View in EDS

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

Saved in:
Bibliographic Details
Title: Perpendicular Bisector Optimization Algorithm (PBOA): A Novel Geometric-Mathematics-Inspired Metaheuristic Algorithm for Controller Parameter Optimization.
Authors: Wu, Dafei, Chen, Wei, Zhang, Ying
Source: Symmetry (20738994); Sep2025, Vol. 17 Issue 9, p1410, 53p
Subject Terms: METAHEURISTIC algorithms, MATHEMATICAL optimization, SYNCHRONIZATION, SYMMETRY, BENCHMARK problems (Computer science), ENGINEERING design, SELF-tuning controllers
Abstract: 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. [ABSTRACT FROM AUTHOR]
Copyright of Symmetry (20738994) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Complementary Index
Description
Abstract: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<sup>−5</sup> mm, with stable anti-interference performance. [ABSTRACT FROM AUTHOR]
ISSN:20738994
DOI:10.3390/sym17091410