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.