A new hybrid structure for solving academic scheduling issues is proposed in this paper that uses a combination of Topological Data Analysis (TDA) and Quantum Annealing (QA). The new framework allows for the modelling and solving of multi-constraint university scheduling problems by combining the characteristics of both QA and TDA. Using TDA, scheduling data is topologically analysed to provide structural and geometric information that can be used with the global optimization properties of QA to develop solutions to complex grement configurations.To test the proposed hybrid framework, the authors used real world data from the TUM for three datasets. The three datasets reflect different levels of complexity, with all datasets containing Certificate and Diploma Programs leading to the Undergraduate and Postgraduate timetable.Four model variants were considered: The configurations examined comprised QA-only, TDA-only, hybrid models without refinement, and hybrid models incorporating refinement. Each approach was assessed using four performance metrics: Conflict-Free Rate (CFR), Resource Utilization (RU), Computational Time (CT), and Energy Function Value (EFV). The experimental results demonstrate that hybrid approaches incorporating refinement consistently outperformed all baseline models across every evaluation metric. Notably, the top-performing hybrid configuration, evaluated on the most complex dataset, attained a CFR of 94.3%, a RU of 91.2%, and the lowest EFV among all the methods compared. Experimental results demonstrate that all hybrid-with-refinement configurations consistently outperformed the baseline models by a substantial margin. Notably, on the most challenging dataset, the refined hybrid approach attained a Conflict-Free Rate (CFR) of 94.3% and a Resource Utilization (RU) of 91.2%, while also yielding the minimum Energy Function Value (EFV). Additionally, clustering and K-NN analysis results confirmed that the proposed hybrid approach has consistent and robust behaviours across all datasets, demonstrating reliable behaviour regardless of the differing sizes or complexity of the problems.
A new hybrid structure for solving academic scheduling issues is proposed in this paper that uses a combination of Topological Data Analysis (TDA) and Quantum Annealing (QA). The new framework allows for the modelling and solving of multi-constraint university scheduling problems by combining the characteristics of both QA and TDA. Using TDA, scheduling data is topologically analysed to provide structural and geometric information that can be used with the global optimization properties of QA to develop solutions to complex grement configurations.To test the proposed hybrid framework, the authors used real world data from the TUM for three datasets. The three datasets reflect different levels of complexity, with all datasets containing Certificate and Diploma Programs leading to the Undergraduate and Postgraduate timetable.Four model variants were considered: The configurations examined comprised QA-only, TDA-only, hybrid models without refinement, and hybrid models incorporating refinement. Each approach was assessed using four performance metrics: Conflict-Free Rate (CFR), Resource Utilization (RU), Computational Time (CT), and Energy Function Value (EFV). The experimental results demonstrate that hybrid approaches incorporating refinement consistently outperformed all baseline models across every evaluation metric. Notably, the top-performing hybrid configuration, evaluated on the most complex dataset, attained a CFR of 94.3%, a RU of 91.2%, and the lowest EFV among all the methods compared. Experimental results demonstrate that all hybrid-with-refinement configurations consistently outperformed the baseline models by a substantial margin. Notably, on the most challenging dataset, the refined hybrid approach attained a Conflict-Free Rate (CFR) of 94.3% and a Resource Utilization (RU) of 91.2%, while also yielding the minimum Energy Function Value (EFV). Additionally, clustering and K-NN analysis results confirmed that the proposed hybrid approach has consistent and robust behaviours across all datasets, demonstrating reliable behaviour regardless of the differing sizes or complexity of the problems.
