1. Zehra KAMIŞLI ÖZTÜRK Anadolu University, TURKEY Müjgan SAĞIR Eskisehir Osmangazi University, TURKEY

2. GOAL Designing a flexible, computer based and user interactive system for the solution of the Educational Timetabling Problems (ETP). 2

3. A general ETP includes; course room instructor time period student 3

4. Outline Difficulties on the solution of ETP. the need for heuristics Hyper heuristics on deciding the best heuristic to solve the problem. Small01 (a test problem from the literature) Mathematical model (course-room-time slot assignment) 4

5. Outline Dimensional analysis Investigating appropriate heuristics from the literature Evolutionary algorithms (GA) A new genetic algorihm Constructing web interfaces Problem solution Comparison and conclusion 5

6. Difficulties NP-hard structure Varied nature Conflicting objectives Size 6

7. SOLUTION METHODS 7 Mathematical programming Mathematical programming Heuristics Heuristics Meta heuristics Meta heuristics Hybrid meta heuristics Hybrid meta heuristics Case Based Reasoning Case Based Reasoning Hyper heuristics … Hyper heuristics …

8. CASE: Small01 * course-room-time slot assignment 8 Small01 # of courses100 # of rooms5 # of features5 # of students80 Total time period (9 timeperiod/day* 5 days) 45 *http://iridia.ulb.ac.be/supp/IridiaSupp2002-001/index.htmlhttp://iridia.ulb.ac.be/supp/IridiaSupp2002-001/index.html

9. Building the Mathematical Model 9

10. HARD CONSTRAINTS no student attends more than one event at the same time the room is big enough for all the attending students and satisfies all the features required by the event only one event is in each room at any timeslot 10

11. no student has a event in the last slot of the day no student has more than two different events consecutively no student is allowed to have only one event on a day SOFT CONSTRAINTS 11

12. Objectives To minimize soft constraint violations Solution quality 12

13. SMALL01 Parameters Student Event Matrix (SE) Room Feature Matrix (RF) Event Feature Matrix (EF) Room capasities 13

14. Student Event Matrix S/ES/E12345678910…8889909899100 10000000000100100 20000000010100100 30000000010100100 40000000010100100 50000000000110100 60000010000110000 … 540011000100000000 551001000100000000 800000000000100100 14

15. Room Feature Matrix R/FR/F12345 111111 210111 310010 400001 501010 15

16. Event Feature Matrix E/F 12345 1 01010 2 11111 3 10111 4 00000 5 10011 6 00000 7 00001 8 01010 9 10010 10 00110 16

17. Mathematical Model Decision variables 17

18. Mathematical Model (cont.) 18

19. Mathematical Model (cont.) 19

20. Dimension Analysis Const.index# of total constraints 1 j,k,lj × k × l 2 j,kj × k 3 j,kj × k 4 jj 5 k,tk × t 6 j,kj × k 7 i, ti × t 8 j, t j × t 9 j, t j × t 20

21. Dimension Analysis (cont.) Goal noIndex# of total goals 1-1 2 i,ds j × i 3ii × 5 7 × (3!) × 21

22. 7 × (3!) × variableindex# of total variables j,k,tj × k × t j,kj × k j,tj × t -2 i,j × i × 2 ii × 5 × 2 Dimension Analysis (cont.) 22

23. 3jk + 2jt + jkl +j + kt + it + 5i + 42i # of total constraints # of total variables jkt + jk + jt + 10i + 84i +2 for Small01 total constraints: 420525 total variables: 834702 Dimension Analysis (cont.) 23

24. HYPERHEURISTICS 24 Investigating appropriate heuristics from the literature Hyper heuristicLLH1LLH2Problem…LLHn Burke et.al. (2003) Han and Kendall (2003) Burke and Nevall (2004) …

25. HYPERHEURISTICS 25 performance of LLH Hyper Heuristic Heuristic selection Low Level Heuristics Problem Solution quality variability in the solution Investigating appropriate heuristics from the literature

26. Year StudyAuthors 1994 A Genetic Algorithm based University Timetabling System Burke EK, Elliman DG and Weare RF 1992 A genetic algorithm, to solve the timetable problem. Colorni, A., Dorigo, M. and Maniezzo, V. 2002 A genetic algorithm for a university weekly courses timetabling problem Yu, E. and Sung K.S. 2001 A Constructive Evolutionary Approach to School Timetabling Filho, G.R. and Lorena, L.A.N. 2002School Tımetable Generating Using Genetic Algorithm Voráč, J, I. Vondrák, and K. Vlček 1994Fast Practical Evolutionary Timetabling Corne, D. Ross, P. and Fang,.L. 1995 A Genetic Algorithm Solving a Weekly Course- Timetabling Problem Erben, W. and Keppler, J. 26

