Abstract
A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.
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Original Russian Text © V.A. Emelichev, K.G. Kuz’min, 2007, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2007, No. 5, pp. 45–51.
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Emelichev, V.A., Kuz’min, K.G. On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm. J. Comput. Syst. Sci. Int. 46, 714–720 (2007). https://doi.org/10.1134/S1064230707050048
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DOI: https://doi.org/10.1134/S1064230707050048