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Perpendicular Bisector Optimization Algorithm (PBOA): A Novel Geometric-Mathematics-Inspired Metaheuristic Algorithm for Controller Parameter Optimization

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Publicado en:Symmetry vol. 17, no. 9 (2025), p. 1410-1463
Autor principal: Wu, Dafei
Otros Autores: Chen, Wei, Zhang, Ying
Publicado:
MDPI AG
Materias:
Accuracy
Search process
Design optimization
Principles
Convergence
Exploitation
Design engineering
Optimization techniques
Hydrologic cycle
Mutation
Genetic algorithms
Decision making
Optimization
Solution space
Synchronism
Algorithms
Foraging behavior
Segments
Optimization algorithms
Geometry
Symmetry
Heuristic methods
Acceso en línea:Citation/Abstract
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Resumen:To address the inadequate balance between exploration and exploitation of existing algorithms in complex solution spaces, this paper proposes a novel mathematical metaheuristic optimization algorithm—the Perpendicular Bisector Optimization Algorithm (PBOA). Inspired by the geometric symmetry of perpendicular bisectors (the endpoints of a line segment are symmetric about them), the algorithm designs differentiated convergence strategies. In the exploration phase, a slow convergence strategy is adopted (deliberately steering particles away from the optimal region defined by the perpendicular bisector) to expand the search space; in the exploitation phase, fast convergence refines the search process and improves accuracy. It selects 4 particles to construct line segments and perpendicular bisectors with the current particle, enhancing global exploration capability. The experimental results on 27 benchmark functions, compared with 15 state-of-the-art algorithms, show that the PBOA outperforms others in accuracy, stability, and efficiency. When applied to 5 engineering design problems, its fitness values are significantly lower. For H-type motion platforms, the PBOA-optimized platform not only achieves high unidirectional motion accuracy, but also the average synchronization error of the two Y-direction motion mechanisms reaches ±2.6 × 10−5 mm, with stable anti-interference performance.
ISSN:2073-8994
DOI:10.3390/sym17091410
Fuente:Engineering Database