A Multiobjective Genetic Algorithm for the Class/Teacher Timetabling Problem

Abstract

The drawing up of school timetables is a slow, laborious task, performed by people working on the strength of their knowledge of resources and constraints of a specific institution. This paper begins by presenting the timetabling problems that emerge in the context of educational institutions. This is followed by a description of the basic characteristics of the class/teacher timetabling problem. Timetables are considered feasible provided the so-called hard constraints are respected. However, to obtain high-quality timetabling solutions, other conditions should be satisfied in this case — those of soft constraints — which impose satisfaction of a set of desirable conditions for classes and teachers. A multiobjective genetic algorithm was proposed for this timetabling problem, incorporating two distinct objectives. They concern precisely the minimization of the violations of both types of constraints, hard and soft, while respecting the two competing aspects — teachers and classes. A brief description of the characteristics of a genetic multiobjective metaheuristic is presented, followed by the nondominated sorting genetic algorithm, using a standard fitness-sharing scheme improved with an elitist secondary population. This approach represents each timetabling solution with a matrix—type chromosome and is based on special-purpose genetic operators of crossover and mutation developed to act over a secondary population and a fixed-dimension main population of chromosomes. The paper concludes with a discussion of the favorable results obtained through an application of the algorithm to a real instance taken from a university establishment in Portugal.