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

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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.

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Notes

  1. N is a nonempty and stable set of points in general position i.e., for all \(z, z'\in N, z\ne z',\) we have \(z_i\ne z'_i\) for all \(i=1,\ldots ,m,\) see Dächert et al. (2017) for more details.

  2. We use the phrase “the “raw” updating procedure” to mean the application of this procedure for a set of randomly generated points as implemented in Klamroth et al. (2015).

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Acknowledgements

We would like to thank the editors and anonymous referees for their useful comments which helped us to improve the paper greatly.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet Road, Hanoi, Vietnam

    Pham Thi Hoai & Nguyen Canh Nam

  2. Département Informatique et Applications, LGIPM, Université de Lorraine, 57000, Metz, France

    Hoai An Le Thi

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  1. Pham Thi Hoai
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Correspondence to Hoai An Le Thi.

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This research is funded by Hanoi University of Science and Technology (HUST) under project number T2018-PC-119.

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Hoai, P.T., Le Thi, H.A. & Nam, N.C. Half-open polyblock for the representation of the search region in multiobjective optimization problems: its application and computational aspects. 4OR-Q J Oper Res 19, 41–70 (2021). https://doi.org/10.1007/s10288-020-00430-5

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  • DOI: https://doi.org/10.1007/s10288-020-00430-5

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