Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problem

Abstract

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-theart 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.

Multi-start team orienteering problem for UAS mission re-planning with data-efficient deep reinforcement learning

“…Additionally, Bono et al [15] proposed a modified Transformer model to handle the dynamic and stochastic VRPs (DS-VRPs) by using online measurements of the environment to online select the next vehicle via a vehicle-customer intersection module. More recently, Li et al [25] improved the AM to solve the Heterogeneous Capacitated VRP (HCVRP). Li et al [26] proposed the attention-dynamic model to solve the covering salesman problem (CSP).…”

“…However, Kool et al [3] showed that a greedy rollout baseline yields better results than a (learned) critic baseline. Many subsequent works, including [6,[25][26][27], and [7], used the greedy rollout baseline. Although the greedy rollout baseline is effective, it requires an additional forward-pass of the model, increasing the computational load on the device.…”