Simulated Annealing Algorithm for Vehicle Routing with Stochastic Travel Times and Soft Time Windows

In the context of urban logistics, travel time uncertainty is a critical challenge for efficient route planning. Thus, this study proposes an algorithm based on Simulated Annealing (SA) that addresses this problem through a dual approach. On the one hand, the effectiveness of the algorithm is validated in deterministic VRPTW scenarios, using classical Solomon instances and achieving an average GAP of 3.42% in the most complex cases. On the other hand, a stochastic model fed with empirical data from Google Maps is integrated, designed to capture real-time traffic variability, thus addressing the VRPSTTW problem. The results show that the algorithm not only maintains a standard deviation of 2,048 energy units, consolidating its robustness to fluctuations in the optimal parameters, but also stands out for its ability to generate robust solutions in urban contexts with high temporal uncertainty. This proposal, being based on real data and not on theoretical simulations, positions the algorithm as a strategic tool to optimize logistic operations in dynamic and volatile environments.