多配送中心危险货物配送路径鲁棒优化

针对危险货物配送路径对不确定因素敏感度较高的问题，提出了鲁棒性可调的多配送中心危险货物配送路径鲁棒优化方法。首先，以最小化运输风险和最小化运输成本为目标，根据Bertsimas鲁棒离散优化理论，建立鲁棒优化模型；然后，在改进型强度Pareto进化算法（SPEA2）的基础上设计一种三段式编码的多目标遗传算法进行求解，在遗传操作中对不同染色体段分别采用不同的交叉和变异操作，有效避免了种群进化过程中不可行解的产生；最后，以庆阳市西峰区部分路网为例进行实证研究，并将配送方案落实到运输过程的路段中，形成具体的运输路径。研究结果表明：在多配送中心下，运用该鲁棒优化模型及算法，能快速得到具有较好鲁棒性的危险货物配送路径。

Robust vehicle route optimization for multi-depot hazardous materials transportation

Focused on the issue that the sensitivity of hazardous materials transportation routes to uncertain factors is excessively high, a robust vehicle route optimization method for multi-depot hazardous materials transportation was proposed. Firstly, a robust optimization model was designed under the Bertsimas robust discrete optimization theory with the objective function of minimizing transportation risks and minimizing transportation costs. Secondly, on the basis of Strength Pareto Evolutionary Algorithm 2 (SPEA2), a multi-objective genetic algorithm with three-stage encoding was designed for the model. Then, different crossover and mutation operations were performed on the different segments of chromosomes during genetic manipulation,which effectively avoided the generation of infeasible solutions during population evolution. Finally, part of Qingyang Xifeng district road network was chosen as an empirical research example. Distribution plan was carried out at transportation process to form some specific transportation routes. The results show that better robust hazardous materials transportation routes can be quickly obtained by using the robust model and algorithm under multi-depot situation.