Hybrid fleet capacitated vehicle routing problem with flexible Monte–Carlo Tree search

Abstract

The rise in EVs popularity, combined with reducing emissions and cutting costs, encouraged delivery companies to integrate them in their fleets. The fleet heterogeneity brings new challenges to the Capacitated Vehicle Routing Problem (CVRP). Driving range and different vehicles' capacity constraints must be considered. A cluster-first, route-second heuristic approach is proposed to maximise the number of parcels delivered. Clustering is achieved with two algorithms: a capacitated k-median algorithm that groups parcel drop-offs based on customer location and parcel weight; and a hierarchical constrained minimum weight matching clustering algorithm which considers EVs' range. This reduces the solution space in a meaningful way for the routing. The routing heuristic introduces a novel Monte–Carlo Tree Search enriched with a custom objective function, rollout policy and a tree pruning technique. Moreover, EVs are preferred overother vehicles when assigning parcels to vehicles. A Tabu Search step further optimises the solution. This two-step procedure allows problems with thousands of customers and hundreds of vehicles to be solved accomodating customised vehicle constraints. The solution quality is similar to other CVRP implementations when applied to classic VRP test-instances; and its quality is superior in real-world scenarios when constraints for EVs must be used.