Abstract
In multiple-objective optimization literature, a properly efficient solution has been interpreted as a point in which the trade-offs between all objectives are bounded. In this paper, it is shown that this boundedness does not necessarily hold for problems with three or more objective functions. It is possible that in a properly efficient solution the trade-offs between some objectives are unbounded. To overcome this, in this paper strongly proper efficient solutions are introduced, in which the trade-offs between all objectives are bounded. This notion is defined in different senses, and the relationships between them are investigated. In addition to theoretical discussions, some clarifying examples are given.
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Acknowledgments
The authors would like to express their gratitude to anonymous referees and the editor of JOTA for their time and effort about the paper. The research of the third author has been supported by a grant from IPM (No. 94260124).
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Khaledian, K., Khorram, E. & Soleimani-damaneh, M. Strongly Proper Efficient Solutions: Efficient Solutions with Bounded Trade-Offs. J Optim Theory Appl 168, 864–883 (2016). https://doi.org/10.1007/s10957-015-0841-6
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DOI: https://doi.org/10.1007/s10957-015-0841-6