Multi-depot Electric Bus Scheduling Considering Operational Constraint and Partial Charging: A Case Study in Shenzhen, China

Electric buses (e-buses) demonstrate great potential in improving urban air quality thanks to zero tailpipe emissions and thus being increasingly introduced to the public transportation systems. In the transit operation planning, a common requirement is that long-distance non-service travel of the buses among bus terminals should be avoided in the schedule as it is not cost-effective. In addition, e-buses should begin and end a day of operation at their base depots. Based on the unique route configurations in Shenzhen, the above two requirements add further constraint to the form of feasible schedules and make the e-bus scheduling problem more difficult. We call these two requirements the vehicle relocation constraint. This paper addresses a multi-depot e-bus scheduling problem considering the vehicle relocation constraint and partial charging. A mixed integer programming model is formulated with the aim to minimize the operational cost. A Large Neighborhood Search (LNS) heuristic is devised with novel destroy-and-repair operators to tackle the vehicle relocation constraint. Numerical experiments are conducted based on multi-route operation cases in Shenzhen to verify the model and effectiveness of the LNS heuristic. A few insights are derived on the decision of battery capacity, charging rate and deployment of the charging infrastructure.

Robust Optimization Model for Single Line Dynamic Bus Dispatching

For effective bus operations, it is important to flexibly arrange the departure times of buses at the first station according to real-time passenger flows and traffic conditions. In dynamic bus dispatching research, existing optimization models are usually based on the prediction and simulation of passenger flow data. The bus departure schemes are formulated accordingly, and the passenger arrival rate uncertainty must be considered. Robust optimization is a common and effective method to handle such uncertainty problems. This paper introduces a robust optimization method for single-line dynamic bus scheduling. By setting three scenarios—the benchmark passenger flow, high passenger flow, and low passenger flow—the robust optimization model of dynamic bus departures is established with consideration of different passenger arrival rates in different scenarios. A genetic algorithm (GA) is improved for minimizing the total passenger waiting time. The results obtained by the proposed optimization method are compared with those from a stochastic programming method. The standard deviation of the relative regret value with stochastic optimization is 5.42%, whereas that of the relative regret value with robust optimization is 0.62%. The stability of robust optimization is better, and the fluctuation degree is greatly reduced.

Optimal Electric Bus Scheduling under Travel Time Uncertainty: A Robust Model and Solution Method

With the increasing adoption of electric buses (e-buses), e-bus scheduling problem has become an essential part of transit operation planning. As e-buses have a limited battery capacity, e-bus scheduling problem aims to assign vehicles to timetabled service trips on the bus routes considering their charging demand. Affected by the dynamic operation environment, the travel time and energy consumption of the e-buses often display considerable randomness, resulting in unexpected trip start delays and battery energy shortages. In this paper, we addressed the e-bus scheduling problem under travel time uncertainty by robust optimization approaches. We consider the cardinality constrained uncertainty set to formulate a robust multidepot EVSP model considering trip time uncertainty and partial recharging. The model is developed based on the dynamic programming equations that we formulated for trip chain robustness checking. A branch-and-price (BP) algorithm is devised to generate provably high-quality solutions for large-scale instances. In the BP algorithm, an efficient label setting algorithm is developed to solve the robust resource-constrained shortest path subproblem. Comprehensive numerical experiments are conducted based on the bus routes in Shenzhen to demonstrate the effectiveness of the suggested methodology. The robustness of the schedules was evaluated through Monte Carlo simulation. The results show that the trip start delay and battery energy shortage caused by the travel time uncertainty can be effectively reduced at the expense of an increase in the operational cost. A trade-off should be made between the reduction in infeasibility rate and increase in operational cost to choose a proper uncertainty budget.

Dynamic Bus Scheduling of Multiple Routes Based on Joint Optimization of Departure Time and Speed

Dynamic bus scheduling is a rational solution to the urban traffic congestion problem. Most previous studies have considered a single bus line, and research on multiple bus lines remains limited. Departure schedules have been typically planned by making separate decisions regarding departure times. In this study, a joint optimization model of the bus departure time and speed scheduling is constructed for multiple routes, and a coevolutionary algorithm (CEA) is developed with the objective function of minimizing the total waiting time of passengers. Six bus lines are selected in Shenyang, with several transfer stations between them, as a typical case. Experiments are then conducted for high-, medium-, and low-intensity case of smooth, increasing and decreasing passenger flow. The results indicate that combining the scheduling departure time and speed produces better performances than when using only scheduling departure time. The total passengers waiting time of the genetic algorithm (GA) group was reduced by approximately 25%–30% when compared to the fixed speed group. The total passengers waiting time of the CEA group can be reduced by approximately 17%–24% when compared to that in the GA group, which also holds true for a multisegment convex passenger flow. The feasibility and efficiency of the constructed algorithm were demonstrated experimentally.

Expression and Validation of Online Bus Headways considering Passenger Crowding

Passenger crowding in a city bus is uneven and the most crowded area always appears in the wheelbase of the carriage. The present study aimed to provide a sensitive indicator of the most crowded area to schedule bus headways online using a binocular camera sensor. The algorithm of standee density in the wheelbase area (SDWA) was given by a nonlinear regression model considering standees’ preferences for the standing area, and its goodness of fit and continuity were tested. Considering the characteristics of city bus operation, the proportion of the number of interstops determined from the SDWA was used as a judgment index for passenger crowding. Based on the SDWA algorithm and the judgment index, an online headway model of city buses was proposed, and the feasibility of such a model was verified through a case study in Xi’an city. The proposed model might be beneficial to bus scheduling, seating provision, and bus design.

Research on Optimization of Multi-Objective Regional Public Transportation Scheduling

The optimization of bus scheduling is a key method to improve bus service. So, the purpose of this paper is to address the regional public transportation dispatching problem, while taking into account the association between the departure time of buses and the waiting time of passengers. A bi-objective optimization model for regional public transportation scheduling is established to minimize the total waiting cost of passengers and to maximize the comprehensive service rate of buses. Moreover, a NSGA-II algorithm with adaptive adjusted model for crossover and mutation probability is designed to obtain the Pareto solution set of this problem, and the entropy weight-TOPSIS method is utilized to make a decision. Then the algorithms are compared with examples, and the results show that the model is feasible, and the proposed algorithms are achievable in solving the regional public transportation scheduling problem.