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Optimization and Engineering

, Volume 20, Issue 4, pp 1067–1084 | Cite as

DeCODe: a community-based algorithm for generating high-quality decompositions of optimization problems

  • Andrew Allman
  • Wentao Tang
  • Prodromos DaoutidisEmail author
Research Article

Abstract

Nonconvex optimization problems, such as those often seen in chemical engineering applications due to integer decisions and inherent system physics, are known to scale poorly with problem size. Decomposition methods, such as Benders or Lagrangean decomposition, offer much promise for improving solution efficiency. However, automatically identifying subproblems for use with these solution methods remains an open problem. Herein, a general algorithmic framework entitled Detection of Communities for Optimization Decomposition (DeCODe) is presented. DeCODe uses community detection, a concept originating from network theory, to generate optimization subproblems which are strongly interacting within individual subproblems but weakly interacting between different ones. The importance of communities in solving problems using decomposition solution methods is showcased via a least squares regression problem. The ability of DeCODe to identify nontrivial decompositions of optimization problems is demonstrated through a large renewable energy and chemical production optimal design problem and two mixed integer nonlinear program test problems.

Keywords

Decomposition Community detection Automated subproblem generation Variable–constraint graph Structure detection 

Notes

Acknowledgements

Financial support from the National Science Foundation and the University of Minnesota Initiative for Renewable Energy and the Environment (IREE) is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Andrew Allman
    • 1
  • Wentao Tang
    • 1
  • Prodromos Daoutidis
    • 1
    Email author
  1. 1.Department of Chemical Engineering and Materials ScienceUniversity of Minnesota, Twin CitiesMinneapolisUSA

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