An adaptive memetic approach for heterogeneous vehicle routing problems with two-dimensional loading constraints

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.