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Approximating Multiobjective Knapsack Problems

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Author Info

  • Thomas Erlebach

    ()
    (Computer Engineering and Networks Laboratory, ETH Zürich, CH-8092 Zürich, Switzerland)

  • Hans Kellerer

    ()
    (University of Graz, Department of Statistics and Operations Research, Universitätsstr. 15, A-8010 Graz, Austria)

  • Ulrich Pferschy

    ()
    (University of Graz, Department of Statistics and Operations Research, Universitätsstr. 15, A-8010 Graz, Austria)

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    Abstract

    For multiobjective optimization problems, it is meaningful to compute a set of solutions covering all possible trade-offs between the different objectives. The multiobjective knapsack problem is a generalization of the classical knapsack problem in which each item has several profit values. For this problem, efficient algorithms for computing a provably good approximation to the set of all nondominated feasible solutions, the Pareto frontier, are studied. For the multiobjective one-dimensional knapsack problem, a practical fully polynomial-time approximation scheme (FPTAS) is derived. It is based on a new approach to the single-objective knapsack problem using a partition of the profit space into intervals of exponentially increasing length. For the multiobjective m-dimensional knapsack problem, the first known polynomial-time approximation scheme (PTAS), based on linear programming, is presented.

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    File URL: http://dx.doi.org/10.1287/mnsc.48.12.1603.445
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 48 (2002)
    Issue (Month): 12 (December)
    Pages: 1603-1612

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    Handle: RePEc:inm:ormnsc:v:48:y:2002:i:12:p:1603-1612

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    Related research

    Keywords: knapsack problem; multiobjective optimization; approximation scheme;

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    Cited by:
    1. José Figueira & Luís Paquete & Marco Simões & Daniel Vanderpooten, 2013. "Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem," Computational Optimization and Applications, Springer, vol. 56(1), pages 97-111, September.
    2. Laumanns, Marco & Zenklusen, Rico, 2011. "Stochastic convergence of random search methods to fixed size Pareto front approximations," European Journal of Operational Research, Elsevier, vol. 213(2), pages 414-421, September.

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