Solving the maximum cut problem using Harris Hawk Optimization algorithm

The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging c...

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Vydáno v:	PloS one Ročník 19; číslo 12; s. e0315842
Hlavní autoři:	Islam, Md. Rafiqul, Islam, Md. Shahidul, Boni, Pritam Khan, Sarker, Aldrin Saurov, Anam, Md. Asif
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States Public Library of Science 30.12.2024 Public Library of Science (PLoS)
Témata:	Acceptance criteria Algorithms Analysis Apexes Biology and Life Sciences Chemical reactions Combinatorial analysis Computer and Information Sciences Computer Simulation Ecology and Environmental Sciences Eigenvalues Genetic algorithms Graph theory Hawks Health aspects Heuristic Mathematical optimization Observations Operators Optimization Optimization algorithms Parameter estimation Parameter modification Parameter sensitivity Physical Sciences Rank tests Research and Analysis Methods Search algorithms Bangladesh
ISSN:	1932-6203, 1932-6203
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Abstract	The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems, and tons of application areas make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO). Though HHO effectively solved some engineering optimization problems, is sensitive to parameter settings and may converge slowly, potentially getting trapped in local optima. Thus, HHO and some additional operators are used to solve the max-cut problem. Crossover and refinement operators are used to modify the fitness of the hawk in such a way that they can provide precise results. A mutation mechanism along with an adjustment operator has improvised the outcome obtained from the updated hawk. To accept the potential result, the acceptance criterion has been used, and then the repair operator is applied in the proposed approach. The proposed system provided comparatively better outcomes on the G-set dataset than other state-of-the-art algorithms. It obtained 533 cuts more than the discrete cuckoo search algorithm in 9 instances, 1036 cuts more than PSO-EDA in 14 instances, and 1021 cuts more than TSHEA in 9 instances. But for four instances, the cuts are lower than PSO-EDA and TSHEA. Besides, the statistical significance has also been tested using the Wilcoxon signed rank test to provide proof of the superior performance of the proposed method. In terms of solution quality, MC-HHO can produce outcomes that are quite competitive when compared to other related state-of-the-art algorithms.
AbstractList	The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems, and tons of application areas make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO). Though HHO effectively solved some engineering optimization problems, is sensitive to parameter settings and may converge slowly, potentially getting trapped in local optima. Thus, HHO and some additional operators are used to solve the max-cut problem. Crossover and refinement operators are used to modify the fitness of the hawk in such a way that they can provide precise results. A mutation mechanism along with an adjustment operator has improvised the outcome obtained from the updated hawk. To accept the potential result, the acceptance criterion has been used, and then the repair operator is applied in the proposed approach. The proposed system provided comparatively better outcomes on the G-set dataset than other state-of-the-art algorithms. It obtained 533 cuts more than the discrete cuckoo search algorithm in 9 instances, 1036 cuts more than PSO-EDA in 14 instances, and 1021 cuts more than TSHEA in 9 instances. But for four instances, the cuts are lower than PSO-EDA and TSHEA. Besides, the statistical significance has also been tested using the Wilcoxon signed rank test to provide proof of the superior performance of the proposed method. In terms of solution quality, MC-HHO can produce outcomes that are quite competitive when compared to other related state-of-the-art algorithms. The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems, and tons of application areas make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO). Though HHO effectively solved some engineering optimization problems, is sensitive to parameter settings and may converge slowly, potentially getting trapped in local optima. Thus, HHO and some additional operators are used to solve the max-cut problem. Crossover and refinement operators are used to modify the fitness of the hawk in such a way that they can provide precise results. A mutation mechanism along with an adjustment operator has improvised the outcome obtained from the updated hawk. To accept the potential result, the acceptance criterion has been used, and then the repair operator is applied in the proposed approach. The proposed system provided comparatively better outcomes on the G-set