Solving the University Timetabling Problem with Optimized Enrolment of Students by a Parallel Self-adaptive Genetic Algorithm

The timetabling problem is well known to be NP complete combinatorial problem. The problem becomes even more complex when addressed to individual timetables of students. The core of dealing with the problem in this application is a timetable builder based on mixed direct-indirect encoding evolved by a genetic algorithm with a self-adaptation paradigm, where the parameters of the genetic algorithm are optimized during the same evolution cycle as the problem itself. The aim of this paper is to present an encoding for self-adaptation of genetic algorithms that is suitable for timetabling problem. Comparing to previous approaches we designed the encoding for selfadaptation not only one parameter or several ones but for all possible parameters of genetic algorithms at the same time. Genetic algorithms are naturally parallel so also the parallel representation of the self-adaptive genetic algorithm is presented. The proposed parallel self-adaptive genetic algorithm is then applied for solving the real university timetabling problem and compared with a standard genetic algorithm. The main advantage of this approach is, that it makes possible to solve wide range of timetabling and scheduling problems without setting parameters for each kind of problem in advance. Unlike common timetabling problems the algorithm was applied to the problem in which each student has an individual timetable, so also we present and discuss the algorithm for optimized enrolment of students that minimize the number of clashing constraints for students.