PEACH: A Multi-Objective Evolutionary Algorithm for Complex Vehicle Routing with Three-Dimensional Loading Constraints

The Split Delivery Vehicle Routing Problem with Three-Dimensional Loading Constraints (3L-SDVRP) combines routing and packing challenges with two objectives (minimizing travel distance and maximizing vehicle loading rate). Meta-heuristic algorithms are effective in addressing 3L-SDVRP, with the balance between exploration (searching broadly for new solutions) and exploitation (focusing near known effective solutions) playing a pivotal role in their performance. However, achieving an optimal balance between exploration and exploitation, especially within the limited computational resources, remains an ongoing challenge. This paper introduces a Pareto-based Evolutionary Algorithm with Concurrent execution of crossover and Hierarchical neighborhood mutation (PEACH) with two novel features. Firstly, a new hierarchical neighborhood mutation is proposed. This mutation employs multiple neighborhood structures to produce diverse offspring from a single parent, thus increasing solution diversity for better exploitation. Additionally, our mutation is hierarchical rather than random, prioritizing mutation for individuals with higher nondomination ranks and guiding the search towards promising regions. Secondly, PEACH applies crossover and mutation concurrently, allowing each individual to undergo either or both processes simultaneously, rather than sequentially. Our experimental results demonstrate PEACH's effectiveness in tackling 3L-SDVRP.