27. Classes of Search Techniques Search Techniqes Calculus Base Techniques Guided random search techniqes Enumerative Techniques BFSDFS Dynamic Programming Tabu SearchHill Climbing Simulated Anealing Evolutionary Algorithms Genetic Algorithms Fibonacci Sort 27

28. Building the Genetic Algorithm 28

29. Basic Operators in GA’s population parents offsprings selection mutation crossover selection 29

30. Basic Steps Definition of encoding principles (gene, chromosome) Definition initialization procedure (creation) Selection of parents (reproduction) Genetic operators (mutation, recombination) Evaluation function (environment) Termination condition 30

31. Encoding Principles Binary representation (0,1) Permutation representation Matrix representation 31

32. MATRIX Representation Mon1Mon2…Fri5Fri6 Place 1 Event 1- 1 Event 2-2……… ……………… Place i…Event i-2…Event i-5… Lab 1…………… ……………… Lab j…………Event j-6 32

33. Abramson, 1991 MATRIX Representation 33

34. PERMUTATION Representation Course no: 1234 … 50 Time period: 532045 … 1414 Course no:1234 … 50 classroom:1254 … 6 Course no:11223344...49 50 5132205454103146 timeperiodclassroom Chromosome length :50 Chromosome length :100 34

35. Restrictions for different representations 1. Matrix representation needs some special genetic operators (PMX, imitation etc.) can not handle all resources. does not guarantee feasible solution. 2. Binary and permutation representation needs some special genetic operators takes too much space can not handle all resources. does not guarantee feasible solution. 35

36. New cromosomes Course: 12345 Time period 12345 Course:12345 Time period53421 Course: 12345 Time period53345 Course: 12345 Time period12422 Restrictions for different representations 36

37. GA for ETP Most of the studies allow Hard Constraint Violations (Hcvs)!!! (Burke vd.,2003; Rossi-Doria vd. 2003, vs.). Assumption No Hcvs  37

38. Create initial population 14689587…7708929858643513 EE-1 … 4321 small01.tim İnclude parameters # of events, rooms, features, students and capasities Calculate total num.of students for each event Construct correlated events matrix Decode cromosome as constructing feasible solutions and evaluate them. Reproduction, crossover, Mutation and Elitist operators 1234E-1E 351358649298770895871468 121113 33525 43 4 5 ARAR322512 R 335413  (35*3)/100  +1=2 38

39. Solution 1 Derslik 2Derslik 3 S2S2 G1G1 G2G2 G3G3 G4G4 G5G5 G1G1 G2G2 G3G3 G2G2 G3G3 G4G4 G5G5 Z1Z1 44 31Z1Z1 35 Z2Z2 1810 Z2Z2 Z3Z3 Z3Z3 14 Z4Z4 2332Z4Z4 34 Z5Z5 Z5Z5 1 Z6Z6 Z6Z6 Z7Z7 Z7Z7 Z8Z8 Z8Z8 9 Z9Z9 Z9Z9 Derslik 4Derlsik 5 S4S4 G1G1 G2G2 G3G3 G4G4 G5G5 S5S5 G1G1 G2G2 G3G3 G4G4 G5G5 Z1Z1 9 14 Z1Z1 2519 Z2Z2 3142Z2Z2 1220 Z3Z3 1339 Z3Z3 251727 Z4Z4 39 Z4Z4 2431435 Z5Z5 25Z5Z5 186 Z6Z6 4236 Z6Z6 3421 Z7Z7 16Z7Z7 10718636 Z8Z8 412Z8Z8 1514 Z9Z9 13 25Z9Z9 2921 31 Room 1 R1R1 D1D1 D2D2 D3D3 D4D4 D5D5 T1T1 43 26 T2T2 411443 T3T3 338 T4T4 428113 T5T5 398 182 T6T6 02767 T7T7 1231219 T8T8 42274 T9T9 232521 39

40. Solution 2 Trial no: solution (fitness function) 1149 2154 3127 490 5147 6125 7116 892 40

41. Case: GA based HH HLH: GA LLHs: 41 NHV ( no hard constraint violation) Maximum number of event correlations Maximum number of students Maximum number of features required by the events

42. Ongoing studies … 42

43. Ongoing studies … 43

44. Conclusion Feasible solutions without hard constraint violations A general solution methodolgy by HHs Hybrid methodolgies for future work… 44

45. Future work 45