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Branch-and-Bound and Dynamic Programming Approaches for the Knapsack Problem

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  • Evgenii Burashnikov

    (National Research University Higher School of Economics (HSE University))

Abstract

The knapsack problem is one of the most popular NP-hard problems in combinatorial optimization. For 0-1 Knapsack Problem, there are two common approaches which guarantee the optimality of the solutions: Branch-and-Bound (BnB) and Dynamic Programming (DP) algorithms. Both algorithms suffer from a large amount of redundant calculations. To handle this problem, we proposed modifications of these algorithms. For DP, we suggest some new pre-processing and search rules which help us to avoid unneeded calculations. For BnB, we develop a combination of common BnB method with DP with list approach. Computational experiments on artificially generated data and common benchmarks show the effectiveness of the proposed algorithms.

Suggested Citation

  • Evgenii Burashnikov, 2024. "Branch-and-Bound and Dynamic Programming Approaches for the Knapsack Problem," SN Operations Research Forum, Springer, vol. 5(4), pages 1-19, December.
    • Handle: RePEc:spr:snopef:v:5:y:2024:i:4:d:10.1007_s43069-024-00372-2
    DOI: 10.1007/s43069-024-00372-2
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    References listed on IDEAS

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