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arXiv Machine Learning By Youssef Kamel Rezk, Pawe{\l} Gora

GNN-Guided Graph Coarsening and Adaptive QUBO Penalties for the Capacitated Vehicle Routing Problem with Time Windows on a Quantum Annealer

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The paper presents a method for reducing the size of Quadratic Unconstrained Binary Optimization (QUBO) models used to solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) on quantum annealers. It introduces adaptive penalty calibration to improve constraint satisfaction and replaces hand‑tuned merge heuristics with a graph neural network (GNN) that consistently achieves higher feasibility across Solomon benchmark families. Experiments on simulated annealing and a D‑Wave Advantage2 processor show significant reductions in constraint violations and improved feasibility rates, with the QUBO size remaining 5–6 times smaller.

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