The integration of drones into last-mile delivery operations has the potential to significantly enhance responsiveness and reduce delivery costs. In this paper, we study the Coordinated Truck-Drone Routing Problem (CTDRP), where a truck serves as mobile base station that launches and retrieves a drone to deliver to geographically dispersed customers. Some customers are served by the truck, while others are served by the drone. The objective is to optimize the truck route and drone assignments in order to minimize the total delivery distance, including both ground and aerial travel. We model the CTDRP as a combinatorial optimization problem and solve it using the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm that offers promising capabilities for discrete optimization. The proposed method is benchmarked against classical solutions obtained using the Gurobi optimizer, and the results show that QAOA delivers competitive performance. These findings demonstrate the applicability of QAOA in solving integrated aerial-ground logistics problems and support its potential for advancing quantum-enhanced transportation systems.
The integration of drones into last-mile delivery operations has the potential to significantly enhance responsiveness and reduce delivery costs. In this paper, we study the Coordinated Truck-Drone Routing Problem (CTDRP), where a truck serves as mobile base station that launches and retrieves a drone to deliver to geographically dispersed customers. Some customers are served by the truck, while others are served by the drone. The objective is to optimize the truck route and drone assignments in order to minimize the total delivery distance, including both ground and aerial travel. We model the CTDRP as a combinatorial optimization problem and solve it using the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm that offers promising capabilities for discrete optimization. The proposed method is benchmarked against classical solutions obtained using the Gurobi optimizer, and the results show that QAOA delivers competitive performance. These findings demonstrate the applicability of QAOA in solving integrated aerial-ground logistics problems and support its potential for advancing quantum-enhanced transportation systems.
Quantum computing holds transformative potential for optimizing large-scale drone fleet operations, yet its nearterm limitations necessitate hybrid approaches blending classical and quantum techniques. This work introduces Quantum Unmanned Aerial Delivery Routing Optimization (QUADRO), a novel hybrid framework addressing the Energy-Constrained Capacitated Unmanned Aerial Vehicle Routing Problem and the Unmanned Aerial Vehicle Scheduling Problem. By formulating these challenges as Quadratic Unconstrained Binary Optimization problems, QUADRO leverages the Quantum Approximate Optimization Algorithm for routing and scheduling, enhanced by classical heuristics and post-processing. We minimize total transit time in routing, considering payload and battery constraints, and optimize makespan scheduling across various drone fleets. Evaluated on adapted Augerat benchmarks (16-51 nodes), QUADRO competes against classical and prior hybrid methods, achieving scalable solutions with fewer than one hundred qubits. The proposed results underscore the viability of hybrid quantumclassical strategies for real-world drone logistics, paving the way for quantum-enhanced optimization in the Noisy Intermediate Scale Quantum era.
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.
The rise of e-commerce and calls for sustainability make things hard for businesses in cities, showing where standard shipping methods fail. The study shows a new hybrid quantum-classical optimization scheme that bridges three major gaps: AV-drone coordination that does not work well in the real world; environmental claims that have not been proven; and real-world limits that are not considered enough. In a modern design, the Quantum Approximate Optimization Algorithm (QAOA) and Deep Q-Networks (DQN) are put together. There are two main variables used for optimization: regulatory factors (β =0.32) and energy limits (β =0.56). The framework cuts costs by 28% and speeds up delivery times by 32%, while keeping 89% of solution accuracy on noisy quantum simulations. Run 1,000 Monte Carlo models and compare them to real data to do this. Checking the methods with three steps—computer simulation, stakeholder analysis (n=25, ±=0.81), and policy paper review—is what makes sure they work. The results make it possible to measure the difference in success between models and real life. They show that in the real world, savings of 40% in efficiency drop to 22%. It turns out that regulatory division is the main problem, causing 92% of practical errors. The study produces the idea of energy-constrained quantum advantage and shows that it can only be useful with solid-state batteries (≥400 Wh/kg) and regulatory unification. These efforts set new standards for urban mobility research that involves multiple fields and show how driverless operations can be used in a way that is viable.
Drone-delivery planning combines routing decisions with operational constraints such as payload capacity and limited onboard energy, resulting in combinatorial optimization problems that can become costly to encode directly in binary form. This work investigates a hybrid quantum--classical approach in which candidate drone missions are generated and evaluated classically before constructing a quadratic unconstrained binary optimization (QUBO) model for mission selection. Payload- and energy-infeasible missions are removed during preprocessing, while the reduced QUBO is solved using exact enumeration, simulated annealing (SA), and the Quantum Approximate Optimization Algorithm (QAOA), with mixed-integer linear programming (MILP) used as a classical reference. Experiments on controlled synthetic delivery instances evaluate solution quality, the effect of preprocessing, and computational scaling. Exact QUBO optimization reproduces the MILP optimum on the evaluated small instances, while SA achieves 100% feasibility with a median optimality gap of 0%. Combined payload-and-energy preprocessing reduces the mean number of QUBO variables by 29.60% and quadratic interactions by 49.20%, while reducing mean SA runtime by 31.26%. In contrast, the evaluated shallow statevector-based QAOA configuration achieves lower feasibility and is restricted to small QUBO instances. These results indicate that, in the considered setting, the main practical benefit of the hybrid architecture comes from classical feasibility preprocessing that reduces the binary search space before QUBO-based optimization.
This paper presents a novel hybrid approach to solving real-world drone routing problems by leveraging the capabilities of quantum computing. The proposed method, coined Quantum for Drone Routing (Q4DR), integrates the two most prominent paradigms in the field: quantum gate-based computing, through the Eclipse Qrisp programming language; and quantum annealers, by means of D-Wave System’s devices. The algorithm is divided into two different phases: an initial clustering phase executed using a Quantum Approximate Optimization Algorithm (QAOA), and a routing phase employing quantum annealers. The efficacy of Q4DR is demonstrated through three use cases of increasing complexity, each incorporating real-world constraints such as asymmetric costs, forbidden paths, and itinerant charging points. This research contributes to the growing body of work in quantum optimization, showcasing the practical applications of quantum computing in logistics and route planning.
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.