Graph Coarsening Approach to the Vehicle Routing Problem: An Approximation Strategy

In the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing, solving complex optimization problems such as the Vehicle Routing Problem (VRP) remains a formidable challenge. To overcome this obstacle, we introduce a novel method in this paper that focuses on reducing the number of edges in a graph based on Euclidean distances between vertices while preserving the crucial characteristics needed for solving the VRP. Our graph coarsening approach combined with the inflation method enables the reduced graph to be processed efficiently by classical, quantum or hybrid (quantum-classical) solvers, resulting in a faster computation time. When using the proposed method with hybrid algorithms, we have demonstrated an improvement of approximately 50% in the solution found by the hybrid solver. The practicality of our method on quantum hardware highlights its potential to contribute to the advancement of quantum and hybrid algorithms and applications during the NISQ era.