Collaborative optimization of vehicle formation and timetable for modular autonomous bus considering demand uncertainty:A data-driven continuous approximate method

The emerging modular autonomous vehicle (MAV) provides new opportunities to address the imbalance between supply and demand in the public transportation system. The continuous approximation (CA) model can efficiently solve the optimal time-varying headway of bus corridors, but the current CA model for MAV corridors does not consider the demand uncertainty, and its vehicle formation method still has limitations. To solve these gaps, this paper proposes collaborative optimization of vehicle formation and timetable for modular autonomous bus considering demand uncertainty based on a data-driven continuous approximate method. First, a time-dependent passenger flow disturbance parameter is introduced to capture the uncertainty demand, and the CA model is extended under demand uncertainty. Second, data-driven stochastic optimization methods (i.e., stochastic programming and distributed robust optimization) are developed to address the loss function term with the random passenger flow in the CA model. Then, based on the proposed CA model, a mixed integer linear programming (MILP) model is developed to obtain the optimal vehicle formation. Finally, two numerical experiments were conducted to verify the effectiveness and superiority of the proposed model. Results show that, (1) the proposed vehicle formation model achieves up to a 9.8% reduction in average total system cost compared to the benchmark model. (2) stochastic programming and distributed robust optimization do not significantly reduce the average system total cost when demand is uncertain, but can significantly improve the robustness of timetables and vehicle formation. Compared to the deterministic model, the proposed method achieves a reduction of over 90% in both the sample standard deviation and the interquartile range on the test dataset. In summary, the proposed method can provide theoretical support for modular bus operation and scheduling under passenger flow uncertainty.