: This paper considers a solution to the school timetabling problem. The timetabling problem involves scheduling a number of tuples, each consisting of class of students, a teacher, a subject and a room, to a fixed number of time slots. A Monte Carlo scheme called simulated annealing is used as an optimisation technique. The paper introduces the timetabling problem, and then describes the simulated annealing method. Annealing is then applied to the timetabling problem. A prototype timetabling environment is described followed by some experimental results. A parallel algorithm which can be implemented on a multiprocessor is presented. This algorithm can provide a faster solution than the equivalent sequential algorithm. Some further experimental results are given. 1 INTRODUCTION This paper considers a solution to the school timetabling problem. The timetabling problem involves scheduling a number of tuples, each consisting of class of students, a teacher, a subject and a room, to a fixe...

The construction of timetables for universities or schools is an extremely complex problem, whose manual solution requires much effort. The set of all possible solutions, that is the search space of the problem, is very large, at least in the realworld examples. An acceptable solution is one that satisfies all the problem constraints. The problem becomes even more difficult if someone wants to generate an optimum timetable according to some heuristic criteria. Various attempts have been made so far on the automatic solving of the timetabling problem by a computer. In this paper, a method is proposed for the construction of optimum timetables for university courses. A specific system is presented which has been used for the timetabling procedure of the Department of Informatics of the University of Athens. The software platform of the implementation is an instance of the Constraint Logic Programming class of languages, the ECL i PS e system. ECL i PS e is proved to be an appropriate vehicle for managing the complexity of the timetabling problem.

In this paper we present the results of an investigation of the possibilities offered by three wellknown metaheuristic algorithms to solve the timetable problem, a multi-constrained, NP-hard, combinatorial optimization problem with real-world applications. First, we present our model of the problem, including the definition of a hierarchical structure for the objective function, and of the neighborhood search operators which we apply to matrices representing timetables. Then we report about the outcomes of the utilization of the implemented systems to the specific case of the generation of a school timetable. We compare the results obtained by simulated annealing, tabu search and two versions, with and without local search, of the genetic algorithm. Our results show that GA with local search and tabu search based on temporary problem relaxations both outperform simulated annealing and handmade timetables. 1. Introduction Metaheuristic algorithms [23] constitute a class of computation...

In this paper we present the results of an investigation of the possibilities offered by genetic algorithms to solve the timetable problem. This problem has been chosen since it is representative of the class of multi-constrained, NP-hard, combinatorial optimization problems with real-world application. First we present our model, including the definition of a hierarchical structure for the objective function and the generalized genetic operators which can be applied to matrices representing timetables. Then we report about the outcomes of the utilization of the implemented system to the specific case of the generation of a school timetable. We compare two versions of the genetic algorithm (GA), with and without local search, both to a handmade timetable and to two other approaches based on simulated annealing and tabu search. Our results show that GA with local search and tabu search with relaxation both outperform simulated annealing and handmade timetables. (Introduction) Evolutio...

The timetabling problem consists in fixing a sequence of meetings between teachers and students in a given period of time, satisfying a set of different constraints. There are a number of different versions of the timetabling problem. These include school timetabling (where students are grouped in classes with similar degree plans), university timetabling (where students are considered individually) and examination timetabling (i.e. scheduling of university exams, avoiding student double booking). Several other problems are also associated with the more general timetabling problem, including room allocation, meeting scheduling, staff allocation and invigilator assignment.

Unlike in many other universities, preparation of class timetable in IIT Kanpur is very laborious and complicated. It contains different types of classes, among which most of the common classes are either split or grouped. Many split classes are divided up to five parts, while many sets of group classes contain up to twenty classes. The entire timetable is composed of two phases. The first phase contains all the common compulsory classes of the institute, which are scheduled by a central team. The second phase contains the individual departmental classes. Presently this timetable is prepared manually, by manipulating those of earlier years, with the only aim of producing a feasible timetable. The potentiality of evolutionary algorithms (EAs) have been exploited in the present work to schedule the classes of the first phase of the problem. Using NSGA-II-UCTO, a multi-objective EA-based university class timetable optimizer, a number of trade-off solutions, in terms of multiple objectives of the problem, could be obtained very easily. Moreover, each of the obtained solutions has been found much better than a manually prepared solution which is in use.