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

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

Abstract

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:

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

^[1]

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

Publication Date:: Sun Nov 27 00:00:00 EST 2016

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1340699

Alternate Identifier(s):: OSTI ID: 1411451

Report Number(s):: SAND-2016-12289J
Journal ID: ISSN 0167-6377; PII: S0167637716302152

Grant/Contract Number:: AC04-94AL85000

Resource Type:: Accepted Manuscript

Journal Name:: Operations Research Letters

Additional Journal Information:: Journal Volume: 45; Journal Issue: 1; Journal ID: ISSN 0167-6377

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; stochastic programming; progressive hedging; branch and bound

Citation Formats


                    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., 2016. 
Web.  doi:10.1016/j.orl.2016.11.006.

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                    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.  https://doi.org/10.1016/j.orl.2016.11.006

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                    Barnett, Jason, Watson, Jean -Paul, and Woodruff, David L. Sun .  
"BBPH: Using progressive hedging within branch and bound to solve multi-stage stochastic mixed integer programs".  United States.  https://doi.org/10.1016/j.orl.2016.11.006.  https://www.osti.gov/servlets/purl/1340699.

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@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         = {Sun Nov 27 00:00:00 EST 2016},

  month        = {Sun Nov 27 00:00:00 EST 2016}

}

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https://doi.org/10.1016/j.orl.2016.11.006

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Cited by: 11 works

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Works referenced in this record:

Dual decomposition in stochastic integer programming
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Carøe, Claus C.; Schultz, Rüdiger
Operations Research Letters, Vol. 24, Issue 1-2
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Progressive hedging-based metaheuristics for stochastic network design
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Scenario grouping in a progressive hedging-based meta-heuristic for stochastic network design
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Crainic, Teodor Gabriel; Hewitt, Mike; Rei, Walter
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BFC-MSMIP: an exact branch-and-fix coordination approach for solving multistage stochastic mixed 0–1 problems
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Escudero, Laureano F.; Garín, Araceli; Merino, María
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Solving Stochastic Transportation Network Protection Problems Using the Progressive Hedging-based Method
journal, March 2008

Fan, Yueyue; Liu, Changzheng
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Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs
journal, April 2016

Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.
Mathematical Programming, Vol. 157, Issue 1
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Pyomo: modeling and solving mathematical programs in Python
journal, August 2011

Hart, William E.; Watson, Jean-Paul; Woodruff, David L.
Mathematical Programming Computation, Vol. 3, Issue 3
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Solving a Dynamic and Stochastic Vehicle Routing Problem with a Sample Scenario Hedging Heuristic
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Hvattum, Lars M.; Løkketangen, Arne; Laporte, Gilbert
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journal, November 2010

Watson, Jean-Paul; Wets, Roger J-B; Woodruff, David L.
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Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems
journal, July 2010

Watson, Jean-Paul; Woodruff, David L.
Computational Management Science, Vol. 8, Issue 4
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Watson, Jean-Paul; Woodruff, David L.; Hart, William E.
Mathematical Programming Computation, Vol. 4, Issue 2
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Works referencing / citing this record:

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

Atakan, Semih; Sen, Suvrajeet
Computational Management Science, Vol. 15, Issue 3-4
DOI: 10.1007/s10287-018-0311-3

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Similar Records

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

Abstract

Citation Formats

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

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

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

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