Abstract This study proposes a continuous maximal covering location problem (C-MCLP) that is often confronted in the rescuing scenes of natural disasters such as earthquakes, floods, and storms. The aim of the research is to optimize (dynamically and rapidly) the continuous locations of the communication hub-centers (e.g., moving vehicles or boats) of the self-organizing mobile network that is quickly established in such signal-free fields. The proposed C-MCLP well represents the real emergency rescues, but it is more complex to solve than the traditional discrete MCLP models, where the hub facilities are typically immobile and placed only within a limited set of candidate sites. We developed two mixed-integer linear programming (MILP) models for the C-MCLP. The first model is the single-period C-MCLP model, which is applicable to a stochastic rescuing environment where the rescue teams (RTs) do not have planned movements and can move towards any direction. The second one is the multi-period C-MCLP model, which is for cases where RTs have planned movements in multiple periods/phases. We introduced a new linearization method for the non-linear Euclidean distance with a controllable approximation error allowance, by which the proposed models are linearized and can be solved optimally using commercial MIP solvers such as CPLEX and Lingo. To solve large-sized problems, we provide a MILP-based fix-and-optimize heuristic approach to obtain near-optimal solutions with high computational efficiency. Then we conduct simulation experiments to verify the proposed models and heuristic approach with an intended time-limit setting on small-sized and large-sized test problem instances, respectively, with up to 1000 nodes of rescue teams. Finally, experimental results are analyzed and compared with those obtained using the traditional k-means clustering algorithms, which confirm that the proposed models and approach are applicable for the C-MCLPs in emergency rescue scenes, and can yield rapid and good solutions.

中文翻译：

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大规模自然灾害救援场景中的连续最大覆盖定位问题

摘要 本研究提出了地震、洪水、风暴等自然灾害救援场景中经常遇到的连续最大覆盖位置问题（C-MCLP）。研究的目的是优化（动态和快速）自组织移动网络的通信枢纽中心（例如，移动的车辆或船只）的连续位置，该网络在此类无信号领域中快速建立。所提出的 C-MCLP 很好地代表了真正的紧急救援，但它比传统的离散 MCLP 模型更复杂，在传统离散 MCLP 模型中，枢纽设施通常是固定的，并且仅放置在有限的候选站点集内。我们为 C-MCLP 开发了两个混合整数线性规划 (MILP) 模型。第一个模型是单周期 C-MCLP 模型，适用于随机救援环境，救援队（RT）没有计划的移动，可以向任何方向移动。第二个是多周期 C-MCLP 模型，适用于 RT 计划在多个周期/阶段进行移动的情况。我们为非线性欧几里得距离引入了一种新的线性化方法，具有可控的近似误差容限，通过该方法对所提出的模型进行线性化，并且可以使用商业 MIP 求解器（例如 CPLEX 和 Lingo）进行优化求解。为了解决大型问题，我们提供了一种基于 MILP 的修复和优化启发式方法，以获得具有高计算效率的近似最优解。然后我们进行模拟实验，分别在小型和大型测试问题实例上分别使用多达 1000 个救援队节点，以预期的时间限制设置来验证所提出的模型和启发式方法。最后，将实验结果与使用传统k-means聚类算法获得的结果进行分析和比较，证实所提出的模型和方法适用于应急救援场景中的C-MCLPs，并且可以产生快速和良好的解决方案。