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<p>To efficiently solve the multiple knapsack problem (MKP) using Fick’s law algorithm (FLA), this paper first proposes a new type of transfer functions: F-shaped transfer functions. Combining it with a modulo operation advances a discretization method for mapping continuous variables to integers. On this basis, a discrete FLA, named FFLA, suitable for solving MKP is proposed. Moreover, an optimization operator AOP is proposed based on the aggregation strategy of the remaining capacities of knapsacks, which can significantly enhance solution quality. To verify the effectiveness of FFLA, it is used to solve 30 standard MKP benchmark instances. The comparison with state-of-the-art metaheuristic algorithms for solving MKP shows that FFLA has superior performance in terms of best solution quality, average performance, convergence speed, and robustness. This work not only proposes a more competitive algorithm FFLA for solving MKP, but also breaks through the previous excessive reliance on curve shapes to design transfer functions, providing a new thinking orientation for designing transfer functions.</p>

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Discrete Fick’s law algorithm with new transfer function and aggregation optimization strategy for solving multiple knapsack problem

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Manman Meng,
  • Yichao He,
  • Wenbin Li,
  • Guoxin Chen,
  • Ju Chen,
  • Zexian Gao

摘要

To efficiently solve the multiple knapsack problem (MKP) using Fick’s law algorithm (FLA), this paper first proposes a new type of transfer functions: F-shaped transfer functions. Combining it with a modulo operation advances a discretization method for mapping continuous variables to integers. On this basis, a discrete FLA, named FFLA, suitable for solving MKP is proposed. Moreover, an optimization operator AOP is proposed based on the aggregation strategy of the remaining capacities of knapsacks, which can significantly enhance solution quality. To verify the effectiveness of FFLA, it is used to solve 30 standard MKP benchmark instances. The comparison with state-of-the-art metaheuristic algorithms for solving MKP shows that FFLA has superior performance in terms of best solution quality, average performance, convergence speed, and robustness. This work not only proposes a more competitive algorithm FFLA for solving MKP, but also breaks through the previous excessive reliance on curve shapes to design transfer functions, providing a new thinking orientation for designing transfer functions.