Knowledge-Guided Optimization for Complex Vehicle Routing with 3D Loading Constraints

The split delivery vehicle routing problem with three-dimensional loading constraints (3L-SDVRP) intertwines complex routing and packing challenges. The current study addresses 3L-SDVRP using intelligent optimization algorithms, which iteratively evolve towards optimal solutions. A pivotal aspect of these algorithms is search operators that determine the search direction and the search step size. Effective operators significantly improve algorithmic performance. Traditional operators like swap, shift, and 2-opt fall short in complex scenarios like 3L-SDVRP, mainly due to their limited capacity to leverage domain knowledge. Additionally, the search step size is crucial: smaller steps enhance fine-grained search (exploitation), while larger steps facilitate exploring new areas (exploration). However, optimally balancing these step sizes remains an unresolved issue in 3L-SDVRP. To address this, we introduce an adaptive knowledge-guided insertion (AKI) operator. This innovative operator uses node distribution characteristics for adaptive node insertion, enhancing search abilities through domain knowledge integration and larger step sizes. Integrating AKI with the local search framework, we develop an adaptive knowledge-guided search (AKS) algorithm, which effectively balances exploitation and exploration by combining traditional neighbourhood operators for detailed searches with the AKI operator for broader exploration. Our experiments demonstrate that the AKS algorithm significantly outperforms the state-of-the-art method in solving various 3L-SDVRP instances.