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A new approach to approximate the bounded Pareto front

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Abstract

In this paper, a sequential approach, recently addressed by Mueller-Gritschneder et al. [SIAM J Optim 20(2):915–934, 2009] is studied. After a brief review, some weaknesses of the mentioned approach are pointed out. These weaknesses are due to a redundant assumption and the inability to generate the entire Pareto front. We present two improvements for the mentioned approach, firstly by eliminating the assumption of equality between the Pareto front and the weak Pareto front and secondly by presenting a new definition of the boundary of the Pareto front and establishing some theoretical results about it.

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Acknowledgments

The authors would like to express their gratitude to anonymous referees for their helpful comments on this paper. This research was in part supported by a Grant from IPM (No. 93260124).

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, 424, Hafez Avenue, Tehran, 15914, Iran

    Kazhal Khaledian

  2. School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran

    Majid Soleimani-damaneh

  3. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Majid Soleimani-damaneh

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  1. Kazhal Khaledian
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  2. Majid Soleimani-damaneh
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Correspondence to Majid Soleimani-damaneh.

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Khaledian, K., Soleimani-damaneh, M. A new approach to approximate the bounded Pareto front. Math Meth Oper Res 82, 211–228 (2015). https://doi.org/10.1007/s00186-015-0510-4

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  • DOI: https://doi.org/10.1007/s00186-015-0510-4

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