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Multidimensional Knapsack Problems

In: Knapsack Problems

Author

Listed:
  • Hans Kellerer

    (University of Graz, Department of Statistics and Operations Research)

  • Ulrich Pferschy

    (University of Graz, Department of Statistics and Operations Research)

  • David Pisinger

    (University of Copenhagen, DIKU, Department of Computer Science)

Abstract

In this first chapter of extensions and generalizations of the basic knapsack problem (KP) we will add additional constraints to the single weight constraint (1.2) thus attaining the multidimensional knapsack problem. After the introduction we will deal extensively with relaxations and reductions in Section 9.2. Exact algorithms to compute optimal solutions will be covered in Section 9.3 followed by results on approximation in Section 9.4. A detailed treatment of heuristic methods will be given in Section 9.5. Separate sections are devoted to two special cases, namely the two-dimensional knapsack problem (Section 9.6) and the cardinality constrained knapsack problem (Section 9.7). Finally, we will consider the combination of multiple constraints and multiple-choice selection of items from classes (see Chapter 11 for the one-dimensional case) in Section 9.8.

Suggested Citation

  • Hans Kellerer & Ulrich Pferschy & David Pisinger, 2004. "Multidimensional Knapsack Problems," Springer Books, in: Knapsack Problems, chapter 9, pages 235-283, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-24777-7_9
    DOI: 10.1007/978-3-540-24777-7_9
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