用最少总覆盖面积放置m个传感器，确保每个目标至少被指定数量的传感器覆盖。
Multi-Covering a Point Set by $m$ Disks with Minimum Total Area
- 设计快速启发式算法确定传感器初始位置
- 通过整数规划优化，使总覆盖面积最小化
- 适用于需要高鲁棒性覆盖的机器人传感部署
机器人传感中常见问题是：为一组资产部署传感器以实现稳健监控，要求每个资产p至少被κ(p)个传感器覆盖。给定需被m个传感器覆盖的n个资产，每个传感器具有圆形感知范围，如何布置传感器以最小化总覆盖面积？本文提出并分析了一种快速启发式方法，并用其初始化精确的整数规划求解。随后，通过修改整数规划公式和调整候选圆盘集合，施加传感器间的分离约束，提升解的质量与实用性。
原文摘要 · Abstract (English)
A common robotics sensing problem is to place sensors to robustly monitor a set of assets, where robustness is assured by requiring asset $p$ to be monitored by at least $κ(p)$ sensors. Given $n$ assets that must be observed by $m$ sensors, each with a disk-shaped sensing region, where should the sensors be placed to minimize the total area observed? We provide and analyze a fast heuristic for this problem. We then use the heuristic to initialize an exact Integer Programming solution. Subsequently, we enforce separation constraints between the sensors by modifying the integer program formulation and by changing the disk candidate set.
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