A Study of Genetic Algorithms to Solve the School Timetabling Problem

Abstract

AbstractThis paper examines the use of genetic algorithms (GAs) to solve the school timetabling problem. The school timetabling problem falls into the category of NP-hard problems. Instances of this problem vary drastically from school to school and country to country. Previous work in this area has used genetic algorithms to solve a particular school timetabling problem and has not evaluated the performance of a GA on different problems. Furthermore, GAs have not previously been applied to solving the South African primary or high school timetabling problem. The paper presents a two-phased genetic algorithm approach to solving the school timetabling problem and provides an analysis of the effect of different low-level construction heuristics, selection methods and genetic operators on the success of the GA approach in solving these problems with respect to feasibility and timetable quality. The GA approach is tested on a benchmark set of “hard” school timetabling problems, the Greek high school timetabling problem and a South African primary and high school timetabling problem. The performance of the GA approach was found to be comparable to other methods applied to the same problems. This study has also revealed that different combinations of low-level construction heuristics, selection methods and genetic operators are needed to produce feasible timetables of good quality for the different school timetabling problems. Future work will investigate methods for the automatic configuration of GA architectures of both phases.KeywordsTimetablinggenetic algorithmscombinatorial optimizationevolutionary computation