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Computing the nadir point for multiobjective discrete optimization problems

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Abstract

We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with \(p\) objective functions. The proposed algorithm is based on an exhaustive search of the \((p-2)\)-dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives.

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Notes

  1. \(\mathcal {Y}_P^k\) represents the list of nondominated solutions until \(y_k^N\) is obtained. At termination, \(\mathcal {Y}_P^k\) may not include all nondominated solutions, i.e. \(\mathcal {Y}_P^k \subseteq \mathcal {Y}_{ND}\) for each \(k \in \{1,\ldots ,p\}\).

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Acknowledgments

This work is supported by TUBITAK (Scientific & Technical Research Council of Turkey), Project No. 112M217. We thank anonymous reviewers whose comments improved the presentation of the paper.

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Authors and Affiliations

  1. Graduate School of Sciences and Engineering, Koç University, Sariyer, 34450 , Istanbul, Turkey

    Gokhan Kirlik

  2. College of Administrative Sciences and Economics, Koç University, Sariyer, 34450 , Istanbul, Turkey

    Serpil Sayın

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  1. Gokhan Kirlik
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  2. Serpil Sayın
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Correspondence to Serpil Sayın.

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Kirlik, G., Sayın, S. Computing the nadir point for multiobjective discrete optimization problems. J Glob Optim 62, 79–99 (2015). https://doi.org/10.1007/s10898-014-0227-6

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