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Binary salp swarm algorithm for discounted {0-1} knapsack problem

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  • Binh Thanh Dang
  • Tung Khac Truong

Abstract

While the classical knapsack problem has been the object to be solved by optimization algorithm proposals for many years, another version of this problem, discounted {0-1} knapsack problem, is gaining a lot of attention recently. The original knapsack problem requires selecting specific items from an item set to maximize the total benefit while ensuring that the total weight does not exceed the knapsack capacity. Meanwhile, discounted {0-1} knapsack problem has more stringent requirements in which items are divided into groups, and only up to one item from a particular group can be selected. This constraint, which does not exist in the original knapsack problem, makes discounted {0-1} knapsack problem even more challenging. In this paper, we propose a new algorithm based on salp swarm algorithm in the form of four different variants to resolve the discounted {0-1} knapsack problem. In addition, we also make use of an effective data modeling mechanism and a greedy repair operator that helps overcome local optima when finding the global optimal solution. Experimental and statistical results show that our algorithm is superior to currently available algorithms in terms of solution quality, convergence, and other statistical criteria.

Suggested Citation

  • Binh Thanh Dang & Tung Khac Truong, 2022. "Binary salp swarm algorithm for discounted {0-1} knapsack problem," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-28, April.
    • Handle: RePEc:plo:pone00:0266537
    DOI: 10.1371/journal.pone.0266537
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    References listed on IDEAS

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    1. Egon Balas & Eitan Zemel, 1980. "An Algorithm for Large Zero-One Knapsack Problems," Operations Research, INFORMS, vol. 28(5), pages 1130-1154, October.
    2. Silvano Martello & David Pisinger & Paolo Toth, 1999. "Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 45(3), pages 414-424, March.
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