A Hybrid Quantum Annealing Algorithm for Solving a Constraint-Based University Timetabling Problem

Abstract

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.