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A GENETIC ALGORITHM BASED HYPERHEURISTIC TO COURSE-TIME SLOT-ROOM ASSIGNMENT PROBLEM

A GENETIC ALGORITHM BASED HYPERHEURISTIC TO COURSE-TIME SLOT-ROOM ASSIGNMENT PROBLEM. Zehra KAMIŞLI ÖZTÜRK Anadolu University , TURKEY Müjgan SAĞIR Eskisehir Osmangazi University , TURKEY. GOAL.

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A GENETIC ALGORITHM BASED HYPERHEURISTIC TO COURSE-TIME SLOT-ROOM ASSIGNMENT PROBLEM

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  1. A GENETIC ALGORITHM BASED HYPERHEURISTIC TO COURSE-TIME SLOT-ROOM ASSIGNMENT PROBLEM 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).

  3. A general ETP includes;

  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)

  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

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

  7. SOLUTION METHODS • Mathematicalprogramming • Heuristics • Meta heuristics • Hybrid meta heuristics • CaseBasedReasoning • Hyperheuristics …

  8. CASE: Small01*course-room-time slot assignment *http://iridia.ulb.ac.be/supp/IridiaSupp2002-001/index.html

  9. BuildingtheMathematical Model

  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 thefeatures required by the event • only one event is in each room at any timeslot

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

  12. Objectives To minimize soft constraint violations Solution quality

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

  14. StudentEventMatrix

  15. RoomFeatureMatrix

  16. EventFeatureMatrix

  17. Mathematical Model • Decision variables

  18. Mathematical Model (cont.)

  19. Mathematical Model (cont.)

  20. Dimension Analysis

  21. Dimension Analysis (cont.) 7×(3!) ×

  22. DimensionAnalysis(cont.) 7×(3!) ×

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

  24. Investigating appropriate heuristics from the literature HYPERHEURISTICS Burke et.al. (2003) Han andKendall (2003) BurkeandNevall (2004) …

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

  26. Investigating appropriate heuristics from the literature

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

  28. Building the Genetic Algorithm

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

  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

  31. MATRIX Representation

  32. MATRIX Representation Abramson, 1991

  33. PERMUTATION Representation Chromosome length :50 Chromosome length :50 Chromosome length :100 timeperiod classroom

  34. Restrictionsfordifferentrepresentations • Matrix representation • needs some special genetic operators (PMX, imitation etc.) • can not handle all resources. • does not guarantee feasible solution. • Binary and permutation representation • needs some special genetic operators • takes too much space • can not handle all resources. • does not guarantee feasible solution.

  35. Restrictionsfordifferentrepresentations New cromosomes

  36. small01.tim İnclude parameters # of events, rooms, features, students and capasities 1 2 3 4 … E-1 E Create initial population 3513 5864 9298 7708 … 9587 1468 Calculate total num.of students for each event Construct correlated events matrix Decode cromosome as constructing feasible solutions and evaluate them.  (35*3)/100 +1=2 Reproduction, crossover, Mutation and Elitist operators

  37. Solution 1

  38. Solution 2

  39. Case: GA based HH • HLH: GA • LLHs:

  40. Ongoing studies …

  41. Ongoing studies …

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

  43. Future work database Userinterface(FLASH) GAMS & C++ optimisation

  44. QUESTIONS ?

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