Graph-Coarsening Approach for the Capacitated Vehicle Routing Problem with Time Windows

TL;DR

This paper presents a multilevel graph coarsening method for the Capacitated Vehicle Routing Problem with Time Windows, improving computational efficiency and solution quality, especially on structured instances, using classical and quantum solvers.

Contribution

It introduces a novel graph coarsening and refinement strategy that enhances solution efficiency for large-scale CVRPTW instances with classical heuristics and quantum annealing.

Findings

Coarsening reduces computation time significantly.

On clustered instances, coarsening improves solution quality and feasibility.

Effectiveness of coarsening depends on instance structure, with better results on C-type instances.

Abstract

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a fundamental NP-hard optimization problem in logistics. Solving large-scale instances remains computationally challenging for exact solvers. This paper introduces a multilevel graph coarsening and refinement strategy that aggregates customers into meta-nodes based on a spatio-temporal distance metric. The reduced problem is solved using both classical heuristics and quantum annealing hardware, then expanded back into the original space with arrival times recomputed and constraint violations recorded. Comprehensive experiments on Solomon benchmarks demonstrate that our method significantly reduces computation time while preserving solution quality for classical heuristics. For quantum solvers, experiments across all 56 Solomon instances at $N=5$ and $N=10$ customers show that coarsening consistently reduces computation time and, on clustered (C-type) instances, simultaneously reduces vehicle count and route duration with no feasibility loss. Coarsening effectiveness is strongly instance-structure dependent: C-type instances achieve %100 post-coarsening feasibility with measurable quality improvements, while narrow-window random (R-type) instances present structural constraints that limit achievable coarsening depth.