A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

TL;DR

This paper introduces a hybrid metaheuristic for solving a broad class of Rich Vehicle Routing Problems with heterogeneous fleets, combining local search, set partitioning, and combined neighborhoods to efficiently find high-quality solutions.

Contribution

It presents the first unified approach capable of solving over 12 variants of heterogeneous fleet RVRPs, demonstrating effectiveness on extensive benchmarks.

Findings

Achieved solutions for 71.70% of benchmark instances

Produced high-quality solutions with low standard deviation

Combined neighborhoods did not significantly improve solution quality

Abstract

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments.