Bus scheduling with heterogeneous fleets: Formulation and hybrid metaheuristic algorithms

This paper focuses on optimizing mixed-fleet bus scheduling (MFBS) with vehicles of different sizes in public transport systems. We develop a novel mixed-integer nonlinear programming (MINLP) model to address the MFBS problem by optimizing vehicle assignment and dispatching programs. The model considers user costs, operator costs, and the crowding inconvenience of standing and sitting passengers. To tackle the complexity of the MFBS problem, we employ Genetic Algorithm (GA) and Grey Wolf Optimizer (GWO). Besides, we develop two hybrid metaheuristics, including GA-SA [a combination of GA and Simulated Annealing (SA)] and GWO-SA (a combination of GWO and SA), to improve optimization capabilities for the MFBS problem. We also employ a Taguchi approach to fine-tune the metaheuristics’ parameters. We widely examine and compare the metaheuristics’ performance across various-sized samples (small, medium, and large), considering solution quality, computational time, and the result stability of each algorithm. We also compare the metaheuristics’ solutions with the optimal solutions acquired by GAMS software in small and medium-scale samples. Our findings show that the GWO-SA outperforms the other metaheuristics. Applying our model to a real bus corridor in Santiago, Chile, we find that precise dispatching plans generated by more sophisticated/advanced algorithms (GA-SA and GWO-SA) lead to larger cost savings and improved performance compared to simpler algorithms (GA and GWO). Interestingly, utilizing more advanced algorithms makes a difference in terms of fleet planning in crowded scenarios, whereas for low and medium-demand cases, simpler dispatching algorithms could be used without a drop in accuracy.