<scp>AI</scp> ‐Infused Evolutionary Optimization for Multi‐Depot Vehicle Routing: A Case Study of Beverage Distribution

ABSTRACT This study addresses the multi‐depot vehicle routing problem (MDVRP) using real‐world data from a beverage distribution company in Istanbul. Seven models are evaluated: Slime Mold Algorithm (SMA), Deep Q‐Network (DQN), Attention, Attention‐based SMA (ATSMA), Graph Neural Network+Long Short‐Term Memory (LSTM)+Reinforcement Learning (NGL‐RL), Graph Neural Network+RL (GR), and Evolutionary Optimization+Fuzzy Logic (EF). A key contribution is the construction of a time‐distance matrix based on historical GPS data from the Mobiliz tracking system, avoiding reliance on third‐party APIs like OSRM and enabling more accurate long‐term traffic estimation. This AI‐infused approach combines evolutionary optimization with deep learning and RL, enhancing the adaptability and performance of MDVRP solutions. Model performance is evaluated using metrics such as mean squared error, mean absolute error, reward‐based analysis, ANOVA, and so forth. Among all models, ATSMA achieves the highest accuracy and route efficiency, while the Attention model shows strong generalization by effectively aligning customer demand with vehicle capacity. The results highlight the superiority of hybrid AI‐infused methods in addressing complex logistics optimization problems.