An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning
Abstract To address the limitations of the standard equilibrium optimizer (EO) in terms of insufficient optimization capability, multiple strategies are proposed to enhance its performance. These include a reverse equilibrium state pool, a non-uniform equilibrium state selection strategy, and an equ...
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Nature Portfolio
2025-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-15316-x |
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| author | Jianguo Yu Yanyang Lu Hamid Reza Karimi Derong Zhu Bin Li Yiming Wang |
| author_facet | Jianguo Yu Yanyang Lu Hamid Reza Karimi Derong Zhu Bin Li Yiming Wang |
| author_sort | Jianguo Yu |
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| description | Abstract To address the limitations of the standard equilibrium optimizer (EO) in terms of insufficient optimization capability, multiple strategies are proposed to enhance its performance. These include a reverse equilibrium state pool, a non-uniform equilibrium state selection strategy, and an equilibrium state mutation strategy. The reverse equilibrium state pool is introduced to encourage candidate solutions with poorer positions to search in a wider search space, under such considerations the global search ability of the improved EO can be enhanced. The non-uniform equilibrium state selection strategy is proposed to select equilibrium state. Under the proposed selection strategy, the candidate solutions with better positions are more likely to be chosen as the equilibrium state, allowing for sufficient exploration of positions near the current optimal point. The equilibrium state mutation strategy leads to cross mutation between candidate solutions and equilibrium state, increasing the likelihood of the group exploring the global optimal solution. To verify and further analyze the performance and superiority of the improved EO, i.e., reverse equilibrium states EO (R $$\mathrm {E^{2}}$$ O), 29 benchmark functions are adopted. It is verified theoretically from the experimental results that the R $$\mathrm {E^{2}}$$ O is with a significant improvement in performance by comparison between the standard EO and certain frequently-used heuristic optimization algorithms. Finally, the R $$\mathrm {E^{2}}$$ O is successfully applied in path planning for surface marine vehicles under the situations of both dynamic and static obstacles. |
| format | Article |
| id | doaj-art-e1792a9bae6a4bc8b636d74a2ead1b61 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-e1792a9bae6a4bc8b636d74a2ead1b612025-08-24T11:25:46ZengNature PortfolioScientific Reports2045-23222025-08-0115111610.1038/s41598-025-15316-xAn improved multi-strategy equilibrium optimizer for surface marine vehicle path planningJianguo Yu0Yanyang Lu1Hamid Reza Karimi2Derong Zhu3Bin Li4Yiming Wang5Zhengzhou University of Aeronautics, School of Computer ScienceLuoyang Institute of Science and Technology, School of Intelligent ManufacturingPolitecnico Di Milano, Department of Mechanical EngineeringLuoyang Institute of Science and Technology, School of Intelligent ManufacturingLuoyang Institute of Science and Technology, School of Intelligent ManufacturingLuoyang Institute of Science and Technology, Henan International Joint Laboratory of Composite Cutting Tools and Precision MachiningAbstract To address the limitations of the standard equilibrium optimizer (EO) in terms of insufficient optimization capability, multiple strategies are proposed to enhance its performance. These include a reverse equilibrium state pool, a non-uniform equilibrium state selection strategy, and an equilibrium state mutation strategy. The reverse equilibrium state pool is introduced to encourage candidate solutions with poorer positions to search in a wider search space, under such considerations the global search ability of the improved EO can be enhanced. The non-uniform equilibrium state selection strategy is proposed to select equilibrium state. Under the proposed selection strategy, the candidate solutions with better positions are more likely to be chosen as the equilibrium state, allowing for sufficient exploration of positions near the current optimal point. The equilibrium state mutation strategy leads to cross mutation between candidate solutions and equilibrium state, increasing the likelihood of the group exploring the global optimal solution. To verify and further analyze the performance and superiority of the improved EO, i.e., reverse equilibrium states EO (R $$\mathrm {E^{2}}$$ O), 29 benchmark functions are adopted. It is verified theoretically from the experimental results that the R $$\mathrm {E^{2}}$$ O is with a significant improvement in performance by comparison between the standard EO and certain frequently-used heuristic optimization algorithms. Finally, the R $$\mathrm {E^{2}}$$ O is successfully applied in path planning for surface marine vehicles under the situations of both dynamic and static obstacles.https://doi.org/10.1038/s41598-025-15316-xEquilibrium optimizerMultiple strategiesReverse equilibriumPath planningSurface marine vehicles |
| spellingShingle | Jianguo Yu Yanyang Lu Hamid Reza Karimi Derong Zhu Bin Li Yiming Wang An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning Scientific Reports Equilibrium optimizer Multiple strategies Reverse equilibrium Path planning Surface marine vehicles |
| title | An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning |
| title_full | An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning |
| title_fullStr | An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning |
| title_full_unstemmed | An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning |
| title_short | An improved multi-strategy equilibrium optimizer for surface marine vehicle path planning |
| title_sort | improved multi strategy equilibrium optimizer for surface marine vehicle path planning |
| topic | Equilibrium optimizer Multiple strategies Reverse equilibrium Path planning Surface marine vehicles |
| url | https://doi.org/10.1038/s41598-025-15316-x |
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