167-6377(98)00050-9	journal	February 1999
Scenario grouping in a progressive hedging-based meta-heuristic for stochastic network design Crainic, Teodor Gabriel; Hewitt, Mike; Rei, Walter Computers & Operations Research, Vol. 43 https://doi.org/10.1016/j.cor.2013.08.020	journal	March 2014
Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs Watson, Jean-Paul; Wets, Roger J-B; Woodruff, David L. INFORMS Journal on Computing, Vol. 22, Issue 4 https://doi.org/10.1287/ijoc.1090.0372	journal	November 2010
Scenarios and Policy Aggregation in Optimization Under Uncertainty Rockafellar, R. T.; Wets, Roger J. -B. Mathematics of Operations Research, Vol. 16, Issue 1 https://doi.org/10.1287/moor.16.1.119	journal	February 1991
Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic Hvattum, Lars M.; Løkketangen, Arne; Laporte, Gilbert Transportation Science, Vol. 40, Issue 4 https://doi.org/10.1287/trsc.1060.0166	journal	November 2006

Cited By (1)

A Progressive Hedging based branch-and-bound algorithm for mixed-integer stochastic programs Atakan, Semih; Sen, Suvrajeet Computational Management Science, Vol. 15, Issue 3-4 https://doi.org/10.1007/s10287-018-0311-3	journal	June 2018

Similar Records

Integration of progressive hedging and dual decomposition in stochastic integer programs

Journal Article · Mon Apr 06 20:00:00 EDT 2015 · Operations Research Letters · OSTI ID:1235345

PIPS-SBB: A Parallel Distributed-Memory Branch-and-Bound Algorithm for Stochastic Mixed-Integer Programs

Journal Article · Sat Apr 30 20:00:00 EDT 2016 · Parallel and Distributed Processing Symposium Workshops, 2016 IEEE International · OSTI ID:1321445

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Journal Article · Fri Apr 01 20:00:00 EDT 2016 · Mathematical Programming · OSTI ID:1310314

Related Subjects

97 MATHEMATICS AND COMPUTING
branch and bound
progressive hedging
stochastic programming

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

Citation Formats

References (14)

Cited By (1)

Similar Records

Related Subjects