A Comparative Study of Genetic Algorithms Using a Direct and Indirect Representation in Solving the South African School Timetabling Problem

Previous work applying genetic algorithms to solve the school timetabling problem have generally used a direct representation, in which each chromosome represents a timetable directly. This study proposes and evaluates a genetic algorithm employing an indirect chromosome representation. Each chromosome is a string comprised of instructions which are used to build a timetable. The fitness of each chromosome is a function of the hard and soft constraint violations of the timetable constructed using the chromosome. Tournament selection is used to choose parents which the mutation and crossover operators are applied to in order to create successive generations. The performance of the genetic algorithm using an indirect representation (IGA) was compared to that using a direct representation (DGA) in solving the school timetabling problem for a South African primary and high school. Both genetic algorithms were able to produce feasible timetables of good quality with the IGA performing better than the DGA. The difference in performance was found to be statistically significant.