Abstract
This thesis addresses developing new hybrid metaheuristic approaches and a graph based approach for solving school and university course (curriculum-based and post-enrollment based) timetabling problems. Although these problems may appear to be similar, an ap- proach found to solve one type will not achieve the same success for another type and hence they are solved in isolation from each other. Further, for each of the problem types, this also extends to each problem instance as problem instances can differ drasti- cally in terms of dimensions and constraints. These combinatorial optimization problems are extensively studied and attracted the attention of scientific community from several disciplines such as Computer Science (CS), Operational Research (OR) and many other applied areas. The manual generation of timetables is very time-consuming and takes countless effort. Furthermore, the resulting timetables are usually incompetent and ex- pensive in terms of resources and money. It necessitates the development of automated timetables which minimizes errors, reduces their time of creation and satisfies desirable objectives as much as possible. They are defined as involving the allocation of events (meetings between groups of students and lecturers in a specific venue or between classes and teachers) to timetable periods while at the same time satisfying a set of hard con- straints and minimizing a set of soft constraints violations. Finding an optimal, or even a high-quality timetable for them is also a challenging task, especially when resources are limited. Using events based on groupings of students, a new hybrid algorithm com- bining genetic algorithm with local search is proposed to solve a post-enrollment based university course timetabling problem. A list of events are ordered, and mutually dis- joint groups of students taking them are formed in such a way that once a student is selected for any group, he is excluded from further selection in other groups. The union of all the events taken by all the students of each group is formed. The number of events in each group is termed as its group size whose upper bound is restricted by the total number of timeslots and can be reduced to the maximum number of events per student.
The above process of forming groups is repeated till the size of each group is reduced within this bound by not choosing those events which are common to all the students in the group. Next, two different variants of post-enrollment based university course timetabling problems using the grouping of students are solved by using ant colony op- timization approach. Also, a hybrid metaheuristic approach combining the merits of genetic algorithm (for diversification) and the merits of iterated local search algorithm (for intensification) is developed for solving curriculum-based and post-enrollment based university course timetabling problems. The proposed algorithm iteratively explores so- lution search space by a genetic algorithm using various kinds of neighborhood moves and then exploits it using iterated local search to converge to the optimal solution as
local optimal solutions are escaped by applying perturbations. Further, a general univer- sity course timetabling problem is converted into a Constraint Satisfaction Problem and solved by combining the usual backtracking algorithm with a local search Min-Conflicts- Hill-Climbing algorithm. This algorithm incrementally constructs a solution as is done by backtracking algorithm. Whenever a dead-end is encountered, rather than backtrack- ing to the previously assigned variable, it resolves the cause of dead-end by using the Min-Conflicts-Hill-Climbing algorithm and then continues further progressively. Finally, a school timetabling problem is considered and solved by developing a graph edge color- ing algorithm in two phases. In the first phase, a weekly requirement matrix representing the total number of lectures scheduled for the classes and the teachers is obtained by solving a system of linear equations for the variables taking integer values. Next, these total numbers of lectures are distributed uniformly among all the classes first, and then over all the teachers and finally among the days of a week. A bipartite multigraph is further used for every day of the week to obtain a daily requirement matrix representing the total number of lectures scheduled for the classes and the teachers from the weekly requirement matrix. In the second phase, for each day, again a bipartite graph is used to assign teachers for classes over the time periods such that all the constraints are satisfied simultaneously. This assignment is done without taking any preferences over the timeslots. All the approaches are validated by experimenting them on a number of benchmarks and randomly generated datasets of various complexities. The fitness function value, the number of iterations and the amount of CPU time (in seconds) used as the performance measure. The experimental results are summarized in tables and graphs and observed that our approaches produce promising results in comparison to other existing approaches.
Finally, the conclusions are summarized, and the scope of future works in which direction the thesis can be extended are also provided.
Keywords: Course timetabling, School timetabling, Metaheuristic, Hybridization, Ge- netic algorithm, Ant colony optimization, Iterated local search, Constraint satisfaction problem, Graph edge coloring.
xiv
