The Sparrow Search Algorithm (SSA), characterized by its simple structure and ease of implementation, nevertheless suffers from an insufficient balance between exploration and exploitation, making it prone to premature convergence and slow optimization progress. To address these shortcomings, this paper proposes a Geometric Sparrow Search Algorithm (GeoSSA). By integrating Good Nodes Set initialization, a Sine-Cosine Enhanced Producer position update strategy, and a Triangular-Walk Enhanced Edge Sparrow update strategy, GeoSSA significantly improves the global exploration ability, local exploitation efficiency, and convergence stability of the original SSA. To thoroughly validate the effectiveness of GeoSSA, we conducted ablation studies, qualitative analysis, and comparative experiments on 23 benchmark functions against state-of-the-art algorithms. Experimental results show that GeoSSA achieves the best or near-best performance in terms of average fitness, standard deviation, Wilcoxon tests, and Friedman rankings, with an Overall Effectiveness ($OE$) of 95.65\%. Its overall performance is significantly superior to all compared algorithms. In three-dimensional UAV path planning tasks, GeoSSA demonstrates excellent stability and superior path quality. In four categories of engineering design optimization problems, GeoSSA consistently attains the highest solution accuracy and strongest stability. GeoSSA not only exhibits outstanding global optimization performance on standard benchmark functions but also shows strong robustness and generalization ability in practical applications such as UAV path planning and engineering design. Therefore, GeoSSA provides an efficient and reliable solution framework for complex optimization problems.

翻译：麻雀搜索算法（SSA）结构简单、易于实现，但其探索与开发之间的平衡不足，容易陷入早熟收敛且优化进程缓慢。为克服这些缺陷，本文提出一种几何麻雀搜索算法（GeoSSA）。通过融合Good Nodes Set初始化策略、正弦-余弦增强的生产者位置更新策略以及三角游走增强的边缘麻雀更新策略，GeoSSA显著提升了原始SSA的全局探索能力、局部开发效率与收敛稳定性。为全面验证GeoSSA的有效性，我们在23个基准函数上进行了消融实验、定性分析及与前沿算法的对比实验。实验结果表明，GeoSSA在平均适应度、标准差、Wilcoxon检验和Friedman排序方面均取得最优或接近最优的性能，其综合有效性（$OE$）达95.65%，整体表现显著优于所有对比算法。在三维无人机路径规划任务中，GeoSSA展现出优异的稳定性与卓越的路径质量。在四类工程优化设计问题中，GeoSSA均能持续获得最高的求解精度与最强的稳定性。GeoSSA不仅在标准基准函数上表现出突出的全局优化性能，在无人机路径规划与工程设计等实际应用中也展现出强大的鲁棒性与泛化能力。因此，GeoSSA为复杂优化问题提供了一个高效可靠的求解框架。