A lightweight genetic algorithm with variable neighborhood search for multi-depot vehicle routing problem with time windows

A multi-depot green vehicle routing problem with time windows considering customer satisfaction (MDGVRPTW-CS) was constructed. To optimize it, we proposed a lightweight genetic algorithm with variable neighborhood search (LGAVNS), which takes the genetic algorithm as the upper algorithm and the variable neighborhood algorithm as the neighborhood search algorithm. In our constructed algorithm, the neighborhood search operators were applied to the optimal gene instead of all genes. Additionally, an enhanced crossover operator was developed to facilitate the effective transmission of gene information. Finally, we extended and optimized the parameters of the algorithm. Experimental results demonstrated that our approach exhibited significant advantages in terms of optimization effectiveness and convergence speed compared to six state-of-the-art algorithms, particularly when addressing MDGVRPTW-CS in large-scale scenarios. Moreover, the lightweight nature of our algorithm can be utilized for optimizing both the number and location of depots while further exploring the optimization potential of MDGVRPTW-CS.