Real-time Optimization For Urban Bus Rapid Transit Adjustment Strategy Based On Model Predictive Control

With the strategic goals of "carbon peaking" and "carbon neutrality" put forward,vigorously developing urban public transportation has become the key to promote the transformation of urban road transportation in low-carbon life.The outline of the national "14th Five-Year Plan" proposes to raise "bus priority" to a national strategy and turn "green travel" into a public consensus.However,at present,there are various problems in urban public transport,such as frequent "bus bunching" phenomenon,unbalanced headway,large operation delay,etc.,which lead to lower bus operation efficiency and passenger satisfaction,and lower attractiveness compared with other modes of transportation.Urban Bus Rapid Transit(BRT)is a new type of public transport with large traffic volume and high speed,and its operation and service level still has great room for improvement.Therefore,it is of great theoretical significance and practical application value to study the real-time optimization and adjustment of urban BRT.Based on the model predictive control method,this paper studies the real-time optimization and adjustment strategy of BRT in certain environment and uncertain environment,so as to balance the headway of bus lines and reduce the waiting time of passengers.The main research content of this paper includes the following three parts:Firstly,the real-time optimization and adjustment of BRT based on determining passenger demand is studied.A nonlinear dynamic programming model is constructed,which takes the minimization of headway deviation,schedule deviation and control amount as the optimization goal,considering the constraints of departure time,passenger flow,and holding time,and taking the control quantities of dwell time and running time as decision variables.Then,a mixed integer quadratic programming model is obtained by linearization method.Finally,a bus real-time optimization and adjustment algorithm based on model predictive control is designed,and the optimization problem is solved online according to real-time feedback information,so as to meet the dynamic and realtime requirements of bus optimization and adjustment.Secondly,the real-time optimization and adjustment of BRT in uncertain environment is studied.By using the scenario set with known probability to describe the uncertainty of passenger arrival rate and running time disturbance,A bus robust optimization and adjustment model based on situational passenger flow demand and running time disturbance is constructed.This model aims to minimize the headway deviation,schedule deviation and control amount in all scenarios,and considers four types of constraints: timetable constraints,passenger flow constraints,control constraints and other constraints in each scenario.Then a bus real-time robust optimization and adjustment algorithm based on model predictive control is designed,which generates an optimization and adjustment strategy that is less sensitive to uncertain disturbances and better for all scenarios.At the same time,the algorithm can simplify complex optimization and adjustment problems and ensure the real-time optimization and adjustment of bus.Thirdly,taking Beijing BRT Line 3 as a simulation example,the effectiveness of the proposed optimization adjustment model and real-time algorithm is verified.Firstly,the optimization and adjustment strategy under certain environment is simulated.Compared with the adjustment strategy without adjustment and based on timetable,it shows that the real-time optimization and adjustment strategy based on model predictive control can reduce timetable delay and headway delay by 60% and 83% respectively.Then,the actual case of Beijing BRT Line 3 is also used to verify the scenario robust optimization adjustment strategy,The results show that the relative error of the timetable deviation and headway deviation of each scenario under the robust adjustment strategy is very small compared with the optimal value obtained by the deterministic model,which shows that the robust optimization adjustment strategy has a good adjustment effect on the scenario set and can effectively reduce the sensitivity to uncertain parameters.Finally,by changing the size of the scenario scale,it is found that the solution time is still less than 10 s when the scale is large,which verifies the real-time performance of the model predictive control algorithm under the scenario robust optimization.