A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs

Published Online:https://doi.org/10.1287/mnsc.2013.1802

References

  • Aneja YP, Nair KPK (1979) Bicriteria transportation problem. Management Sci. 25(1):73–78.LinkGoogle Scholar
  • Bukchin J, Masin M (2004) Multi-objective design of team oriented assembly systems. Eur. J. Oper. Res. 156(2):326–352.CrossrefGoogle Scholar
  • Cohon J (1978) Multiobjective Programming and Planning (Academic Press, New York).Google Scholar
  • Ehrgott M (2005) Multicriteria Optimization, 2nd ed. (Springer Verlag, Berlin).Google Scholar
  • Ehrgott M, Gandibleux X (2000) A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22(4):425–460.CrossrefGoogle Scholar
  • Hooker JN (2000) Logic-Based Methods for Optimization (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • IBM ILOG (2012) CPLEX 12.1.1. IBM ILOG, Armonk, NY.Google Scholar
  • Kiziltan G, Yucaoglu E (1983) An algorithm for multiobjective zero-one linear programming. Management Sci. 29(12):1444–1453.LinkGoogle Scholar
  • Klein D, Hannan E (1982) An algorithm for the multiple objective integer linear programming problem. Eur. J. Oper. Res. 9(4):378–385.CrossrefGoogle Scholar
  • Land AH, Doig AG (1960) An automatic method of solving discrete programming problems. Econometrica: J. Econometric Soc. 28(3):497–520.CrossrefGoogle Scholar
  • Masin M, Bukchin Y (2008) Diversity maximization approach for multiobjective optimization. Oper. Res. 56(2):411–424.LinkGoogle Scholar
  • Mavrotas G, Diakoulaki D (1998) A branch and bound algorithm for mixed zero-one multiple objective linear programming. Eur. J. Oper. Res. 107(3):530–541.CrossrefGoogle Scholar
  • Mavrotas G, Diakoulaki D (2005) Multi-criteria branch and bound: A vector maximization algorithm for mixed 0-1 multiple objective linear programming. Appl. Math. Comput. 171(1):53–71.CrossrefGoogle Scholar
  • Mezmaz M, Melab N, Talbi EG (2007) A grid-based parallel approach of the multi-objective branch and bound. 15th EUROMICRO Internat. Conf. Parallel, Distributed and Network-Based Processing (PDP07) (Institute of Electrical and Electronics Engineers, Washington, DC), 23–30.CrossrefGoogle Scholar
  • Özpeynirci Ö, Köksalan M (2010) An exact algorithm for finding extreme supported nondominated points of multiobjective mixed integer programs. Management Sci. 56(12):2302–2315.LinkGoogle Scholar
  • Pedersen CR, Nielsen LR, Andersen KA (2008) The bicriterion multi-modal assignment problem: Introduction, analysis, and experimental results. INFORMS J. Comput. 20(3):400–411.LinkGoogle Scholar
  • Przybylski A, Gandibleux X, Ehrgott M (2008) Two phase algorithms for the bi-objective assignment problem. Eur. J. Oper. Res. 185(2):509–533.CrossrefGoogle Scholar
  • Przybylski A, Gandibleux X, Ehrgott M (2010a) A recursive algorithm for finding all nondominated extreme points in the outcome set of a multiobjective integer programme. INFORMS J. Comput. 22(3):371–386.LinkGoogle Scholar
  • Przybylski A, Gandibleux X, Ehrgott M (2010b) A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optim. 7(3):149–165.CrossrefGoogle Scholar
  • Przybylski A, Gandibleux X, Ehrgott M (2011) The two phase method for multiobjective combinatorial optimization problems. Mahjoub R, ed. Progress in Combinatorial Optimization (ISTE-Wiley, Hoboken, NJ), 559–596.Google Scholar
  • Raith A, Ehrgott M (2009) A two-phase algorithm for the biobjective integer minimum cost flow problem. Comput. Oper. Res. 36(6):1299–1331.CrossrefGoogle Scholar
  • Sourd F, Spanjaard O (2008) A multiobjective branch-and-bound framework: Application to the biobjective spanning tree problem. INFORMS J. Comput. 20(3):471–484.LinkGoogle Scholar
  • Sourd F, Spanjaard O, Perny P (2006) Multi-objective branch-and-bound: Application to the bi-objective spanning tree problem. MOPGP'06: 7th Internat. Conf. Multi-Objective Programming and Goal Programming, Loire Valley, France.Google Scholar
  • Steuer RE (1986) Multiple Criteria Optimization: Theory, Computation and Application (John Wiley & Sons, New York).Google Scholar
  • Tuyttens D, Teghem J, Fortemps Ph, Nieuwenhuyze VK (2000) Performance of the MOSA method for the bicriteria assignment problem. J. Heuristics 6(3):295–310.CrossrefGoogle Scholar
  • Ulungu EL (1993) Optimisation combinatoire multicritère: Détermination de l'ensemble des solutions efficaces et méthodes intéractives. Ph.D. thesis, Faculté des Sciences, Université de Mons-Hainault, Mons, Belgium.Google Scholar
  • Ulungu EL, Teghem J (1995) The two phases method: An efficient procedure to solve bi-objective combinatorial optimization problems. Foundations Comput. Decision Sci. 20(2):149–165.Google Scholar
  • Vincent T (2009) Multi-objective branch and bound for mixed 0-1 linear programming: Corrections and improvements. Master's thesis, Department of Computer Science, Technische Universität Kaiserslautern, Kaiserslautern, Germany.Google Scholar
  • Vincent T, Seipp F, Ruzika S, Przybylski A, Gandibleux X (2013) Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case. Comput. Oper. Res. 40(1):498–509.CrossrefGoogle Scholar
  • Visée M, Teghem J, Pirlot M, Ulungu EL (1998) Two-phases method and branch-and-bound procedures to solve the bi-objective knapsack problem. J. Global Optim. 12(2):139–155.CrossrefGoogle Scholar
  • White DJ (1984) A branch and bound method for multi-objective boolean problems. Eur. J. Oper. Res. 15(1):126–130.CrossrefGoogle Scholar
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