Model and algorithm for resolving regional bus scheduling problems with fuzzy travel times

Regional bus scheduling is necessary to urban public transport that is complicated by the necessity of assigning trips that belong to several routes to buses located at different depots while reducing fleet size and operating costs. Considering the reality of emergencies that may interfere with the ability of vehicles to complete trips on time, it is reasonable to use fuzzy numbers to express uncertain delay times. Based on this idea, this paper proposes a chance-constrained programming model of regional bus scheduling that will reflect additional constraints such as the capacities of related depots and fueling needs. The objective of this paper is to maximize utilization of fleet vehicles. To overcome the defect of premature convergence in the particle swarm optimization algorithm (PSO), an improved PSO is proposed by using an organic fusion with group search optimization. Finally, an example demonstrates the correctness and effectiveness of the model and algorithm.