{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T04:14:29Z","timestamp":1789100069402,"version":"build-2803163510"},"reference-count":71,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T00:00:00Z","timestamp":1756512000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Research Fund Project of Yunnan Provincial Department of Education","award":["2023J1598"],"award-info":[{"award-number":["2023J1598"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2014the 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 \u00b12.6 \u00d7 10\u22125 mm, with stable anti-interference performance.<\/jats:p>","DOI":"10.3390\/sym17091410","type":"journal-article","created":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T08:28:15Z","timestamp":1756715295000},"page":"1410","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Perpendicular Bisector Optimization Algorithm (PBOA): A Novel Geometric-Mathematics-Inspired Metaheuristic Algorithm for Controller Parameter Optimization"],"prefix":"10.3390","volume":"17","author":[{"given":"Dafei","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Yunnan Land and Resources Vocational College, Kunming 650500, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Yunnan Land and Resources Vocational College, Kunming 650500, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Yunnan Land and Resources Vocational College, Kunming 650500, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1007\/s11831-020-09412-6","article-title":"A Comprehensive Analysis of Nature-Inspired Meta-Heuristic Techniques for Feature Selection Problem","volume":"28","author":"Sharma","year":"2021","journal-title":"Arch. 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