University timetabling is a classical NP-Hard combinatorial constraint problem that involves scheduling of courses, lecturers, students, classrooms, and timeslots while satisfying a set of constraints, with the main goal of minimizing conflicts. To solve this problem, we propose a novel Quantum Annealing and Topological Data Analysis (QA–TDA) algorithm that starts with an initial feasible solution, followed by iterative refinement using Quantum annealing configurations. TDA analyses the optimization landscape through persistent homology by detecting promising regions of interest in the solution space, which are clustered and subjected to quantum re-annealing using customized Hamiltonians-adaptive annealing schedules. QA-TDA model achieves a balance between global exploration and local exploitation, which improves convergence efficiency and solution robustness. Experimental results demonstrate that our hybrid model consistently outperforms baseline models across all evaluation metrics. In particularly on the most complex dataset, QA– TDA achieved a Conflict-Free Rate (CFR) of 94.3%. Additionally, an ablation study was conducted to validate the contribution of each component of the proposed model. Furthermore, clustering and K-Nearest Neighbour (K-NN) analyses confirm the robustness and consistency of the proposed approach across datasets of varying sizes and complexity. These findings highlight the great performance, scalability, and reliability of the integrated QA–TDA model for real-world academic scheduling applications.
• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.
An effective approach to solving complex problems is to decompose them and integrate dedicated solvers for those subproblems. We introduce a hybrid decomposition that incorporates: (1) a quantum annealer that samples from the configuration space of a relaxed problem to obtain strong candidate solutions, and (2) a classical processor that maintains a global search tree and enforces constraints on the relaxed components of the problem. Our framework is the first to use quantum annealing as part of a complete search. We consider variants of our approach with differing amounts of guidance from the quantum annealer. We empirically test our algorithm and compare the variants on problems from three scheduling domains: graph-coloring-type scheduling, simplified Mars Lander task scheduling, and airport runway scheduling. While we were only able to test on problems of small sizes, due to the limitation of currently available quantum annealing hardware, the empirical results show that results obtained from the quantum annealer can be used for more effective search node pruning and to improve node selection heuristics when compared to a standard classical approach.
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.
Efficient production planning is essential in modern manufacturing to improve performance indicators such as lead time and to reduce reliance on human intuition. While mathematical optimization approaches, formulated as job shop scheduling problems, have been applied to automate this process, solving large-scale production planning problems remains computationally demanding. Moreover, many practical scenarios involve conflicting objectives, making traditional scalarization techniques ineffective in finding diverse and useful Pareto-optimal solutions. To address these challenges, we developed a quantum-classical hybrid algorithm that decomposes the problem into two subproblems: resource allocation and task scheduling. Resource allocation is formulated as a quadratic unconstrained binary optimization problem and solved using annealing-based methods that efficiently explore complex solutions. Task scheduling is modeled as a mixed-integer linear programming problem and solved using conventional solvers to satisfy detailed scheduling constraints. We validated the proposed method using benchmark instances based on foundry production scenarios. Experimental results demonstrate that our hybrid approach achieves superior solution quality and computational efficiency compared to traditional monolithic methods. This work offers a promising direction for high-speed, multi-objective scheduling in industrial applications.
Hybrid quantum computing (QC) combines classical and quantum resources to tackle challenging optimization problems, leveraging the strengths of both within the current constraints of quantum computers, which are limited in size and power. Therefore, we explore the efficacy of a hybrid quantum annealing (QA) search algorithm in improving portfolio optimization. This study pioneers the application of the trend ratio (TR) to a quantum annealing computer, converting it into a constrained quadratic model with a flexible presentation. The TR serves as a promising indicator in portfolio evaluation, considering the great balance between expected returns and risks. Utilizing D- Wave's hybrid solver, we present a thorough analysis and discussion of the proposed model realized in the QA structure. The experimental results demonstrate that our model can discover solutions of comparable quality in a significantly shorter amount of time than an exhaustive search. When extending the search space to sizes challenging for exhaustive search, we conducted experiments comparing our approach with state-of-the-art quantum-inspired artificial intelligence (AI) algorithms. The results show that our method not only constructs higher-quality solutions but also requires the least computation time. The hybrid quantum-classical AI represents a forward-looking technology paradigm poised to revolutionize problem-solving methods.