: 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...

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...

Scheduling term-end exams (TEE) at the United States Military Academy in West Point is unlike any other exam timetabling problem we know of. Exam timetabling normally produces a con‡ict-free timetable covering a reasonably long exam period, where every exam is scheduled exactly once for all the students enrolled in the corresponding class. The situation is quite di¤erent at West Point. There are hundreds of exams to schedule over such a short time period that there is simply no feasible solution. The challenge is then to allow something that is not even considered elsewhere, that is, creating multiple sessions of some exams, scheduled at di¤erent times within the exam period, to allow each student to take all exams he/she must take. The overall objective is to …nd a feasible exam schedule with a minimum number of such duplicate exams. The paper describes a system that has been developed at GAMS Development Corp. in close cooperation with the scheduling sta ¤ at West Point, and that has been used successfully since 2001. It uses mathematical optimization in several modules, and some of the techniques proposed are new. It is fast and ‡exible, and allows for human interaction, such as adding initially unexpected constraints, coming for instance from instructors’preferences and dislikes, as well as their hierarchical rankings. It is robust and can be used by people familiar with the organization at West Point, without the need for them to be technically-trained. Overall, using the course and student information databases, it is an e¤ective decision support system that calls optimization tools in an unobtrusive way.