Modeling and Solving the Repair Crew Scheduling for the Damaged Road Networks Based on Q-Learning
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摘要: 受损路网的修复是灾害应急响应中的一个重要环节, 主要研究如何规划道路抢修队的修复活动, 为灾后救援快速打通生命通道.本文首先构建了抢修队修复和路线规划的数学模型, 然后引入马尔科夫决策过程来模拟抢修队的修复活动, 并基于Q学习算法求解抢修队的最优调度策略.对比实验结果表明, 本文方法能够让抢修队从全局和长远角度实施受损路段的修复活动, 在一定程度上提高了运输效率和修复效率, 可以为政府实施应急救援和快速安全疏散灾民提供有益的参考.Abstract: Repairing the damaged road network is an important issue in disaster emergency response, which mainly focuses on how to schedule the repair activities of the repair crew to clear the life path as soon as possible. In this paper, we first present a mathematical model of the repairing and scheduling of the repair crew. Next, we introduce the Markov decision process to simulate the repair activities of the repair crew. Additionally, the Q-learning algorithm is proposed to search for the optimal scheduling strategy of the repair crew for the damaged road network. Finally, the comparative experimental results demonstrate that the proposed approach is able to make the repair crew repair the damaged road network from the global and long-term perspective, improves the transport and repair efficiencies to a certain extent, and provides a useful reference for our government to carry out the emergency rescue and evacuate the victims as quickly and safely as possible.
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Key words:
- Disaster emergency response /
- damaged road network /
- repair crew scheduling /
- Markov decision process /
- Q-learning
1) 本文责任编委 张敏灵 -
图 4 两种算法在每个测试实例下的目标函数值
Fig. 4 The objective function values of the two algorithms for each test instance
图 5 灾情严重情况下两种算法的受损路段修复率
Fig. 5 Repair rate of the damaged edges of the two algorithms under a serious disaster
图 6 两种算法的修复路段数和应急点可达率
Fig. 6 The average numbers of repaired edges and node accessibilities of the two algorithms
表 1 受损路网和Q-learning算法的基本参数设置
Table 1 Basic parameter settings of the damaged road network and the Q-learning algorithm
$|V|$ $\frac{|E_r|}{|E|}$ $\frac{D_i}{\mathcal{D}_{i0}}$ $I_i$ $l_{ij}$ $t_{ij}$ $v$ $\lambda$ 训练周期数 $\varepsilon$ $\alpha$ $\gamma$ $\{26, 31, 36, 41\}$ $\{0.1, 0.25, 0.5\}$ $\{1.05, 1.25, 1.5\}$ [1,10] [1,10] [1,10] 1 0.9 $[100, 10\, 000]$ 0.1 0.4 0.2 
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表 2 36个不同测试实例的参数设置
Table 2 Parameter settings of the 36 different test instances
测试实例 1 2 3 4 5 6 7 8 9 $|V| = 26$ $\frac{|E_r|}{|E|}$ 0.1 0.1 0.1 0.25 0.25 0.25 0.5 0.5 0.5 $\frac{D_i}{\mathcal{D}_{i0}}$ 1.05 1.25 1.5 1.05 1.25 1.5 1.05 1.25 1.5 训练周期数 100 100 100 500 500 500 1 000 1 000 1 000 $|V| = 31$ $\frac{|E_r|}{|E|}$ 0.1 0.1 0.1 0.25 0.25 0.25 0.5 0.5 0.5 $\frac{D_i}{\mathcal{D}_{i0}}$ 1.05 1.25 1.5 1.05 1.25 1.5 1.05 1.25 1.5 训练周期数 500 500 500 1 000 1 000 1 000 3 000 3 000 3 000 $|V| = 36$ $\frac{|E_r|}{|E|}$ 0.1 0.1 0.1 0.25 0.25 0.25 0.5 0.5 0.5 $\frac{D_i}{\mathcal{D}_{i0}}$ 1.05 1.25 1.5 1.05 1.25 1.5 1.05 1.25 1.5 训练周期数 300 300 300 900 900 900 5 000 5 000 5 000 $|V| = 41$ $\frac{|E_r|}{|E|}$ 0.1 0.1 0.1 0.25 0.25 0.25 0.5 0.5 0.5 $\frac{D_i}{\mathcal{D}_{i0}}$ 1.05 1.25 1.5 1.05 1.25 1.5 1.05 1.25 1.5 训练周期数 300 300 300 3 000 3 000 3 000 10 000 10 000 10 000
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表 3 36个不同测试实例的加权目标函数值(均值$\pm$标准差)
Table 3 Weighted objective function values (mean and standard deviation) of the 36 different test instances
测试实例 $|V| = 26$ $|V| = 31$ $|V| = 36$ $|V| = 41$ Q-learning DP Q-learning DP Q-learning DP Q-learning DP 1 2 176.40 ± 4.21 2 160.05 5 388.19 ± 0.91 - 3 655.55 ± 34.83 3 739.2 6 096.11 ± 63.38 6 832.49 2 2 201.18 ± 1.7 2 192.71 5 438.54 ± 53.68 - 3 540.41 ± 0.76 3 964.6 6 005.27 ± 56.46 - 3 2 201.18 ± 1.7 2 192.71 5 427.4 ± 41.31 - 3 625.27 ± 36.28 3 960.7 6 276.5 ± 126.58 - 4 3 265.48 ± 4.71 3 924.92 2 800.84 ± 63.33 2 880.5 4 919.75 ± 33.79 5 657.62 4 844.56 ± 288.19 6 011.95 5 3 318.17 ± 43.28 3 839.56 2 697.35 ± 43.7 2 851.61 4 756.02 ± 94.22 5 765.13 4 586.82 ± 238.45 6 233.67 6 3 367.82 ± 75.62 3 705.91 2 784.31 ± 82.92 2 578.67 4 663.86 ± 71.74 6 777.95 4 309.49 ± 129.79 6 355.16 7 3 222.2 ± 179.3 - 4 405.91 ± 39.26 - 3 566.12 ± 62.31 - 6 189.04 ± 125.91 - 8 2 813.94 ± 15.41 - 3 824.53 ± 145 - 3 350.95 ± 76.4 - 5 891.23 ± 184.08 - 9 2 930.07 ± 69.46 - 3 919.55 ± 201.8 - 3 004.85 ± 135.9 - 5 356.4 ± 177.42 -
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