AI-Powered Quantum-Topological Optimization: A Hybrid Framework for Intelligent Academic Timetabling

This paper presents a novel hybrid optimization framework that combines Quantum Annealing (QA) with Topological Data Analysis (TDA) for solving academic timetabling problems. The proposed model addresses the multi-constraint nature of university scheduling by integrating quantum-based global search capabilities with topological insights that capture structural data complexity. Empirical evaluations were conducted on real-world scheduling data from the Technical University of Mombasa (TUM), encompassing three datasets of increasing complexity: certificate/diploma, undergraduate, and postgraduate program schedules. The performance of four configurations—QA-only, TDA-only, hybrid without refinement, and full hybrid with refinement—was assessed using four key metrics: Conflict-Free Rate (CFR), Resource Utilization (RU), Computation Time (CT), and Energy Function Value (EFV). Results show that the full hybrid configuration significantly outperforms all baselines, achieving a CFR of 94.3\% and RU of 91.2\% on the most complex dataset, while also yielding the lowest EFV. Clustering and K-Nearest Neighbor (KNN) analyses were conducted to explore configuration similarities and performance consistency, confirming the hybrid model’s robustness across different problem scales.