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Half-open polyblock for the representation of the search region in multiobjective optimization problems: its application and computational aspects

Author

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  • Pham Thi Hoai

    (Hanoi University of Science and Technology)

  • Hoai An Le Thi

    (Université de Lorraine)

  • Nguyen Canh Nam

    (Hanoi University of Science and Technology)

Abstract

The search region in multiobjective optimization problems is a part of the objective space where nondominated points could lie. It plays an important role in the generation of the nondominated set of multiobjective combinatorial optimization (MOCO) problems. In this paper, we establish the representation of the search region by half-open polyblocks (a variant concept of “polyblock” in monotonic optimization) and propose a new procedure for updating the search region. We also study the impact of stack policies to the new procedure and the existing methods that update the search region. Stack policies are then analyzed, pointing out their performance effectiveness by means of the results of rich computational experiments on finding the whole set of nondominated points of MOCO problems.

Suggested Citation

  • Pham Thi Hoai & Hoai An Le Thi & Nguyen Canh Nam, 2021. "Half-open polyblock for the representation of the search region in multiobjective optimization problems: its application and computational aspects," 4OR, Springer, vol. 19(1), pages 41-70, March.
    • Handle: RePEc:spr:aqjoor:v:19:y:2021:i:1:d:10.1007_s10288-020-00430-5
    DOI: 10.1007/s10288-020-00430-5
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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.
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    5. 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.
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    Cited by:

    1. Eichfelder, Gabriele & Warnow, Leo, 2023. "Advancements in the computation of enclosures for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 310(1), pages 315-327.

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