[Paper Review] A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

Puca Huachi Vaz Penna, Anand Subramanian+3 more|arXiv (Cornell University)|Mar 5, 2018

Vehicle Routing Optimization Methods78 references21 citations

TL;DR

This paper proposes a hybrid matheuristic combining iterated local search with variable neighborhood descent and set partitioning to solve a broad class of heterogeneous fleet vehicle routing problems (HFRVRPs), including variants with time windows, backhauls, split deliveries, and site dependency. The method achieves high-quality solutions, retrieving or improving 71.70% of best-known results across 643 benchmark instances, with low solution variance, and reveals that intensive route optimization outperforms complex fleet reassignment strategies.

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.

Motivation & Objective

• To address the lack of unified solution methods for rich vehicle routing problems (RVRPs) with heterogeneous fleets, which combine multiple real-world constraints such as time windows, backhauls, and site dependency.
• To extend existing matheuristic frameworks—originally designed for homogeneous fleets—to handle heterogeneous fleets and complex attributes simultaneously.
• To evaluate whether combined neighborhoods that jointly optimize routes and reassign vehicles yield significant solution improvements over standard approaches.
• To demonstrate the effectiveness of infeasible solution handling and advanced perturbation schemes in solving heterogeneous fleet problems with time windows.
• To provide a general-purpose algorithm capable of solving over 12 distinct HFRVRP variants using a single, unified framework.

Proposed method

• The algorithm integrates iterated local search (ILS) with randomized variable neighborhood descent (RVND) for local intensification, enabling exploration of diverse solution neighborhoods.
• A set partitioning (SP) formulation is used to recombine promising routes generated during the ILS phase, optimizing the final solution via a MIP solver.
• A novel perturbation scheme is introduced that exploits fleet heterogeneity by varying vehicle types during solution diversification.
• The method accepts infeasible solutions during search, particularly beneficial for time window constraints, and uses efficient move evaluation techniques from Vidal et al. (2014b).
• Combined neighborhoods are tested that jointly modify route sequences and reassign vehicles via heuristic or exact re-optimization, though these show limited benefit.
• The algorithm generalizes the ILS-RVND-SP matheuristic of Subramanian et al. (2013), extending it to heterogeneous fleets and multiple problem attributes.

Experimental results

Research questions

• RQ1 Can a unified matheuristic approach effectively solve a broad class of heterogeneous fleet rich VRPs with multiple attributes?
• RQ2 Does the integration of set partitioning and ILS with RVND significantly improve solution quality compared to prior methods?
• RQ3 Is the use of combined neighborhoods—simultaneously modifying routes and reassigning vehicles—more effective than standard local search in HFRVRPs?
• RQ4 How does the acceptance of infeasible solutions impact performance on time window-constrained instances?
• RQ5 Does intensive route-level optimization yield better results than frequent, complex fleet reassignments in heterogeneous fleet settings?

Key findings

• The proposed hybrid matheuristic retrieved or improved the best-known solution for 71.70% of the 643 benchmark instances tested across 20 problem sets and 12 VRP variants.
• The algorithm achieved high solution quality with low standard deviation, indicating consistent performance across diverse problem instances.
• On average, the method reduced solution gaps by 15.72% across the 12 problem variants, with the largest improvements observed in HFFVRPMBTW (RC) instances, where the average gap was -15.72%.
• For the SDepVRPTW problem, the algorithm matched or slightly exceeded the best-known solutions, with an average gap of 0.34% and an average solution time of 1,424.57 seconds.
• Despite theoretical appeal, combined neighborhoods that reassign vehicles during route modification did not yield significant quality gains, suggesting that computational effort is better spent on deeper route optimization.
• The use of infeasible solutions and a fleet-aware perturbation scheme proved crucial for handling time window constraints, especially in complex variants like HFFVRPMBTW.