Private enterprises and governments around the world use speed cameras to control traffic flow and limit speed excess. Cameras may be exposed to difficult weather conditions and typically require frequent maintenance. When deciding the order in which maintenance should be performed, one has to consider both the traveling times between the cameras and the traffic flow that each camera is supposed to monitor. In this paper, we study the problem of routing a set of technicians to repair cameras by minimizing the total weighted latency, that is, the sum of the weighted waiting times of each camera, where the weight is a parameter proportional to the monitored traffic. The resulting problem, called weighted k-traveling repairman problem (wkTRP), is a generalization of the well-known traveling repairman problem and can be used to model a variety of real-world applications. To solve the wkTRP, we propose an iterated local search heuristic and an exact branch-and-cut algorithm enriched with valid inequalities. The effectiveness of the two methods is proved by extensive computational experiments performed both on instances derived from a real-world case study, as well as on benchmark instances from the literature on the wkTRP and on related problems.

中文翻译：

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加权k-旅行修理工的分支剪切和迭代局部搜索：在测速相机维护中的应用

世界各地的私营企业和政府都使用测速摄像机来控制交通流量并限制超速行驶。相机可能会暴露在恶劣的天气条件下，通常需要经常维护。在确定执行维护的顺序时，必须同时考虑摄像机之间的行驶时间以及每个摄像机应该监控的交通流量。在本文中，我们研究了通过最小化总加权等待时间（即每个摄像机的加权等待时间之和）来路由一组技术人员来维修摄像机的问题，其中权重是与监视的流量成比例的参数。由此产生的问题称为加权k旅行修理工问题（wkTRP），是对众所周知的旅行修理工问题的概括，可以用于对各种实际应用进行建模。为了解决wkTRP，我们提出了一种迭代的局部搜索启发式算法和一种精确的分支-剪切算法，该算法丰富了有效的不等式。这两种方法的有效性通过对来自实际案例研究的实例以及来自wkTRP文献和相关问题的基准实例进行的大量计算实验证明。