An effective Bezier curve-based optimization (BCO) for large-scale numerical problems and 3D unmanned aerial vehicle path planning with efficient multiple threats evasion

In this paper, based on mathematical principles, we propose a new optimization algorithm, for solving large-scale numerical problems and complex real-world engineering tasks. This optimizer, named Bezier curve-based optimization (BCO), draws inspiration from Bezier curve theory. Drawing upon the geometric properties of different-order Bezier curves, BCO employs the linear Bezier curve to achieve exploitation, the quadratic Bezier curve to facilitate local optima avoidance, and the cubic Bezier curve to implement exploration. Furthermore, in the algorithm, we incorporate an adaptive exploitation-exploration balance factor that automatically maintains the balance between local exploitation and global exploration throughout the search process. First, we test BCO on 23 standard benchmark functions. Next, we evaluate its performance using the CEC2017 test suite with 10-, 30-, 50-, and 100-dimensional problems. Then, we further validate BCO’s effectiveness by combining test sets from CEC2014, CEC2020, and CEC2022 suites. Finally, we confirm BCO’s practicality by successfully applying it to 15 real-world engineering problems with constraints. The results of BCO are compared against those of 27 well-chosen algorithms, including 6 well-known, 8 cutting-edge, 8 top-performing hybrid, and 5 CEC champion algorithms. These comparisons show that BCO exhibits competitive capabilities in exploration and exploitation, balancing the two, convergence rate, avoiding local optima, and applicability. Finally, BCO is successfully applied to 3D unmanned aerial vehicle (UAV) path planning, which covers two types of waypoints, with each type corresponding to eight different terrain scenarios, and also takes into account the requirement of efficiently evading multiple threats. In comparison with 7 outstanding algorithms selected from the original 27, BCO achieves the top rank in the Friedman test, highlighting its superiority and competitiveness. These findings suggest that BCO is a powerful new tool for addressing complex real-world challenges, with promising potential for advancing future optimization research. This paper also presents a comprehensive collection of 312 metaheuristic algorithms, including multiple contributions from various research teams; by analyzing these algorithms, it uncovers non-uniform evolutionary patterns, offering readers a complete overview of the field. The source code of BCO is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/183097-bezier-curve-based-optimization-bco . © 2026 The Author(s).