基于韧性最优的灾后公路网修复调度研究

为有效修复灾后公路网的受损路段从而加快恢复路网畅通,研究以韧性最优为目标的灾后公路网修复调度问题。首先,采用交通需求满足率表示路网性能,并构建路网性能韧性和恢复速度韧性评价指标。其次,构建基于韧性最优的修复调度双层规划模型,其中上层模型是多目标混合整数规划模型,用以确定修复路段的选择和修复先后顺序,下层模型为日变交通流分配模型,模拟修复期间的路网交通流动态演变。然后,采用禁忌搜索算法和Frank-Wolfe算法分别求解上层模型和下层模型,并通过循环迭代得到模型最优解。最后,通过案例分析验证模型和算法的有效性。研究结果表明:在一定数量的修复资金和抢修队约束下,该模型得到的最优修复调度方案能最大限度地提升路网韧性,并且在修复过程中,只有当受灾区域内某线路中的所有受损路段均完成修复后,路网性能才开始呈阶梯式上升,并且路网性能的提升速度表现为先慢后快。对不同参数的敏感性分析表明:修复预算的增加使路网性能韧性和恢复速度韧性分别以15.65%和17.72%的平均速度增长和降低,但当修复预算超过1 800万元后,只增加修复预算不一定能获取更优的修复调度方案;当决策者偏好系数变化时,路网的性能韧性和恢复速度韧性具有相反的变化趋势,且2个韧性指标的平均变化率分别为5.96%和4.48%;增加抢修队数量可提升路网的性能韧性和恢复速度韧性,但增加抢修队数量所产生的边际效益逐步降低,分别由0.11和0.43降至0.01和0.02。

Restoration Scheduling for Post-disaster Road Networks Based on Resilience Optimization

To accelerate the restoration of road network connectivity by effectively repairing damaged road segments in a post-disaster network, the restoration scheduling problem for post-disaster road networks aimed at resilience optimization was studied. First, the traffic demand satisfaction ratio was used to measure road network performance, based on which two road network resilience indicators, that is, network performance resilience and recovery rapidity, were established. Second, a restoration scheduling bi-level programming model based on resilience optimization was proposed, where the upper-level model, that is, a multi-objective mixed-integer programming model, was used to determine the road restoration selection and identify the restoration sequence. The lower-level model, that is, a day-to-day traffic assignment model, was employed to simulate the dynamic evolution of road network traffic flow during the restoration period. Then, the tabu search algorithm and the Frank-Wolfe algorithm were adopted to solve the upper-level and lower-level models, respectively, and the optimal solution was obtained by the iteration of the two algorithms. Finally, the effectiveness of the proposed model and algorithm was tested using a case study. The results show that under the given restoration budget constraint and work crew constraint, the optimal restoration scheduling generated by the proposed method can increase the road network resilience to the full extent. During the restoration process, only after all damaged road segments of a certain line in the affected area are restored, can the road network performance begin to increase in a stepped manner, and the speed of the road network performance improvement is low first and then high. Sensitivity analysis of different parameters shows that, with an increase in restoration budget, the performance resilience and recovery rapidity of the road network increase and decrease at average rates of 15.65% and 17.72%, respectively, and only increasing the restoration budget may not obtain a better restoration schedule. When the decision maker's preferences change, the performance resilience and recovery rapidity of the road network have opposite trends, and the average change rates of the two resilience metrics are 5.96% and 4.48%, respectively. Increasing the number of repair crews can improve the performance resilience and the recovery rapidity; however, the marginal benefit of increasing the number of repair crews drop gradually from 0.11 and 0.43 to 0.01 and 0.02, respectively.