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Algebra of Efficient Sets for Multiobjective Complex Systems

Author

Listed:
  • Melissa Gardenghi

    (Clemson University)

  • Trinidad Gómez

    (University of Málaga)

  • Francisca Miguel

    (University of Málaga)

  • Margaret M. Wiecek

    (Clemson University)

Abstract

Complex systems are modeled as collections of multiobjective programs representing interacting subsystems of the overall system. Since the calculation of efficient sets of these complex systems is challenging, it is desirable to decompose the overall system into component multiobjective programs, that are more easily solved and then construct the efficient set of the overall system. For some classes of complex systems, algebraic properties of set operations and relations are developed between the efficient set of the overall system and the efficient sets of subproblems. The properties indicate that multiple decomposition and coordination schemes, with varying assumptions regarding the system, may be applied to the same initial system.

Suggested Citation

  • Melissa Gardenghi & Trinidad Gómez & Francisca Miguel & Margaret M. Wiecek, 2011. "Algebra of Efficient Sets for Multiobjective Complex Systems," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 385-410, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9786-y
    DOI: 10.1007/s10957-010-9786-y
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    References listed on IDEAS

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    1. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    2. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    3. James Ward, 1989. "Structure of Efficient Sets for Convex Objectives," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 249-257, May.
    4. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 329-345, June.
    5. Matthias Ehrgott & Stefan Nickel, 2002. "On the number of criteria needed to decide Pareto optimality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 329-345, June.
    6. Gomez, T. & Gonzalez, M. & Luque, M. & Miguel, F. & Ruiz, F., 2001. "Multiple objectives decomposition-coordination methods for hierarchical organizations," European Journal of Operational Research, Elsevier, vol. 133(2), pages 323-341, January.
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    Cited by:

    1. José Antonio Cuenca Mira & Francisca Miguel García, 2017. "On the Parametric Decomposition Theorem in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 945-953, September.
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    3. Dinçer Konur & Hadi Farhangi & Cihan H. Dagli, 2016. "A multi-objective military system of systems architecting problem with inflexible and flexible systems: formulation and solution methods," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 967-1006, October.
    4. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 597-618, November.

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