An adaptive grey wolf optimization with differential evolution operator for solving the discount {0–1} knapsack problem

The discount {0–1} knapsack problem (D {0–1} KP) is a new variant of the knapsack problem. It is an NP-hard problem and also a binary optimization problem. As a new intelligent algorithm that imitates the leadership function of wolves, the grey wolf optimizer (GWO) can solve NP problems more effecti...

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Vydáno v:	Neural computing & applications Ročník 37; číslo 27; s. 22369 - 22385
Hlavní autoři:	Wang, Zijian, Fang, Xi, Gao, Fei, Xie, Liang, Meng, Xianchen
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	London Springer London 01.09.2025 Springer Nature B.V
Témata:	Algorithms Artificial Intelligence Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Datasets Discounts Dynamic programming Evolutionary computation Image Processing and Computer Vision Knapsack problem Mathematical models Operators (mathematics) Optimization Parameters Probability and Statistics in Computer Science S.I.: Hybrid Approaches to Nature-inspired Optimization Algorithms and Their Applications Scaling factors Special Issue on Hybrid Approaches to Nature-inspired Optimization Algorithms and Their Applications D {0–1} NP-hard Grey wolf optimizer KP Greedy repair operator Differential evolution operator
ISSN:	0941-0643, 1433-3058
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Abstract	The discount {0–1} knapsack problem (D {0–1} KP) is a new variant of the knapsack problem. It is an NP-hard problem and also a binary optimization problem. As a new intelligent algorithm that imitates the leadership function of wolves, the grey wolf optimizer (GWO) can solve NP problems more effectively than accurate algorithms. At the same time, the GWO has fewer parameters, faster calculations, and easier implementation than other intelligent algorithms. This paper introduces a method of adaptively updating the prey position of wolves and a differential evolution operator with a scaling factor that adaptively changes according to the number of iterations, and selects which operator to use for iteration by the value of the search agent parameter. Finally, it combines the improved greedy repair operator based on D {0–1} KP to form the adaptive grey wolf optimization with differential evolution operator (de-AGWO). The experimental results of the standard test function prove that the algorithm in this paper has a significant improvement in function optimization performance. And the experimental results of D {0–1} KP shows that the proposed algorithm yields superior solution outcomes, except for unrelated datasets, and exhibits significant advantages when solving strongly correlated datasets. Finally, it is verified that more than 80% of the iterations utilize the grey wolf evolution operator, highlighting that the core of the algorithm remains the GWO.
AbstractList	The discount {0–1} knapsack problem (D {0–1} KP) is a new variant of the knapsack problem. It is an NP-hard problem and also a binary optimization problem. As a new intelligent algorithm that imitates the leadership function of wolves, the grey wolf optimizer (GWO) can solve NP problems more effectively than accurate algorithms. At the same time, the GWO has fewer parameters, faster calculations, and easier implementation than other intelligent algorithms. This paper introduces a method of adaptively updating the prey position of wolves and a differential evolution operator with a scaling factor that adaptively changes according to the number of iterations, and selects which operator to use for iteration by the value of the search agent parameter. Finally, it combines the improved greedy repair operator based on D {0–1} KP to form the adaptive grey wolf optimization with differential evolution operator (de-AGWO). The experimental results of the standard test function prove that the algorithm in this paper has a significant improvement in function optimization performance. And the experimental results of D {0–1} KP shows that the proposed algorithm yields superior solution outcomes, except for unrelated datasets, and exhibits significant advantages when solving strongly correlated datasets. Finally, it is verified that more than 80% of the iterations utilize the grey wolf evolution operator, highlighting that the core of the algorithm remains the GWO.
Author	Xie, Liang Fang, Xi Wang, Zijian Gao, Fei Meng, Xianchen
Author_xml	– sequence: 1 givenname: Zijian surname: Wang fullname: Wang, Zijian organization: School of Science, Wuhan University of Technology – sequence: 2 givenname: Xi orcidid: 0000-0002-3783-2041 surname: Fang fullname: Fang, Xi email: fangxi@whut.edu.cn organization: School of Science, Wuhan University of Technology – sequence: 3 givenname: Fei surname: Gao fullname: Gao, Fei organization: School of Science, Wuhan University of Technology – sequence: 4 givenname: Liang surname: Xie fullname: Xie, Liang organization: School of Science, Wuhan University of Technology – sequence: 5 givenname: Xianchen surname: Meng fullname: Meng, Xianchen organization: School of Science, Wuhan University of Technology
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Snippet	The discount {0–1} knapsack problem (D {0–1} KP) is a new variant of the knapsack problem. It is an NP-hard problem and also a binary optimization problem. As...
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SubjectTerms	Algorithms Artificial Intelligence Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Datasets Discounts Dynamic programming Evolutionary computation Image Processing and Computer Vision Knapsack problem Mathematical models Operators (mathematics) Optimization Parameters Probability and Statistics in Computer Science S.I.: Hybrid Approaches to Nature-inspired Optimization Algorithms and Their Applications Scaling factors Special Issue on Hybrid Approaches to Nature-inspired Optimization Algorithms and Their Applications
Title	An adaptive grey wolf optimization with differential evolution operator for solving the discount {0–1} knapsack problem
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