  Existing deep reinforcement learning (DRL) based methods for solving the
capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous
vehicle fleet, in which the fleet is assumed as repetitions of a single
vehicle. Hence, their key to construct a solution solely lies in the selection
of the next node (customer) to visit excluding the selection of vehicle.
However, vehicles in real-world scenarios are likely to be heterogeneous with
different characteristics that affect their capacity (or travel speed),
rendering existing DRL methods less effective. In this paper, we tackle
heterogeneous CVRP (HCVRP), where vehicles are mainly characterized by
different capacities. We consider both min-max and min-sum objectives for
HCVRP, which aim to minimize the longest or total travel time of the vehicle(s)
in the fleet. To solve those problems, we propose a DRL method based on the
attention mechanism with a vehicle selection decoder accounting for the
heterogeneous fleet constraint and a node selection decoder accounting for the
route construction, which learns to construct a solution by automatically
selecting both a vehicle and a node for this vehicle at each step. Experimental
results based on randomly generated instances show that, with desirable
generalization to various problem sizes, our method outperforms the
state-of-the-art DRL method and most of the conventional heuristics, and also
delivers competitive performance against the state-of-the-art heuristic method,
i.e., SISR. Additionally, the results of extended experiments demonstrate that
our method is also able to solve CVRPLib instances with satisfactory
performance.
