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Probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms

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Abstract

Properties of several dual characteristics of the multidimensional knapsack problem (such as the probability of existence of∈-optimal and optimalδ-feasible Lagrange function generalized saddle points, magnitude of relative duality gap, etc.) are investigated for different probabilistic models. Sufficient conditions of “good” asymptotic behavior of the dual characteristics are given. A fast statistically efficient approximate algorithm with linear running time complexity for problems with random coefficients is presented.

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Authors and Affiliations

  1. Division of Management and Economics, Scarborough College, University of Toronto, 1265 Military Trail, M1C 1A4, Scarborough, Ontario, Canada

    Igor Averbakh

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  1. Igor Averbakh
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This paper was written when the author was affiliated with Chelyabinsk State Technical University and the Moscow Physical and Technical Institute, Russia.

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Averbakh, I. Probabilistic properties of the dual structure of the multidimensional knapsack problem and fast statistically efficient algorithms. Mathematical Programming 65, 311–330 (1994). https://doi.org/10.1007/BF01581700

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  • DOI: https://doi.org/10.1007/BF01581700

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