Exact and heuristic methods for a university course scheduling problem

Abstract

The University Course Scheduling Problem (UCSP) is a complex combinatorial optimization problem. Most universities still use hand-operated scheduling, which usually takes a long time and results in numerous irrationalities. The imperative of conceiving a algorithm to navigate this predicament is undeniable. This paper introduces an advanced mixed integer linear programming paradigm, incorporating constraints encompassing both the temporal coherence of courses and the equitable dispersion of these courses throughout the academic week. To tackle this issue, we design a novel two-stage meta-heuristic algorithm; the first stage harnesses the genetic algorithm to cluster courses into sets by exploiting graph coloring techniques, while the subsequent stage leverages an enhanced tabu search heuristic to assign these clusters into distinct temporal intervals. The effectiveness and efficiency of the proposed heuristic has been validated by extensive computational studies based on authentic data gleaned from Huazhong University of Science and Technology’s School of Management and the results are compared with CPLEX and common heuristic. Moreover, our research examines the algorithm’s convergence properties and the effects of fast neighborhood evaluation strategy. Sensitivity analysis is performed to probe the algorithm’s responsiveness to the new constraints.