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Approximating Multiobjective Knapsack Problems

Listed author(s):
  • 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)

Registered author(s):

    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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    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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    1. Frieze, A. M. & Clarke, M. R. B., 1984. "Approximation algorithms for the m-dimensional 0-1 knapsack problem: Worst-case and probabilistic analyses," European Journal of Operational Research, Elsevier, vol. 15(1), pages 100-109, January.
    2. Magazine, M. J. & Oguz, Osman, 1981. "A fully polynomial approximation algorithm for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 8(3), pages 270-273, November.
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