考虑区间重叠的多运营商公交调度优化

为解决多运营商在重叠区间的公交线路调度问题，在分析重叠区间特性的基础上，提出一种双层规划模型.上层模型代表政府机构，目标为使公交乘客总出行时间最小，变量为公交线路分配方案；下层模型代表运营商，目标为各运营商追求自身利润最大化，变量为运营线路的公交车发车间隔.应用NSGA-II算法(Elitist Non-Dominated Sorting Genetic Algorithm) 求解模型，并在长春市南关区北侧区域的公交线网进行案例分析.实验结果表明，优化后网络中公交乘客的总出行时间降低了5.93%，验证了模型的有效性.

Bus Dispatching Optimization of Multi-operators Considering Overlapping Interval

This study aims to address the problem of bus line scheduling of multiple operators in overlapping interval. Based on the analysis of the characteristics of overlapping interval, a bi- level programming model is proposed. The upper model represents the authority, and the objective is to minimize the total travel time of bus passengers. The decision variable is the bus line allocation plan. The lower model represents the operators, and each operator seeks for the maximum profit. The decision variables are the departure interval of the operating lines. The NSGA- II algorithm (Elitist Non-Dominated Sorting Genetic Algorithm) is applied to solve the model. Based on the bus line network of Nanguan District, Changchun City, a case study was performed. The experimental results show that the total travel time of bus passengers in the optimized network is reduced by 5.93%, which verifies the effectiveness of the proposed model.