Mathematical Programming

, Volume 150, Issue 1, pp 99–129 | Cite as

Modified orbital branching for structured symmetry with an application to unit commitment

  • James Ostrowski
  • Miguel F. Anjos
  • Anthony Vannelli
Full Length Paper Series B

Abstract

The past decade has seen advances in general methods for symmetry breaking in mixed-integer linear programming. These methods are advantageous for general problems with general symmetry groups. Some important classes of mixed integer linear programming problems, such as bin packing and graph coloring, contain highly structured symmetry groups. This observation has motivated the development of problem-specific techniques. In this paper we show how to strengthen orbital branching in order to exploit special structures in a problem’s symmetry group. The proposed technique, to which we refer as modified orbital branching, is able to solve problems with structured symmetry groups more efficiently. One class of problems for which this technique is effective is when the solution variables can be expressed as 0/1 matrices where the problem’s symmetry group contains all permutations of the columns. We use the unit commitment problem, an important problem in power systems, to demonstrate the strength of modified orbital branching.

Keywords

Symmetry Integer programming Orbital branching  Orbitopes  Unit commitment 

Mathematics Subject Classification

90C10 90C57 90C90 

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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2014

Authors and Affiliations

  • James Ostrowski
    • 1
  • Miguel F. Anjos
    • 2
  • Anthony Vannelli
    • 3
  1. 1.Department of Industrial and Systems EngineeringUniversity of Tennessee KnoxvilleKnoxvilleUSA
  2. 2.Canada Research Chair in Discrete Nonlinear Optimization in EngineeringGERAD and École Polytechnique de MontréalMontrealCanada
  3. 3.School of EngineeringUniversity of GuelphGuelphCanada

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