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A Minimal Algorithm for the 0-1 Knapsack Problem

Toghraei, Omid | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48777 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezamoddin
  7. Abstract:
  8. Several types of large-sized 0-1 Knapsack Problems (KPs) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. To avoid this, it has been suggested to solve the so-called core of the problem, knapsack problem defined on a small subset of the variables. The exact core cannot, however, be identified before KP is solved to optimality and, thus previously available algorithms had to rely on approximate core sizes. Here, we describe an algorithm for KP recently proposed in the litereture, where the enumerated core size is minimal, and the computational effort for sorting and reduction is also limited in accordance with a hierarchy. The algorithm is based on a dynamic programming approach, where the core size is extended as needed, and the sorting and reduction are performed as well. Computational experiments are made on several types of data instances. The obtained results from these tests show that the approach outperforms other known algorithm for KP. To solve the problem, we make use of methods recently proposed in the literature. These methods are implemented in ANSI-C, where compared to MT2 algorithm for 0-1 knapsack problems, MINKNAP algorithm uses tighter reductions and enumerates considerably less item types. This show that the algorithm outperforms the MT2 algorithm for the 0-1 KP
  9. Keywords:
  10. Knapsack Problem ; Dynamic Programming ; 0-1 Knapsack Problem ; Minimal Core

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