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Quantum-Inspired Differential Evolution with Grey Wolf Optimizer for 0-1 Knapsack Problem

Author

Listed:
  • Yule Wang

    (College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China)

  • Wanliang Wang

    (College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China)

Abstract

The knapsack problem is one of the most widely researched NP-complete combinatorial optimization problems and has numerous practical applications. This paper proposes a quantum-inspired differential evolution algorithm with grey wolf optimizer (QDGWO) to enhance the diversity and convergence performance and improve the performance in high-dimensional cases for 0-1 knapsack problems. The proposed algorithm adopts quantum computing principles such as quantum superposition states and quantum gates. It also uses adaptive mutation operations of differential evolution, crossover operations of differential evolution, and quantum observation to generate new solutions as trial individuals. Selection operations are used to determine the better solutions between the stored individuals and the trial individuals created by mutation and crossover operations. In the event that the trial individuals are worse than the current individuals, the adaptive grey wolf optimizer and quantum rotation gate are used to preserve the diversity of the population as well as speed up the search for the global optimal solution. The experimental results for 0-1 knapsack problems confirm the advantages of QDGWO with the effectiveness and global search capability for knapsack problems, especially for high-dimensional situations.

Suggested Citation

  • Yule Wang & Wanliang Wang, 2021. "Quantum-Inspired Differential Evolution with Grey Wolf Optimizer for 0-1 Knapsack Problem," Mathematics, MDPI, vol. 9(11), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1233-:d:564032
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    References listed on IDEAS

    as
    1. Yangjun Gao & Fengming Zhang & Yu Zhao & Chao Li, 2018. "Quantum-Inspired Wolf Pack Algorithm to Solve the 0-1 Knapsack Problem," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-10, June.
    2. Vasquez, Michel & Vimont, Yannick, 2005. "Improved results on the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 165(1), pages 70-81, August.
    3. Jourdan, L. & Basseur, M. & Talbi, E.-G., 2009. "Hybridizing exact methods and metaheuristics: A taxonomy," European Journal of Operational Research, Elsevier, vol. 199(3), pages 620-629, December.
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