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Extremal values of global tolerances in combinatorial optimization with an additive objective function

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Abstract

The currently adopted notion of a tolerance in combinatorial optimization is defined referring to an arbitrarily chosen optimal solution, i.e., locally. In this paper we introduce global tolerances with respect to the set of all optimal solutions, and show that the assumption of nonembededdness of the set of feasible solutions in the provided relations between the extremal values of upper and lower global tolerances can be relaxed. The equality between globally and locally defined tolerances provides a new criterion for the multiplicity (uniqueness) of the set of optimal solutions to the problem under consideration.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, National Research University Higher School of Economics, Bol’shaya Pechërskaya Street 25/12, Nizhny Novgorod, 603155, Russian Federation

    Vyacheslav V. Chistyakov & Boris I. Goldengorin

  2. Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, Bol’shaya Pechërskaya Street 25/12, Nizhny Novgorod, 603155, Russian Federation

    Vyacheslav V. Chistyakov, Boris I. Goldengorin & Panos M. Pardalos

  3. Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, 303 Weil Hall, P. O. Box 116595, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Authors
  1. Vyacheslav V. Chistyakov
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  2. Boris I. Goldengorin
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  3. Panos M. Pardalos
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Corresponding author

Correspondence to Boris I. Goldengorin.

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Chistyakov, V.V., Goldengorin, B.I. & Pardalos, P.M. Extremal values of global tolerances in combinatorial optimization with an additive objective function. J Glob Optim 53, 475–495 (2012). https://doi.org/10.1007/s10898-012-9847-x

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  • DOI: https://doi.org/10.1007/s10898-012-9847-x

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