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An exact parallel objective space decomposition algorithm for solving multi-objective integer programming problems

Author

Listed:
  • Ozgu Turgut

    (NTNU)

  • Evrim Dalkiran

    (Industrial and Systems Engineering Department Wayne State University)

  • Alper E. Murat

    (Industrial and Systems Engineering Department Wayne State University)

Abstract

The set of all nondominated solutions for a multi-objective integer programming (MOIP) problem is finite if the feasible region is bounded, and it may contain unsupported solutions. Finding these sets is NP-hard for most MOIP problems and current methods are unable to scale with the number of objectives. We propose a deterministic exact parallel algorithm for solving MOIP problems with any number of objectives. The proposed algorithm generates the full set of nondominated solutions based on intelligent iterative decomposition of the objective space utilizing a particular scalarization scheme. The algorithm relies on a set of rules that exploits regional dominance relations among the decomposed partitions for pruning. These expediting rules are both used as part of a pre-solve step as well as judiciously employed throughout the parallel running threads. Using an extensive test-bed of MOIP instances with three, four, five, and six objectives, the performance of the proposed algorithm is evaluated and compared with leading benchmark algorithms for MOIPs. Results of the experimental study demonstrate the effectiveness of the proposed algorithm and the computational advantage of its parallelism.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:1:d:10.1007_s10898-019-00778-x
    DOI: 10.1007/s10898-019-00778-x
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    References listed on IDEAS

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    1. Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2015. "On the representation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 245(3), pages 767-778.
    2. 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.
    3. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "The Quadrant Shrinking Method: A simple and efficient algorithm for solving tri-objective integer programs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 873-885.
    4. Kerstin Dächert & Kathrin Klamroth, 2015. "A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems," Journal of Global Optimization, Springer, vol. 61(4), pages 643-676, April.
    5. Melih Ozlen & Benjamin A. Burton & Cameron A. G. MacRae, 2014. "Multi-Objective Integer Programming: An Improved Recursive Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 470-482, February.
    6. 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.
    7. Dächert, Kerstin & Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2017. "Efficient computation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 841-855.
    8. 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.
    9. Moncef Abbas & Mohamed El-Amine Chergui & Meriem Ait Mehdi, 2012. "Efficient cuts for generating the non-dominated vectors for Multiple Objective Integer Linear Programming," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(3), pages 302-316.
    10. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
    11. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
    12. 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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    2. Nathan Adelgren & Akshay Gupte, 2022. "Branch-and-Bound for Biobjective Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 909-933, March.

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