Random Walk on Bézier Curves for Global Optimization
For metaheuristic optimization, BWE offers an interpretable geometry-driven alternative to nature-inspired methods, balancing exploration and exploitation with competitive results.
Bézier Walk Evolution (BWE) reformulates evolutionary search as adaptive trajectory construction using Bézier curves and a distance-aware random walk, achieving strong performance on 41 benchmark functions (CEC2017/2022) across 10–100 dimensions and outperforming L-SHADE and CMA-ES.
Balancing exploration and exploitation remains a central challenge in metaheuristic optimization. To address this issue, this paper proposes Bézier Walk Evolution (BWE), a geometry-driven optimization framework that reformulates evolutionary search as adaptive trajectory construction in the decision space. BWE integrates Bézier curve modeling with a distance-aware random walk mechanism to generate topology-guided search trajectories. By adaptively varying the curve order during evolution, the proposed method enables a smooth transition from diversified global exploration to refined local exploitation. Higher-order Bézier curves leverage multiple population-derived control points to enhance search diversity, while lower-order curves generate near-linear trajectories to improve convergence efficiency. This adaptive geometric search mechanism provides an interpretable alternative to conventional nature-inspired designs. Extensive experiments on 41 benchmark functions from the CEC2017 and CEC2022 suites, spanning dimensions from 10 to 100, show that BWE achieves strong overall performance and favorable scalability compared with 7 classical and 6 state-of-the-art optimizers, including L-SHADE and CMA-ES. Additional evaluations on five constrained engineering design problems further demonstrate the practical applicability and robustness of BWE.