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Solving the examination timetabling problem: A NASH equilibrium approach with genetic algorithm, tabu search and simulated annealing comparisons

algorithms-and-analysis-of-algorithms
artificial-intelligence
data-science
optimization-theory-and-computation
theory-and-formal-methods

Abstract

The Examination Timetabling Problem (ETP) is a complex optimization challenge involving the scheduling of exams for 11,209 students across 156 subjects with 275 invigilators over 9 days, divided into six 90-minute timeslots per day. This study proposes a novel approach to solving the ETP by integrating a Nash Equilibrium model from game theory with meta-heuristic algorithms, including Genetic Algorithm (GA), Tabu Search (TS), and Simulated Annealing (SA). The Nash Equilibrium framework ensures a balanced consideration of the conflicting interests of students, invigilators, and the academic department. Experimental results, based on real-world data from FPT University’s Spring 2023 semester, demonstrate that Tabu Search outperforms GA and SA in terms of fitness, hypervolume, and stakeholder satisfaction, achieving over 80% satisfaction rates for all groups. These findings highlight the efficacy of combining Nash Equilibrium with Tabu Search for addressing multi-objective optimization in educational scheduling, offering a robust and equitable solution for large-scale timetabling problems.
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