Solving Real-World Optimization Problems using Near-Term Quantum Computing with Applications in Vehicle Routing and Drone Delivery

Abstract

Quantum computing (QC) stands at the cusp of revolutionizing computation, yet its near-term potential, constrained by Noisy Intermediate-Scale Quantum (NISQ) devices, remains underexplored. This dissertation investigates how hybrid quantum-classical algorithms can address combinatorial optimization challenges in logistics, focusing on vehicle routing and drone delivery—NP-hard problems with exponential solution spaces that defy classical exhaustive methods. Amidst NISQ limitations like limited qubits and high noise, we confront key challenges: encoding complex constraints, e.g., time windows, battery capacity, into quantum models, balancing quantum and classical components for scalability, and accessing scarce quantum resources. By integrating quantum annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) with classical heuristics, this work demonstrates QC’s practical utility, advancing both optimization theory and real-world logistics applications. The dissertation unfolds across four core contributions. First, the Hybrid Quantum Tabu Search (HQTS) optimally solves the 50-location Capacitated Vehicle Routing Problem (CVRP), achieving a 4.72% optimality gap. Secondly, we refine HQTS to reach a 2.15% gap with enhanced QA utilization, outperforming prior hybrids on standard datasets. Third, adapting HQTS for the CVRPTWwith D-Wave’s Constrained Quadratic Model solver yields a 3.85% gap on 100-location instances, leveraging a novel heuristic to ensure time-window feasibility where quantum outputs falter. Lastly, QUADRO, a pioneering framework for drone delivery, employs QAOA-driven routing and hybrid scheduling, minimizing transit time and makespan for fleets of 2–11 drones needing fewer than 100 qubits, rivaling classical benchmarks on adapted Augerat datasets. These advances, tested via D-Wave’s Advantage system and Qiskit simulations, showcase hybrid strategies that mitigate NISQ constraints, delivering scalable, feasible solutions to logistics challenges. This work establishes near-term QC’s viability for combinatorial optimization, bridging theoretical promise with practical impact. Synthesizing quantum exploration with classical refinement achieves competitive performance, e.g., matching or surpassing Google ORTools in select CVRPTW cases, while illuminating NISQ limits, such as feasibility degradation beyond small scales. These hybrid strategies deliver scalable, feasible solutions, from a 2.15% optimality gap for CVRP to effective drone fleet management with fewer than 100 qubits, illuminating quantum computing’s potential despite its current constraints. Ultimately, this dissertation positions hybrid QC as a transformative tool for optimization challenges, offering a robust foundation for scaling quantum optimization into operational reality.