In this study, we investigate a bilevel optimization model for the hazmat transportation problem with lane reservation. The problem lies in selecting lanes to be reserved in the network and planning paths for hazmat transportation tasks. The trade-off among transportation cost, risk, and impact on the normal traffic is considered. By using the traffic flow theory, we quantify the impact on the normal traffic and modify the traditional risk measurement model. The problem is formulated as a multiobjective bilevel programming model involving the selection of reserved lanes for government and planning paths for hazmat carriers. Two hybrid metaheuristic algorithms based on the particle swarm optimization algorithm and the genetic algorithm, respectively, are proposed to solve the bilevel model. Their performance on small-scale instances is compared with exact solutions based on the enumeration method. Finally, the computational results on large-scale instances are compared and sensitivity analysis on the key parameters is presented. The results indicate the following: (1) Both algorithms are effective methods for solving this problem, and the method based on the particle swarm optimization algorithm requires a shorter computation time, whereas the method based on the genetic algorithm shows more advantages in optimality. (2) The bilevel model can effectively reduce the total risk of the hazmat transportation while considering the interests of hazmat carriers and ordinary travellers. (3) The utilization rate of reserved lanes increases with an increasing number of tasks. Nevertheless, once the proportion of hazmat vehicles becomes excessive, the advantage of reducing the risk of the reserved lanes gradually decreases.

中文翻译：

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带车道预留的危险品运输问题的双层优化

在这项研究中，我们研究了带车道保留的危险品运输问题的双层优化模型。问题在于选择要在网络中保留的车道并规划危险品运输任务的路径。考虑运输成本，风险以及对正常交通的影响之间的权衡。通过使用交通流理论，我们量化了对正常交通的影响并修改了传统的风险衡量模型。该问题被表述为一个多目标的双层规划模型，涉及选择政府专用车道和危险品运输工具的规划路径。提出了两种分别基于粒子群优化算法和遗传算法的混合元启发式算法来求解双层模型。将它们在小规模实例上的性能与基于枚举方法的精确解决方案进行比较。最后，对大型实例的计算结果进行了比较，并对关键参数进行了敏感性分析。结果表明：（1）两种算法都是解决该问题的有效方法，基于粒子群算法的算法需要较短的计算时间，而基于遗传算法的算法在最优性方面更具优势。（2）双层模型可以有效降低危险品运输的总风险，同时考虑危险品运输者和普通旅行者的利益。（3）预留通道的利用率随着任务数量的增加而增加。不过，