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

Evgenii Burashnikov ()
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Evgenii Burashnikov: National Research University Higher School of Economics (HSE University)

SN Operations Research Forum, 2024, vol. 5, issue 4, 1-19

Abstract: 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.

Keywords: Knapsack 0–1 problem; Branch-and-Bound; Dynamic Programming; Combinatorial optimization (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s43069-024-00372-2

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