Abstract:

To improve the loading efficiency of urban delivery vehicles and reduce carbon emissions during the distribution process, this paper establishes a mathematical model for the Fuel Consumption Vehicle Routing Problem with Three-dimensional Loading constraints and proposes an adaptive Memetic Non-dominated Sorting Genetic Algorithm II (Memetic NSGA-II) for its solution. Firstly, the algorithm utilizes the non-dominated sorting and crowding distance mechanisms of NSGA-II as its global search framework, integrating a three-dimensional packing module that satisfies the Last-In-First-Out (LIFO) constraint with local optimization strategies such as Variable Neighborhood Search (VNS) and Large Neighborhood Search (LNS). Furthermore, a hierarchical stagnation response mechanism is adopted, which adaptively activates various advanced reconstruction strategies based on the evolutionary state to maintain population diversity and effectively escape from local optima. Based on adapted 3L-CVRP benchmark instances, a set of Pareto optimal solutions representing the trade-off between carbon emissions and loading rates is obtained. Ablation studies demonstrate that removing the core components leads to a significant degradation in algorithm performance. To validate its feasibility and superiority, the proposed algorithm is benchmarked against state-of-the-art algorithms such as Hyper-heuristic Ant Colony Optimization (HHACO) and Three-Dimensional Adaptive Large Neighborhood Search (3D-ALNS-H). The results show that the proposed algorithm performs better on most instances, achieving a performance improvement of over 20% on large-scale instances and enabling high-quality solutions for this class of problem.

Key words: low-carbon distribution, three-dimensional packing, vehicle routing problem； multi-objective optimization, memetic algorithm