Aplicación de tiempos de viaje como semimétrica en k-means para la agrupación y optimización de rutas

Abstract

This work explores the adaptation of the K-means algorithm to use travel times as a semimetric, applied to the analysis of georeferenced data in an urban context, specifically in the city of Bogotá. By incorporating travel times obtained via the Google Directions API, the model allows the formation of clusters that reflect not only geographical proximity but also traffic conditions, making the clustering process more realistic in complex urban environments. To evaluate the quality of the clustering, validation indices such as the Silhouette index and the Davies-Bouldin index were employed, which indicated optimal configurations for the clusters. This approach contributes to logistical planning in the city and opens up opportunities for future research. Potential extensions include the use of georeferenced time series to capture traffic patterns throughout the day and the inclusion of different modes of transportation, such as public transit or walking. It is also proposed to investigate variations in the travel time semimetric, which could facilitate the use of advanced techniques such as spectral clustering, further enhancing the analysis of spatial data in urban applications.