The heterogeneous fleet vehicle routing problem with two-dimensional loading constraints (2L- HFVRP) is a complex variant of the classical vehicle routing problem. 2L-HFVRP seeks for minimal cost set of routes to serve a set of customers using a fleet of vehicles of different capacities, fixed and variable operating costs, different dimensions, and restricted loading constraints. To effectively deal with the 2L-HFVRP, we propose a two-stage method that successively calls the routing stage and the packing stage. For the routing stage, we propose an adaptive memetic approach that integrates new multi-parent crossover operators with multi-local search algorithms in an adaptive manner. A time-varying fitness function is proposed to avoid prematurity and improve search performance. An adaptive quality-and-diversity selection mechanism is devised to control the application of the memetic operators and the local search algorithms. In the packing stage, five heuristics are adopted and hybridised to perform the packing process. Experiments on a set of 36 2L-HFVRP benchmark instances demonstrate that the proposed method provides highly competitive results in comparison with state-of-the-art algorithms. In particular, the proposed method obtains the best results for several instances.

具有二维负载约束（2L-HFVRP）的异构机队车辆路径问题是经典车辆路径问题的复杂变体。2L-HFVRP寻求使用最少成本的路线来服务一组使用不同容量，固定和可变运营成本，不同尺寸和有限装载限制的车辆的客户。为了有效处理2L-HFVRP，我们提出了一种两阶段方法，该方法依次调用路由阶段和打包阶段。在路由阶段，我们提出了一种自适应模因方法，该方法以自适应方式将新的多父交叉算子与多局部搜索算法集成在一起。提出了时变适应度函数，以避免过早发生并提高搜索性能。设计了一种自适应的质量和多样性选择机制来控制模因算子和局部搜索算法的应用。在打包阶段，采用五种启发式方法并进行混合以执行打包过程。在一组36个2L-HFVRP基准实例上进行的实验表明，与最先进的算法相比，该方法可提供极具竞争力的结果。特别地，所提出的方法在多个实例中获得了最佳结果。