Can a Meta-GA solve timetabling problems?

1. Can a Meta-GA solve timetabling problems? Christian Blum, Sebastião Correia, Olivia Rossi-Doria, Marko Snoek,Marco Dorigo (team leader), Ben Paechter (problem leader)

2. Contents • Introduction • The timetabling problem • Solution directions • Our approach • Preliminary results • Conclusions and future research directions Timetabling, EvoNet Summer School 2001

3. Introduction Background of participants: • Christian: mathematics • Marko: technology management • Olivia: mathematics • Sebastião: physics Let’s do timetabling! Timetabling, EvoNet Summer School 2001

4. The timetabling problem Goal: assignment of classes to rooms and timeslots, while respecting the hard constraints, and taking into consideration the soft constraints. Timetabling, EvoNet Summer School 2001

5. Problem hardness • NP-hard problem • Problem is highly constrained • Difficult to build feasible solutions Timetabling, EvoNet Summer School 2001

6. Solution directions Direct representation:genotype is the solution Indirect representation:genotype  phenotypephenotype is the solution Timetabling, EvoNet Summer School 2001

7. Solution directions II Characteristics of direct representation:crossover is more likely to be disruptivemost solutions are infeasible Characteristics of indirect representation:need timetable builder to construct solution Timetabling, EvoNet Summer School 2001

8. Summer School Problem Data: • Classes (type of room required) • Rooms (type, size) • Timeslots (45 in a week) • Students (class attendance) Timetabling, EvoNet Summer School 2001

9. Summer School Problem Hard constraints: • Each class in a suitable room • One class per room / timeslot • Each student can follow all his / her classes Soft constraints: • Students should not have only 1 class / day • Students should not have more than 2 classes in a row Timetabling, EvoNet Summer School 2001

10. Our approach • Indirect representation • Toolbox of heuristics is given • Use heuristics to build timetable step-by-step • Let GA evolve which heuristics to use in every step Timetabling, EvoNet Summer School 2001

11. class rules: c1 r1 t1 c2 r2 t2 … … … room rules: time rules: Rules used for insertion of 2nd event in timetable Our approach II Individual: Timetabling, EvoNet Summer School 2001

12. Our approach III • Choose next class to insert in timetable:e.g. pick class with most students • Choose which room to assign:e.g. pick smallest possible room • Choose timeslot:e.g. pick timeslot with most parallel events Timetabling, EvoNet Summer School 2001

13. Heuristics Problem data Timetable builder Meta-GA Timetable Fitness Score Our approach IV Timetabling, EvoNet Summer School 2001

14. Preliminary results (yet!) NO RESULTS Timetabling, EvoNet Summer School 2001

15. Room for improvement • Extend set of heuristics • Use other assignment orders,e.g. choose timeslot, followed by event, and room • Change assignment order during timetable building • Apply local search Timetabling, EvoNet Summer School 2001

16. Conclusions • Advantage of method:adaptation to problem instances • Disadvantage of method:phenotype -/-> genotype • Presented method is new in the field of timetabling • Approach can be improved in various ways Timetabling, EvoNet Summer School 2001