PEAC-HNF: A Novel Multi-Objective Evolutionary Algorithm for Split Delivery Vehicle Routing With Three-Dimensional Loading Constraints

The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading Constraints (3L-SDVRP) integrates routing and packing problems, aiming to maximize the vehicle load efficiency and minimize the total travel distance. Solving 3L-SDVRP is critical for logistics and transportation industries. However, achieving an appropriate balance between exploration (searching for new solutions) and exploitation (refining known solutions) in metaheuristic algorithms for 3L-SDVRP, especially under limited computational resources, remains challenging. Furthermore, the application of multi-objective optimization algorithms to the 3L-SDVRP remains a largely unexplored area, particularly when considering the inherent trade-offs between the two conflicting objectives. To address these challenges, this paper introduces a new Pareto-based Evolutionary Algorithm with Concurrent crossover and Hierarchical Neighborhood Filtering mutation (PEAC-HNF), distinguished by its novel Hierarchical Neighborhood Filtering (HNF) mutation. The HNF mutation uses diverse neighborhood structures to generate offspring, adopts a hierarchical strategy prioritizing individuals with higher nondomination ranks, and incorporates an offspring filtering process to save computational resources. HNF allows PEAC-HNF to improve its exploitation capabilities while maintaining exploration strengths, achieving a balanced performance. Comparisons with state-of-the-art algorithms across various problem instances (242 instances in total) demonstrate the effectiveness of PEAC-HNF. Further analysis highlights the critical role of the HNF mutation in enhancing algorithmic performance. The utilization of the HNF mutation can extend beyond PEAC-HNF to other complex optimization problems.