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

James Ostrowski, Miguel F. Anjos, Anthony Vannelli

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)99-129
JournalMathematical programming
Volume150
Issue number1
Early online date6 Sept 2014
DOIs
Publication statusPublished - 1 Apr 2015

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