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An Algorithm for Multiobjective Zero-One Linear Programming

Author

Listed:
  • Gülseren Kiziltan

    (Marmara Scientific and Industrial Research Institute, Kocaeli, Turkey)

  • Erkut Yucaou{g}lu

    (Turkish Electrical Industries Corporation, Istanbul, Turkey)

Abstract

A branch and bound algorithm is presented which is based on the extension of implicit enumeration techniques to multiobjective zero-one linear programming and which appears to be computationally quite efficient. Domination tests, aiming at identifying paths of the enumeration tree that lead to dominated solutions as high up the tree as possible, are developed. Some computational results are also given.

Suggested Citation

  • Gülseren Kiziltan & Erkut Yucaou{g}lu, 1983. "An Algorithm for Multiobjective Zero-One Linear Programming," Management Science, INFORMS, vol. 29(12), pages 1444-1453, December.
    • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:12:p:1444-1453
    DOI: 10.1287/mnsc.29.12.1444
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    Citations

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    Cited by:

    1. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    2. Karaivanova, Jasmina & Korhonen, Pekka & Narula, Subhash & Wallenius, Jyrki & Vassilev, Vassil, 1995. "A reference direction approach to multiple objective integer linear programming," European Journal of Operational Research, Elsevier, vol. 81(1), pages 176-187, February.
    3. Nathan Adelgren & Pietro Belotti & Akshay Gupte, 2018. "Efficient Storage of Pareto Points in Biobjective Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 324-338, May.
    4. Thomas Stidsen & Kim Allan Andersen & Bernd Dammann, 2014. "A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs," Management Science, INFORMS, vol. 60(4), pages 1009-1032, April.
    5. Liesiö, Juuso & Salo, Ahti, 2012. "Scenario-based portfolio selection of investment projects with incomplete probability and utility information," European Journal of Operational Research, Elsevier, vol. 217(1), pages 162-172.
    6. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    7. Nikolaos Argyris & José Figueira & Alec Morton, 2011. "Identifying preferred solutions to Multi-Objective Binary Optimisation problems, with an application to the Multi-Objective Knapsack Problem," Journal of Global Optimization, Springer, vol. 49(2), pages 213-235, February.
    8. Skriver, Anders J. V. & Andersen, Kim Allan & Holmberg, Kaj, 2004. "Bicriteria network location (BNL) problems with criteria dependent lengths and minisum objectives," European Journal of Operational Research, Elsevier, vol. 156(3), pages 541-549, August.
    9. Forget, Nicolas & Gadegaard, Sune Lauth & Nielsen, Lars Relund, 2022. "Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 302(3), pages 909-924.
    10. Sune Lauth Gadegaard & Lars Relund Nielsen & Matthias Ehrgott, 2019. "Bi-objective Branch-and-Cut Algorithms Based on LP Relaxation and Bound Sets," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 790-804, October.
    11. Zhang, Cai Wen & Ong, Hoon Liong, 2004. "Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic," European Journal of Operational Research, Elsevier, vol. 159(3), pages 545-557, December.
    12. Serpil Say{i}n & Panos Kouvelis, 2005. "The Multiobjective Discrete Optimization Problem: A Weighted Min-Max Two-Stage Optimization Approach and a Bicriteria Algorithm," Management Science, INFORMS, vol. 51(10), pages 1572-1581, October.
    13. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    14. Ozgu Turgut & Evrim Dalkiran & Alper E. Murat, 2019. "An exact parallel objective space decomposition algorithm for solving multi-objective integer programming problems," Journal of Global Optimization, Springer, vol. 75(1), pages 35-62, September.
    15. Barbati, Maria & Greco, Salvatore & Kadziński, Miłosz & Słowiński, Roman, 2018. "Optimization of multiple satisfaction levels in portfolio decision analysis," Omega, Elsevier, vol. 78(C), pages 192-204.
    16. Liesiö, Juuso & Mild, Pekka & Salo, Ahti, 2008. "Robust portfolio modeling with incomplete cost information and project interdependencies," European Journal of Operational Research, Elsevier, vol. 190(3), pages 679-695, November.
    17. Panos Kouvelis & Serpil Sayın, 2006. "Algorithm robust for the bicriteria discrete optimization problem," Annals of Operations Research, Springer, vol. 147(1), pages 71-85, October.
    18. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti & Ilmola-Sheppard, Leena, 2018. "Scenario-based portfolio model for building robust and proactive strategies," European Journal of Operational Research, Elsevier, vol. 266(1), pages 205-220.
    19. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    20. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.

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    Keywords

    programming: multiple criteria;

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