不确定性需求下快速路应急疏散鲁棒优化模型

Robust Optimization Model of Free Way Emergency Evacuation with Uncertain Demand

针对快速路应急疏散时仅知道疏散需求的变化范围和总量的情况,建立了不确定需求下的快速路疏散鲁棒优化模型.通过设定疏散控制过程中主线车流维持自由流状态,并同步化各位置的疏散起始计量时间,简化了模型表述,凸现了对不确定需求的处理.假设匝道到达车流与释放车流之间具有仿射关系,从而可以利用强对偶理论将原有的半无限优化模型转化为可处理的一般优化模型.通过求解该一般化模型可确定前述仿射关系的具体参数,进而利用该仿射关系实现对快速路系统的实际疏散控制.上述一般化模型的目标函数值可提供最差情景下的被疏散者总等待时间的上界,并确保疏散的可行性.通过与随机抽样规划方法的数值计算比较,证实了新模型与方法的有效性.

Aiming at the situation that only the scope and total amount of evacuation requirements were known during the emergency evacuation of expressways,a robust optimization model for expressway evacuation under uncertain demand was established.Through setting the main line traffic flow,the free flow state was maintained in the evacuation control process.The evacuation start measurement time of each location was also synchronized to simplify the model representation and highlight the treatment of uncertain demand.Assuming that there is an affine relationship between the ramp arrival traffic flow and the release traffic flow,the semi-infinite optimization model can be transformed into a computable model by using the strong duality theory.The specific parameters of the affine relation can be determined by solving the generalized model,then the affine relation is used to realize the actual evacuation control of the expressway system.The objective function value of the above generalized model can provide the upper bound of the total waiting time of evacuees in the worst scenario and ensure the feasibility of evacuation.The validity of the new model and method is verified by comparison with the numerical calculation of random sampling planning method.