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Ratios of optimal values of objective functions of the knapsack problem and its linear relaxation

  • Computer Methods
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Abstract

The ratios of the values of objective functions for optimal solutions of linear and integer knapsack problems are considered. Estimates for these ratios are obtained. One-dimensional and multi-dimensional knapsack problems with Boolean variables are studied experimentally. For these problems, a hypothesis is formulated on the asymptotic behavior of the ratio as the number of variables grows.

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Authors and Affiliations

  1. Institute of Mathematical Economics, Russian Academy of Sciences, ul. Chaikovskogo 1, St. Petersburg, 191187, Russia

    N. N. Galim’yanova, A. A. Korbut & I. Kh. Sigal

  2. Computer Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 117967, Russia

    N. N. Galim’yanova, A. A. Korbut & I. Kh. Sigal

  3. Moscow State Transport University, ul. Obraztsova 9/9, Moscow, 127994, Russia

    N. N. Galim’yanova, A. A. Korbut & I. Kh. Sigal

Authors
  1. N. N. Galim’yanova
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  2. A. A. Korbut
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  3. I. Kh. Sigal
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Additional information

Original Russian Text © N.N. Galim’yanova, A.A. Korbut, I.Kh. Sigal, 2009, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2009, No. 6, pp. 62–69.

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Galim’yanova, N.N., Korbut, A.A. & Sigal, I.K. Ratios of optimal values of objective functions of the knapsack problem and its linear relaxation. J. Comput. Syst. Sci. Int. 48, 906–913 (2009). https://doi.org/10.1134/S1064230709060070

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  • DOI: https://doi.org/10.1134/S1064230709060070

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