AN AI-DRIVEN HYBRID QUANTUM-TOPOLOGICAL INTELLIGENT FRAMEWORK FOR ACADEMIC TIMETABLE SCHEDULING

Abstract

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.