dataset than other state-of-the-art algorithms. It obtained 533 cuts more than the discrete cuckoo search algorithm in 9 instances, 1036 cuts more than PSO-EDA in 14 instances, and 1021 cuts more than TSHEA in 9 instances. But for four instances, the cuts are lower than PSO-EDA and TSHEA. Besides, the statistical significance has also been tested using the Wilcoxon signed rank test to provide proof of the superior performance of the proposed method. In terms of solution quality, MC-HHO can produce outcomes that are quite competitive when compared to other related state-of-the-art algorithms.The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of vertices that are divided due to the cut of the edges. Although it is an elementary graph partitioning problem, it is one of the most challenging combinatorial optimization-based problems, and tons of application areas make this problem highly admissible. Due to its admissibility, the problem is solved using the Harris Hawk Optimization algorithm (HHO). Though HHO effectively solved some engineering optimization problems, is sensitive to parameter settings and may converge slowly, potentially getting trapped in local optima. Thus, HHO and some additional operators are used to solve the max-cut problem. Crossover and refinement operators are used to modify the fitness of the hawk in such a way that they can provide precise results. A mutation mechanism along with an adjustment operator has improvised the outcome obtained from the updated hawk. To accept the potential result, the acceptance criterion has been used, and then the repair operator is applied in the proposed approach. The proposed system provided comparatively better outcomes on the G-set dataset than other state-of-the-art algorithms. It obtained 533 cuts more than the discrete cuckoo search algorithm in 9 instances, 1036 cuts more than PSO-EDA in 14 instances, and 1021 cuts more than TSHEA in 9 instances. But for four instances, the cuts are lower than PSO-EDA and TSHEA. Besides, the statistical significance has also been tested using the Wilcoxon signed rank test to provide proof of the superior performance of the proposed method. In terms of solution quality, MC-HHO can produce outcomes that are quite competitive when compared to other related state-of-the-art algorithms.
Audience	Academic
Author	Islam, Md. Shahidul Anam, Md. Asif Boni, Pritam Khan Sarker, Aldrin Saurov Islam, Md. Rafiqul
AuthorAffiliation	2 Department of Computer Science and Engineering, University of Asia Pacific, Dhaka, Bangladesh Nottingham Trent University School of Science and Technology, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND 3 Computer Science and Engineering Discipline, Khulna University, Khulna, Bangladesh 1 Department of Computer Science, American International University - Bangladesh, Dhaka, Bangladesh
AuthorAffiliation_xml	– name: 3 Computer Science and Engineering Discipline, Khulna University, Khulna, Bangladesh – name: 2 Department of Computer Science and Engineering, University of Asia Pacific, Dhaka, Bangladesh – name: 1 Department of Computer Science, American International University - Bangladesh, Dhaka, Bangladesh – name: Nottingham Trent University School of Science and Technology, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
Author_xml	– sequence: 1 givenname: Md. Rafiqul orcidid: 0000-0002-0777-6747 surname: Islam fullname: Islam, Md. Rafiqul – sequence: 2 givenname: Md. Shahidul orcidid: 0000-0003-1159-8688 surname: Islam fullname: Islam, Md. Shahidul – sequence: 3 givenname: Pritam Khan surname: Boni fullname: Boni, Pritam Khan – sequence: 4 givenname: Aldrin Saurov surname: Sarker fullname: Sarker, Aldrin Saurov – sequence: 5 givenname: Md. Asif surname: Anam fullname: Anam, Md. Asif
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CitedBy_id	crossref_primary_10_3390_math13091409 crossref_primary_10_1038_s41598_025_96986_5
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Snippet	The objective of the max-cut problem is to cut any graph in such a way that the total weight of the edges that are cut off is maximum in both subsets of...
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SubjectTerms	Acceptance criteria Algorithms Analysis Apexes Biology and Life Sciences Chemical reactions Combinatorial analysis Computer and Information Sciences Computer Simulation Ecology and Environmental Sciences Eigenvalues Genetic algorithms Graph theory Hawks Health aspects Heuristic Mathematical optimization Observations Operators Optimization Optimization algorithms Parameter estimation Parameter modification Parameter sensitivity Physical Sciences Rank tests Research and Analysis Methods Search algorithms
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Title	Solving the maximum cut problem using Harris Hawk Optimization algorithm
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