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 com plete combinatorial problem. The problem becomes even more compl ex when addressed to individual timetables of students. The core of deal ing with the problem in this application is a timetable builder based on mixed d irect-indirect encoding evolved by a genetic algorithm with a self-adaptati on paradigm, where the parameters of the genetic algorithm are optimized dur ing 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 suita ble for timetabling problem. Comparing to previous approaches we designed the enc oding for selfadaptation not only one parameter or several ones b ut for all possible parameters of genetic algorithms at the same time. Geneti c algorithms are naturally parallel so also the parallel representation of the self-adaptive genetic algorithm is presented. The proposed parallel self-adaptive g enetic algorithm is then applied for solving the real university timetabling p roblem and compared with a standard genetic algorithm. The main advantage of t his approach is, that it makes possible to solve wide range of timetabling a d 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 w e present and discuss the algorithm for optimized enrolment of students that mi ni ize the number of clashing constraints for students.

[1]  Agostinho C. Rosa,et al.  High school weekly timetabling by evolutionary algorithms , 1999, SAC '99.

[2]  Andrea Tettamanzi,et al.  An Evolutionary Algorithm for Solving the School Time-Tabling Problem , 2001, EvoWorkshops.

[3]  Zbigniew Michalewicz,et al.  Genetic algorithms + data structures = evolution programs (3rd ed.) , 1996 .

[4]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[5]  David Abramson,et al.  Constructing school timetables using simulated annealing: sequential and parallel algorithms , 1991 .

[6]  Stefano Marsili-Libelli,et al.  Adaptive mutation in genetic algorithms , 2000, Soft Comput..

[7]  Kathryn A. Dowsland,et al.  A robust simulated annealing based examination timetabling system , 1998, Comput. Oper. Res..

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  Jinn-Moon Yang,et al.  Integrating adaptive mutations and family competition into genetic algorithms as function optimizer , 2000, Soft Comput..

[10]  Ben Paechter,et al.  Timetabling the Classes of an Entire University with an Evolutionary Algorithm , 1998, PPSN.

[11]  Luca Di Gaspero,et al.  Tabu Search Techniques for Examination Timetabling , 2000, PATAT.

[12]  Wojciech Legierski.  Search Strategy for Constraint-Based Class-Teacher Timetabling , 2002, PATAT.

[13]  Edmund K. Burke,et al.  Enhancing Timetable Solutions with Local Search Methods , 2002, PATAT.

[14]  Carlos Alberto Conceição António,et al.  Self-adaptation in Genetic Algorithms applied to structural optimization , 2008 .

[15]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[16]  Peter Ross,et al.  Some Observations about GA-Based Exam Timetabling , 1997, PATAT.

[17]  Tim Fischer,et al.  Automated Solution of a Highly Constrained School Timetabling Problem - Preliminary Results , 2001, EvoWorkshops.

[18]  Chris N. Potts,et al.  Constraint satisfaction problems: Algorithms and applications , 1999, Eur. J. Oper. Res..