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

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.