Research on Multi-commodity Heterogeneous Green Vehicle Routing Problem with Split Pickup and Delivery

Aiming at the vehicle routing problem with simultaneous pickup and delivery, considering the differences in customer commodity demands and vehicle heterogeneity, a mathematical model was established with the objective of minimizing the sum of vehicle carbon emission costs and total delivery distance. This model was used to describe the multi-commodity heterogeneous green vehicle routing problem with split pickup and delivery (MCHGVRPSPD). An enhanced variable neighborhood search (EVNS) algorithm was proposed to solve this problem. In the initial phase of EVNS, distance-capacity balancing (DCB) was designed to generate the initial solution. In the global search perturbation phase, one adaptive perturbation operation was incorporated to prevent the algorithm from prematurely converging to a local optimum. In the local search phase, four types of neighborhood search operations with capacity constraints were used to explore higher-quality neighborhood solution spaces. Finally, test case simulation experiments were conducted using GA, VNS, and ALNS algorithms to verify the effectiveness of EVNS in solving MCHGVRPSPD. The results show that compared to the three benchmark algorithms, the EVNS algorithm improves solution quality by 15% to 25%, while also demonstrating superior convergence and stability. Thus, EVNS is an effective algorithm for solving the MCHGVRPSPD.