Using drones to perform human-related tasks can play a key role in various fields, such as defense, disaster response, agriculture, healthcare, and many others. The drone delivery packing problem (DDPP) arises in the context of logistics in response to an increasing demand in the delivery process, along with the necessity of lowering human intervention. The DDPP is usually formulated as a combinatorial optimization (CO) problem, aiming to minimize drone usage with specific battery constraints while ensuring time-consistent deliveries with fixed locations and energy budget. In this work, we propose two alternative formulations of the DDPP as a quadratic unconstrained binary optimization (QUBO) problem to test the performance of classical and quantum annealing (QA) approaches. We perform extensive experiments showing the advantages as well as the limitations of quantum annealers for this optimization problem, as compared to simulated annealing (SA) and classical state-of-the-art commercial tools for global optimization.
Using drones to perform human-related tasks can play a key role in various fields, such as defense, disaster response, agriculture, healthcare, and many others. The drone delivery packing problem (DDPP) arises in the context of logistics in response to an increasing demand in the delivery process, along with the necessity of lowering human intervention. The DDPP is usually formulated as a combinatorial optimization (CO) problem, aiming to minimize drone usage with specific battery constraints while ensuring time-consistent deliveries with fixed locations and energy budget. In this work, we propose two alternative formulations of the DDPP as a quadratic unconstrained binary optimization (QUBO) problem to test the performance of classical and quantum annealing (QA) approaches. We perform extensive experiments showing the advantages as well as the limitations of quantum annealers for this optimization problem, as compared to simulated annealing (SA) and classical state-of-the-art commercial tools for global optimization.
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.
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.
Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.
The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation, but also demonstrate the potential of quantum computation in effectively solving the bin packing problem, particularly as more reliable quantum technology becomes available.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.
Airline companies struggle every day trying to schedule crew, flights and aircraft.Tail Assignment is the problem of allocating individual aircraft to a set of flights, while ensuring multiple constraints and aiming to minimise an objective function, such as operational costs.Given the enormous amount of possibilities and constraints involved, this problem has been a study case for the last decade.Many solutions have emerged using classical computing, but with limitations regarding performance.Quantum Annealing (QA) is a heuristic technique for finding global minimum energy levels over an energy landscape using quantum mechanics.Due to its characteristics, it has been proved to have a clear advantage in solving some complex optimisation problems, being a promising technique to apply in multiple fields.In this study, Tail Assignment Problem was set as a Quadratic Unconstrained Binary Optimisation (QUBO) model, using two different techniques, and was solved using a classical and two hybrid solvers.Tests were run based on extractions from real-world data, analysing the performance of the implementation in terms of time, scalability and quality (i.e., the lowest operational costs) of the obtained solutions.We concluded that using a library for modelling the problem as well as considering individual flights rather than pre-aggregating them in strings can be a bottleneck when it comes to its scalability.Furthermore, we found out that there was a higher probability of obtaining better solutions for this problem using one of the hybrid solvers when compared with the classical heuristic algorithms such as Simulated Annealing (SA).These findings can serve as foundations for further studies.