Finding Feasible Solutions to Hard Mixed-integer Programming Problems Using Hybrid Heuristics

  • Philipp M. Christophel
  • Leena Suhl
  • Uwe H. Suhl
Part of the Operations Research Proceedings book series (ORP, volume 2005)


In current mixed-integer programming (MIP) solvers heuristics are used to find feasible solutions before the branch-and-bound or branchand-cut algorithm is applied to the problem. Knowing a feasible solution can improve the solutions found or the time to solve the problem very much. This paper discusses hybrid heuristics for this purpose. Hybrid in this context means that these heuristics use the branch-and-bound algorithm to search a smaller subproblem. Several possible hybrid heuristics are presented and computational results are given.


Search Space Feasible Solution Linear Programming Relaxation Relaxation Solution Hybrid Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Balas, Egon; Martin, Clarence H.: Pivot and Complement — A Heuristic for 0–1 Programming. In: Management Science 26(1) (1980), S. 86–96zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Løkketangen, Arne; Glover, Fred: Solving Zero-one Mixed Integer Programming Problems Using Tabu Search. In: European Journal of Operations Research 106(2–3) (1998), S. 624–658zbMATHCrossRefGoogle Scholar
  3. [3]
    Balas, Egon; Ceria, Sebastián; Dawande, Milind; Margot, Francois; Pataki, Gábor: OCTANE: A New Heuristic For Pure 0–1 Programs. In: Operations Research 49(2) (2001), S. 207–225MathSciNetCrossRefGoogle Scholar
  4. [4]
    Fischetti, Matteo; Lodi, Andrea: Local Branching. In: Mathematical Programming 98(1–3) (2003), S. 23–47zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Danna, Emilie; Rothberg, Edward; Le Pape, Claude: Exploring Relaxation Induced Neighborhoods to Improve MIP Solutions. In: Mathematical Programming101(1) (2004), S. 71–90Google Scholar
  6. [6]
    Christopel, Philipp M.: An Improved Heuristic for the MOPS Mixed-integer Programming Solver, University of Paderborn-DS&OR Lab, Diplomarbeit, 2005Google Scholar
  7. [7]
    Yagiura, M.; Ibaraki, T.: Local Search. In: Pardalos, P. M. (Hrsg.); Resende, M. G. C. (Hrsg.): Handbook of Applied Optimization. Oxford University Press, Oxford, 2002Google Scholar
  8. [8]
    Suhl, Uwe H.: MOPS-Mathematical OPtimization System. In: European Journal of Operations Research 72 (1994), S. 312–322zbMATHCrossRefGoogle Scholar
  9. [9]
    Suhl, Uwe H.; Waue, Veronika: Fortschritte bei der Lösung gemischtganzzahliger Optimierungsmodelle. In: Suhl, Leena (Hrsg.); Voss, Stefan (Hrsg.): Quantitative Methoden in ERP und SCM. 2004 (DSOR Beiträge zur Wirtschaftsinformatik, Band 2)Google Scholar
  10. [10]
    Suhl, Uwe H.: Solving Large-scale Mixed-Integer Programs with Fixed Charge Variables. In: Mathematical Programming 32 (1985), S. 165–182zbMATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    Achterberg, Tobias; Martin, Alexander; Koch, Thorsten: The Mixed Integer Problem Library: MIPLIB 2003. Version: 2003. — Online-Ressource, Abruf: 2005-07-28Google Scholar
  12. [12]
    Dolan, Elizabeth D.; Moré, Jorge J.: Benchmarking Optimization Software with Performance Profiles. In: Mathematical Programming 91 (2002), S. 201–213zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Philipp M. Christophel
    • 1
  • Leena Suhl
    • 1
  • Uwe H. Suhl
    • 2
  1. 1.DS&OR LabUniversity of PaderbornPaderborn
  2. 2.Institut für Produktion, Wirtschaftsinformatik und ORFreie Universität BerlinBerlin (Dahlem)

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