Practical School Timetabling: a Hybrid Approach Using Solution Synthesis and Iterative Repair. In

[7] G. Lajos. Complete university modular timetabling using constraint logic programming. A constraint-based approach to high-school timetabling problems: A case study. 14 problem diculty is observed. 6 Conclusions We have proposed a constraint satisfaction model for a local high school timetabling problem. The problem we have studied involves an assignment of eight weekly periods to the sections of school courses. Each of the students provides a list of course selections which are to be satised. The sections of the course are scheduled such that there is at least one section for each course available to the student. However, with as many as 2000 students registered, we have found it becomes impossible to satisfy all of the student's demands. We have reached at least 98% on more than half of the experiments on a random testbed of timetabling problems. The innovation in our solution method is in the heuristic modeling of the problem| which prunes away large parts of the search space|and in the process of iteratively adding constraints to the network. Iterative solutions may be poor at rst but will improve to some upper limit, until no solution can be found. The main advantage of our iterative method is there will always be a timetable output to the scheduler, unless the school has too few rooms to accommodate all of the courses. Because of the iterative constraint addition, a \best" solution always exists at any point in the search. The students are individually scheduled using a simple greedy algorithm once the master timetable is completed. Finally, we have proposed a random model of the school timetabling problem. By identifying the three critical parameters of number students, number of classrooms and number of courses, we have created a diverse testbed of realistic timetabling problems. Furthermore, we have identied some particularly dicult to solve timetabling instances. These particular instances can be recreated, by giving the generator the same parameters and same random seed, so that comparisons can be made with other, improved timetabling algorithms. 13 binary constraints in the problem. In order to manipulate the non-binary constraints, we have also varied the number of rooms in the school. The global capacity constraint says that no more than r courses can be scheduled at one period, given that there are r rooms in the school. As the number of rooms decreases, the quality of the solutions decrease, because in some cases no solution …