In urban rail transit,train frequencies and timetables largely determine the levels of trans-portation service.To address the problem of imbalanced spatial and temporal distribution of passen-ger flow in urban rail transit,this study comprehensively optimizes urban railway train frequencies and timetables under a flexible composition operational mode.The optimization achieves accurate matching between the transportation capacity and passenger demand and guarantees the service level of passengers while reducing the operating costs of the enterprise.First,a train operational line candi-date set is modeled considering train frequencies,safety intervals,and other constraints.Then,with the goal of minimizing the total waiting time of passengers and the total operating costs of the enter-prise,we construct a mixed-integer nonlinear mathematical model to address the integrated optimiza-tion problem.Second,based on the nonlinear characteristics of the model,a heuristic algorithm is de-signed for an efficient solution based on the framework of a variable neighborhood search algorithm.Specifically,in this framework,three types of neighborhood structures are designed and then combin-edunder a simulation process of dynamic passenger loading.Finally,the proposed model and algo-rithm are validated using actual data from a city rail line as a case study.Results show that compared with the fixed composition mode,the proposed method can reduce operating costs by approximately 7.05%under the condition that the average waiting time of passengers increases by only 0.26 min,as this more effectively balancesthe level of passenger service and operating costs.In practical applica-tions,operating companies can set the weighting coefficients according to their operational objec-tives and further balance the level of passenger service with the total operating costsof the enterprise.
维普
万方数据