一种改进的准物理动态算法用于任意凸多边形中的高效圆覆盖
An Improved Quasi-Physical Dynamic Algorithm for Efficient Circular Coverage in Arbitrary Convex
AI总结：
本文提出改进的准物理动态算法，通过结构保持初始化、虚拟力场构建和边界包围策略，提升任意凸多边形中圆覆盖的效率。
摘要：
最优圆覆盖问题旨在找到一种配置，使得在给定区域内覆盖的面积最大。尽管对于简单情况存在理论最优解，但该问题的NP难特性使其在具有众多圆的复杂多边形中计算上是不可行的。现有方法大多局限于规则领域，而为不规则多边形设计的少数算法则面临初始化差、边界效应管理不当以及圆之间重叠过多等问题，导致覆盖效率低下。因此，我们提出了一种改进的准物理动态算法（IQPD）用于任意凸多边形。我们的核心贡献有三个方面：（1）提出一种保持结构的初始化策略，通过缩放和仿射变换将圆的六边形紧密堆积映射到目标多边形中；（2）构建一个包含摩擦力和半径扩展优化迭代模型的虚拟力场；（3）设计一种基于法线和切线梯度的边界包围策略以检索溢出的圆。实验结果表明，我们的算法在七种指标上显著优于四种最先进的方法，适用于各种凸多边形。本工作可能为实际应用中的操作优化或资源分配提供更高效的解决方案。
英文摘要：
The optimal circle coverage problem aims to find a configuration of circles that maximizes the covered area within a given region. Although theoretical optimal solutions exist for simple cases, the problem's NP-hard characteristic makes the problem computationally intractable for complex polygons with numerous circles. Prevailing methods are largely confined to regular domains, while the few algorithms designed for irregular polygons suffer from poor initialization, unmanaged boundary effects, and excessive overlap among circles, resulting in low coverage efficiency. Consequently, we propose an Improved Quasi-Physical Dynamic(IQPD) algorithm for arbitrary convex polygons. Our core contributions are threefold: (1) proposing a structure-preserving initialization strategy that maps a hexagonal close-packing of circles into the target polygon via scaling and affine transformation; (2) constructing a virtual force field incorporating friction and a radius-expansion optimization iteration model; (3) designing a boundary-surrounding strategy based on normal and tangential gradients to retrieve overflowing circles. Experimental results demonstrate that our algorithm significantly outperforms four state-of-the-art methods on seven metrics across a variety of convex polygons. This work could provide a more efficient solution for operational optimization or resource allocation in practical applications.
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