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.

翻译：最优圆形覆盖问题旨在寻找一种圆形配置，使得给定区域内被覆盖的面积最大化。尽管对于简单情形存在理论最优解，但该问题的NP难特性使得对于具有大量圆形的复杂多边形，计算变得难以处理。现有方法主要局限于规则区域，而为不规则多边形设计的少数算法则存在初始化不佳、边界效应未受控制以及圆形间过度重叠等问题，导致覆盖效率低下。因此，我们提出了一种用于任意凸多边形的改进准物理动力学算法。我们的核心贡献有三点：(1) 提出了一种结构保持初始化策略，通过缩放和仿射变换将圆形的六角密堆积映射到目标多边形中；(2) 构建了一个包含摩擦力的虚拟力场以及半径扩展优化迭代模型；(3) 设计了一种基于法向和切向梯度的边界环绕策略，以回收溢出的圆形。实验结果表明，我们的算法在各种凸多边形上，在七项指标上均显著优于四种最先进的方法。这项工作可为实际应用中的操作优化或资源分配提供一种更高效的解决方案。