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...

Full description

Saved in:
Bibliographic Details
Main Authors: Jianguo Yu, Yanyang Lu, Hamid Reza Karimi, Derong Zhu, Bin Li, Yiming Wang
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Scientific Reports
Subjects:
Online Access:https://doi.org/10.1038/s41598-025-15316-x
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849226388212547584
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
collection DOAJ
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
record_format Article
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
work_keys_str_mv AT jianguoyu animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT yanyanglu animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT hamidrezakarimi animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT derongzhu animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT binli animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT yimingwang animprovedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT jianguoyu improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT yanyanglu improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT hamidrezakarimi improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT derongzhu improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT binli improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning
AT yimingwang improvedmultistrategyequilibriumoptimizerforsurfacemarinevehiclepathplanning