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Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization

Author

Listed:
  • Jochen Gorski

    (Bergische Universität Wuppertal)

  • Kathrin Klamroth

    (Bergische Universität Wuppertal)

  • Stefan Ruzika

    (University of Kaiserslautern)

Abstract

Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. However, we show that many classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases) and linear assignment problems. We also extend known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for two variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated instances.

Suggested Citation

  • Jochen Gorski & Kathrin Klamroth & Stefan Ruzika, 2011. "Connectedness of Efficient Solutions in Multiple Objective Combinatorial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 475-497, September.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:3:d:10.1007_s10957-011-9849-8
    DOI: 10.1007/s10957-011-9849-8
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    References listed on IDEAS

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    1. Ehrgott, Matthias & Klamroth, Kathrin, 1997. "Connectedness of efficient solutions in multiple criteria combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 97(1), pages 159-166, February.
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    Cited by:

    1. Pascal Halffmann & Tobias Dietz & Anthony Przybylski & Stefan Ruzika, 2020. "An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem," Journal of Global Optimization, Springer, vol. 77(4), pages 715-742, August.
    2. Michael Stiglmayr & José Figueira & Kathrin Klamroth, 2014. "On the multicriteria allocation problem," Annals of Operations Research, Springer, vol. 222(1), pages 535-549, November.
    3. Pedro Correia & Luís Paquete & José Rui Figueira, 2021. "Finding multi-objective supported efficient spanning trees," Computational Optimization and Applications, Springer, vol. 78(2), pages 491-528, March.
    4. Michael Stiglmayr & José Rui Figueira & Kathrin Klamroth & Luís Paquete & Britta Schulze, 2022. "Decision space robustness for multi-objective integer linear programming," Annals of Operations Research, Springer, vol. 319(2), pages 1769-1791, December.

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