Solving Time-Dependent Vehicle Routing Problem with Modulo Operation Genetic Algorithm Integrated with ALNS

In the era of rapid growth in online shopping, e-commerce and food delivery have become new shopping methods. This paper focuses on the time-constrained vehicle routing problem in logistics, aiming to minimize the number of vehicles and optimize vehicle dispatch routes as a combinatorial optimization objective. An improved strategy for the traditional genetic algorithm is proposed, which integrates a large neighborhood search algorithm and incorporates modulo operation concepts to enhance the traditional genetic algorithm (ALNS-MGA). In the selection strategy, a combination of elite selection and k-tournament selection is employed to ensure global search capability. During the crossover process, a modulo random linear combination operator (MRLCO) and a multi-path optimal cost operator (MOCO) are introduced for chromosome gene exchange. The former ensures sufficient crossover, while the latter accelerates convergence and enhances the algorithm’s local optimization capability. Finally, ALNS is utilized to improve solution quality. The proposed algorithm is tested on the standard Solomon dataset and compared with ALNS-GA, DBO, ALNS algorithms, and the best-known solutions. The experimental results show that the ALNS-MGA algorithm proposed in this paper is closer to the optimal solution than the other compared algorithms, and in some cases, even surpasses the known optimal solutions.