AI 中文总结
针对凸多边形无线节点部署问题，提出改进类物理动态算法IQPD，通过保结构初始化、精细化虚拟力模型与边界环绕策略，实现更高的覆盖率与节点利用率，性能优于多种元启发式算法。
AI 中文摘要
在给定区域内部署无线节点以最大化覆盖面积，是无线传感器网络、无人机路径规划、基站部署等工业领域中的重要挑战。该实际问题在数学上等价于最优圆覆盖问题。尽管数学上对简单情形存在理论最优配置，但该问题的NP难特性使得其在含大量节点的复杂多边形中计算代价过高。现有方法通常针对规则域设计，而适用于不规则多边形的方法常存在初始化差、覆盖重叠过多、无法将节点约束在边界内等问题，导致覆盖效率低、运行时间长。为解决这些问题，我们提出了一种适用于任意凸多边形中无线节点部署的改进类物理动态算法（IQPD）。我们的贡献有三点：（1）提出了一种保结构初始化方法，通过缩放和仿射变换将六角密堆积模式映射到目标多边形，确保接近最优的初始节点分布；（2）构建了一种精细化虚拟力模型，通过引入摩擦力和半径扩展优化机制以减少覆盖面积重叠；（3）开发了一种利用法向和切向梯度的边界环绕策略，用于在初始优化后重新定位部署在边界外的节点。大量实验结果表明，我们的方法在各类凸多边形形状（包括随机生成数据和真实场景）中，始终优于其他新型元启发式算法。我们的方法在所有对比算法中实现了最高的覆盖率和节点利用率，大幅提升了无线覆盖效率。
英文摘要
Deploying wireless nodes to maximize coverage area within a given region is an important challenge in wireless sensor networks, UAV path planning, base station placement and other industrial fields. This practical problem can be mathematically equivalent to an optimal circle covering problem. Although theoretical optimal configurations exist for simple cases in mathematics, the NP-hard nature of this problem makes it computationally prohibitive for complex polygons with numerous nodes. Existing approaches are usually designed for regular domains, while those applicable to irregular polygons often suffer from poor initialization, excessive coverage overlap and failure to constrain nodes within the boundary, leading to low coverage efficiency and long runtime. To address these issues, we propose an improved quasi-physical dynamic algorithm (IQPD) for wireless node deployment in arbitrary convex polygons. Our contributions are threefold: (1) proposing a structure-preserving initialization that maps a hexagonal close packing pattern into the target polygon via scaling and affine transformation, ensuring near-optimal initial node distribution; (2) constructing a refined virtual force model by incorporating friction and a radius-expansion optimization mechanism to reduce coverage area overlap; (3) developing a boundary encircling strategy leveraging normal and tangential gradients to reposition nodes deployed outside boundaries after initial optimization. Extensive experimental results demonstrate that our method consistently outperforms other new metaheuristic algorithms across diverse convex polygon shapes, including randomly generated data and real-world scenarios. Our method achieves the highest coverage rate and node utilization rate among all compared algorithms, greatly improving wireless coverage efficiency.
