基于运营和出行成本的校车路径问题研究

为解决农村地区校车路网布局中校方运营成本过高，以及乘车站点分布散乱导致校车服务质量差的问题，建立混载与不混载场景下多目标校车路径规划问题（SBRP）模型.在不混载情景下，构建以学生出行成本和校方运营成本为优化目标的融合校车服务水平的SBRP数学模型；在混载情景下，构建考虑校车投入成本与运营成本的SBRP数学模型.通过对比多个启发式算法，确定基于模拟退火算法的求解流程和基于遗传算法求解结果的横向比对.最后，在国际基准案例上进行了测试，基于模拟退火算法引入不同搜索算子求解不同场景下构建的SBRP数学模型，应用于山东日照五莲县校车路径优化设计，结果表明不混载SBRP情景下，提出的方法较原校车运营方式，校车投入量、行驶里程、行程成本分别减少28.6％、37.8％、35.6％，考虑到学生的校车服务感知度，学生出行成本降低4.3％；由于混载情景的复杂性，难以有效兼顾出行成本，提出的方法较原校车运营方式的学生出行成本增加了0.5％，但校车投入量、行驶里程、行程成本分别减少37.5％、42.0％、35.8％，更好地验证了构建模型的有效性及模拟退火算法相较于遗传算法，能够更大程度提高农村地区校车服务质量和降低校方运营成本.

School bus routing considering operation and travel costs

In order to solve the problems of high operating cost and poor service quality of school bus due to the scattered distribution of bus stops in rural areas, multi-objective SBRP (School Bus Routing Problem) models were developed for the mixed-load and non-mixed-load scenarios.In the non-mixed-load scenario, a model of the SBRP was developed to optimize the students'' travel cost and school operating cost, while in the mixed-load scenario, another model of the SBRP was developed to consider the input cost and operation cost of the school bus.Several heuristic algorithms were compared, based on which the simulated annealing algorithm was selected to solve the models, and the horizontal comparison of the solution results based on genetic algorithm were determined.Tests were conducted on an international bench mark case and the constructed models were solved by introducing different search operators into the simulated annealing algorithm, then the proposed approach was applied to the optimal design of school bus routes in Wulian county, Rizhao, Shandong province.The results showed that in the non-mixed-load scenario, compared with the original school bus operation mode, the school bus input, mileage and travel cost were reduced by 28.6%, 37.8% and 35.6%, respectively, and students'' travel cost was reduced by 4.3% considering the students'' perception of school bus service.While in the mixed-load scenario, the proposed approach reduced the school bus input, mileage and travel cost by 37.5%, 42.0% and 35.8%, respectively;due to the complexity of the mixed-load scenario, it is difficult to take the travel cost into account, thus the students'' travel cost was increased by 0.5%.The proposed SBRP models were verified to be effective and the simulated annealing approach can optimize service quality and reduce operation cost of rural school bus to a greater extent than the genetic algorithm.