We develop optimization approaches to the graph-clear problem, a pursuit-evasion problem where mobile robots must clear a facility of intruders. The objective is to minimize the number of robots required. We contribute new formal results on progressive and contiguous assumptions and their impact on algorithm completeness. We present mixed-integer linear programming and constraint programming models, as well as new heuristic variants for the problem, comparing them to previously proposed heuristics. Our empirical work indicates that our heuristic variants improve on those from the literature, that constraint programming finds better solutions than the heuristics in run-times reasonable for the application, and that mixed-integer linear programming is superior for proving optimality. Given their performance and the appeal of the model-and-solve framework, we conclude that the proposed optimization methods are currently the most suitable for the graph-clear problem.

中文翻译：

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入侵者警报！解决移动机器人图形清晰问题的优化模型

我们针对图清除问题开发了优化方法，图清除问题是追逃问题，移动机器人必须清除入侵者的设施。目的是最大程度地减少所需的机器人数量。我们根据渐进和连续的假设及其对算法完整性的影响提供新的正式结果。我们提出了混合整数线性规划和约束规划模型，以及针对该问题的新启发式变体，将它们与先前提出的启发式进行了比较。我们的经验工作表明，我们的启发式变量比文献中的启发式变量有所改进，约束编程比适用于应用程序的运行时启发式算法找到了更好的解决方案，并且混合整数线性规划在证明最优性方面更胜一筹。