Milan Hladík. Six ways how to define robust Pareto optimality under double interval uncertainty. In Proceedings of the 16th International Symposium on Operational Research SOR'21, Bled, Slovenia, September 22-24, 2021, pp. 571–576, Slovenian Society INFORMATIKA, Ljubljana, Slovenia, 2021.
We deal with a multiobjective linear programming problem that is subject to a double uncertainty. In both cases, we consider uncertainty in the form of interval values that cover the true unobservable values. First, we suppose that the costs in the objective functions are linear functions with interval coefficients. Second, we suppose that we have an interval estimation of weights of the particular criteria. This double uncertainty mathematically leads to six different concepts of efficiency (Pareto optimality). We provide a characterization of each of them. We also investigate computational complexity of the decision problem whether a given solution is efficient. It turns out that some of the concepts are polynomial, some are polynomial under the assumption of fixed number of criteria, and some are co-NP-hard to check.
@inProceedings{Hla2021d,
author = "Milan Hlad\'{\i}k",
title = "Six ways how to define robust Pareto optimality under double interval uncertainty",
editor = "Drobne et al., S.",
booktitle = "Proceedings of the 16th International Symposium on Operational Research SOR'21, Bled, Slovenia, September 22-24, 2021",
publisher = "Slovenian Society INFORMATIKA",
address = "Ljubljana, Slovenia",
pages = "571-576",
year = "2021",
isbn = "978-961-6165-57-0",
bib2html_dl_pdf = "http://fgg-web.fgg.uni-lj.si/~/sdrobne/sor/SOR'21%20-%20Proceedings.pdf",
abstract = "We deal with a multiobjective linear programming problem that is subject to a double uncertainty. In both cases, we consider uncertainty in the form of interval values that cover the true unobservable values. First, we suppose that the costs in the objective functions are linear functions with interval coefficients. Second, we suppose that we have an interval estimation of weights of the particular criteria. This double uncertainty mathematically leads to six different concepts of efficiency (Pareto optimality). We provide a characterization of each of them. We also investigate computational complexity of the decision problem whether a given solution is efficient. It turns out that some of the concepts are polynomial, some are polynomial under the assumption of fixed number of criteria, and some are co-NP-hard to check.",
keywords = "Multiobjective linear programming; Interval analysis; Robust optimization; Weighted scalarization",
}
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