Mathematical Programming Computation

, Volume 1, Issue 4, pp 249–293 | Cite as

Information-based branching schemes for binary linear mixed integer problems

  • Fatma Kılınç Karzan
  • George L. Nemhauser
  • Martin W. P. Savelsbergh
Full Length Paper

Abstract

Branching variable selection can greatly affect the effectiveness and efficiency of a branch-and-bound algorithm. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We propose an approach which is empowered by exploiting the information contained in a family of fathomed subproblems, collected beforehand from an incomplete branch-and-bound tree. In particular, we use this information to define new branching rules that reduce the risk of incurring inappropriate branchings. We provide computational results that demonstrate the effectiveness of the new branching rules on various benchmark instances.

Keywords

Branch-and-bound Variable selection Computational algorithms 

Mathematics Subject Classification (2000)

90C11 Mixed integer programming 90B40 Search theory 90-08 Computational methods 90-04 Explicit machine computation and programs (not the theory of computation or programming) 

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Copyright information

© Springer and Mathematical Programming Society 2009

Authors and Affiliations

  • Fatma Kılınç Karzan
    • 1
  • George L. Nemhauser
    • 1
  • Martin W. P. Savelsbergh
    • 1
  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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