Efficiency in public transportation: a new flow direction method for optimizing multi-route networks

<p dir="ltr">This study introduces a novel hybrid metaheuristic method, the Flow Direction Method (FDM), to optimize public transportation routes in large-scale networks. The method evaluates route efficiency using a newly defined metric called Flow Direction Performance (FDP), which accounts for the circuity of all possible trips along a route. The proposed model was tested on real-world data from Istanbul's bus network, involving 732 routes and over 5,000 stops. To manage computational complexity, the network was divided into 250 clusters using k-means clustering. Optimization was applied to each cluster individually using both the FDM and a classical Genetic Algorithm (GA) for comparison. The results showed that FDM improved average FDP values in 74.8% of the clusters and outperformed GA significantly. Additionally, route performance was evaluated using both Euclidean and Google Maps-based travel matrices. Even with approximate Euclidean distances, FDM demonstrated robust performance, which further improved when real-world travel data was employed. The method has shown strong potential for practical applications in urban mobility planning, offering more efficient and accessible transit networks for metropolitan areas.