The Triangle Splitting Method for Biobjective Mixed Integer Programming

  • Natashia Boland
  • Hadi Charkhgard
  • Martin Savelsbergh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8494)


We present the first criterion space search algorithm, the triangle splitting method, for finding the efficient frontier of a biobjective mixed integer program. The algorithm is relatively easy to implement and converges quickly to the complete set of nondominated points. A computational study demonstrates the efficacy of the triangle splitting method.


biobjective mixed integer program triangle splitting method efficient frontier 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aneja, Y.P., Nair, K.P.K.: Bicriteria transportation problem. Management Science 27, 73–78 (1979)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Belotti, P., Soylu, B., Wiecek, M.M.: A branch-and-bound algorithm for biobjective mixed-integer programs,
  3. 3.
    Benson, H.P., Sun, E.: A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of multiple objective linear program. European Journal of Operational Research 139, 26–41 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Gardenghi, M., Gómez, T., Miguel, F., Wiecek, M.M.: Algebra of efficient sets for multiobjective complex systems. Journal of Optimization Theory and Applications 149, 385–410 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Isermann, H.: The enumeration of the set of all efficient solutions for a linear multiple objective program. Operational Research Quarterly 28(3), 711–725 (1977)CrossRefzbMATHGoogle Scholar
  6. 6.
    Mavrotas, G., Diakoulaki, D.: A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research 107, 530–541 (1998)CrossRefzbMATHGoogle Scholar
  7. 7.
    Mavrotas, G., Diakoulaki, D.: Multi-criteria branch and bound: A vector maximization algorithm for mixed 0-1 multiple objective linear programming. Applied Mathematics and Computation 171, 53–71 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Vincent, T., Seipp, F., Ruzika, S., Przybylski, A., Gandibleux, X.: Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for biobjective case. Computers & Operations Research 40(1), 498–509 (2013)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Natashia Boland
    • 1
  • Hadi Charkhgard
    • 1
  • Martin Savelsbergh
    • 1
  1. 1.School of Mathematical and Physical SciencesThe University of NewcastleAustralia

Personalised recommendations