Quantum computing is widely discussed for its potential to solve challenging optimization problems much faster. However, real-world airline problem sizes currently exceed the capabilities of existing quantum hardware. Preparing for larger quantum hardware requires developing and benchmarking problem formulations most suitable for quantum implementation. In this study, we use the crew pairing problem from aviation as an use case to benchmark different problem formulations: a set partitioning model and two compact formulations, a constrained flow assignment problem and a satisfiability problem (SAT). For classical benchmarking we solve these formulations using mixed integer programming and SAT solvers. For quantum benchmarking we translate the formulations into quadratic unconstrained binary optimization and Ising formulations. Our benchmarking shows that the problem formulations lead to different classical and quantum properties. Among the formulations considered, the SAT formulation emerges as the most promising candidate for future implementation on quantum hardware with the lowest share of non-zero elements and highest spectral gap, despite its larger ratio of linear term coefficients.
Quantum computing is widely discussed for its potential to solve challenging optimization problems much faster. However, real-world airline problem sizes currently exceed the capabilities of existing quantum hardware. Preparing for larger quantum hardware requires developing and benchmarking problem formulations most suitable for quantum implementation. In this study, we use the crew pairing problem from aviation as an use case to benchmark different problem formulations: a set partitioning model and two compact formulations, a constrained flow assignment problem and a satisfiability problem (SAT). For classical benchmarking we solve these formulations using mixed integer programming and SAT solvers. For quantum benchmarking we translate the formulations into quadratic unconstrained binary optimization and Ising formulations. Our benchmarking shows that the problem formulations lead to different classical and quantum properties. Among the formulations considered, the SAT formulation emerges as the most promising candidate for future implementation on quantum hardware with the lowest share of non-zero elements and highest spectral gap, despite its larger ratio of linear term coefficients.
Airline and space mission scheduling present complex combinatorial optimization challenges, requiring sophisticated coordination of multiple resources under stringent operational constraints. This paper introduces a novel hybrid quantum-classical framework for scheduling optimization, the Quantum Scheduling Optimization Algorithm (QSOA), addressing crew assignment, gate allocation, and trajectory planning through advanced quantum machine learning techniques. We formulate the scheduling problems as stochastic multi-objective optimization and propose three integrated solution approaches: (1) hybrid quantum optimization via QAOA with constraint-aware loss functions and problem decomposition strategies, (2) classical-quantum integration using graph partitioning and variational circuit optimization, and (3) comprehensive baselines including mixed-integer programming, genetic algorithms, and reinforcement learning formulations. For multi-objective handling, we develop Pareto-optimal sampling techniques combining quantum superposition with classical post-processing for constraint repair and solution refinement. Our experimental evaluation on realistic airline crew scheduling benchmarks and space mission simulators demonstrates significant improvements: the hybrid QSOA achieves 19.2\% cost reduction in airline scheduling compared to classical heuristics, while quantum methods provide competitive solutions for moderate-sized space mission subproblems with 15-18\% improvement in multi-objective trade-offs. The framework shows promise for scalable deployment in real-world transportation networks, with practical implications for next-generation scheduling optimization in complex operational environments.
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary Optimization (QUBO) formulation provides a unifying modeling framework for a broad class of NP-hard problems and is naturally suited to quantum computing and quantum-inspired algorithms. Location science, network design, and logistics represent core application domains of discrete optimization, combining high practical impact with substantial computational challenges. In this work, we develop QUBO formulations for several fundamental problems in these domains, including a nonlinear integer formulation of the Discrete Ordered Median Problem (DOMP). Beyond their modeling relevance, these QUBO formulations serve as representative benchmark problems for assessing quantum algorithms and quantum hardware. We further derive a tight bound for the penalty parameter ensuring equivalence between the QUBO formulation and its underlying integer program. Finally, we conduct a comprehensive computational study using QAOA, WS-QAOA, and classical heuristics for QUBO instances of the p-Median Problem and the Fixed-Charge Facility Location Problem (FCFLP), and introduce two effective warm-start strategies for WS-QAOA based on its linear programming relaxation.
Abstract As interest in quantum and related optimization paradigms continues to grow, fairly and systematically comparing their performance across practical problem settings remains challenging. This challenge arises because these approaches often target different problem classes, use different mathematical representations, and are affected differently by modeling choices. As a result, observed performance depends not only on the solver itself, but also on how a problem is formulated, reformulated, and translated into a solver-specific input language. This work presents a publicly available and extensible benchmarking framework that unifies advances in quantum, quantum-hybrid, quantum-inspired, and classical optimization by enabling consistent comparison across use cases, solvers, and models. We address the diversity of solver “languages”—from mixed-integer programming (MIP) formulations for branch-and-bound methods over quadratic unconstrained binary optimization (QUBO) models for quantum annealers to constrained quadratic models (CQM) for hybrid approaches — as well as the influence of modeling choices, such as binary encodings and penalty formulations, on both performance and solution fidelity. By supporting systematic variation across the three dimensions of use case, solver, and model, the framework reveals trade-offs that single-dimension benchmarks overlook, clarifies when native formulations are preferable, and enables rigorous evaluation of practical combinatorial optimization problems. The two case studies, vehicle routing and maximum cut, illustrate this principle: their contrasting outcomes show that the effectiveness of a solver depends strongly on how well the chosen model representation matches the solver backend and the use case.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
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.