Abstract- Course timetabling problems are real world constraint optimization problems that are often coped with in educational institutions, such as universities or high schools. In this paper, we present a variety of new operators that can be also applied in evolutionary algorithms for other timetabling problems, such as, exam timetabling. Operators include violation directed mutations, crossovers, and a successful violation directed hierarchical hill climbing method. Tests are performed on a small portion of a real data and results are promising. 1

Summary. There are several characteristics that make scheduling and timetabling problems particularly difficult to solve: they have huge search spaces, they are often highly constrained, they require sophisticated solution representation schemes, and they usually require very time-consuming fitness evaluation routines. There is a considerable number of memetic algorithms that have been proposed in the literature to solve scheduling and timetabling problems. In this chapter, we concentrate on identifying and discussing those strategies that appear to be particularly useful when designing memetic algorithms for this type of problems. For example, the many different ways in which knowledge of the problem domain can be incorporated into memetic algorithms is very helpful to design effective strategies to deal with infeasibility of solutions. Memetic algorithms employ local search, which serves as an effective intensification mechanism that is very useful when using sophisticated representation schemes and time-consuming fitness evaluation functions. These algorithms also incorporate a population, which gives them an effective explorative ability to sample huge search spaces. Another important aspect that has been investigated when designing memetic algorithms for scheduling and timetabling problems, is how to establish the right balance between the work performed by the genetic search and the work performed by the local search. Recently, researchers have put considerable attention in the design of self-adaptive memetic algorithms. That is, to incorporate memes that adapt themselves according to the problem domain being solved and also to the particular conditions of the search process. This chapter also discusses some recent ideas proposed by researchers that might be useful when designing self-adaptive memetic algorithms. Finally, we give a summary of the issues discussed throughout the chapter and propose some future research directions in the design of memetic algorithms for scheduling and timetabling problems. 1

Abstract: There is a variety of approaches developed by researchers to solve different instances of timetabling problems. During these studies different data formats are used to represent a timetabling problem instance and its solution, causing difficulties in the evaluation and comparison of approaches and sharing data. In this paper, a model for timetabling problems and a new XML data format for them based on MathML is proposed.

In this paper we describe the timetabling problem and its solvability in a Constraint Logic Programming Language. A solution to the problem has been developed and implemented in ECL i PS e , since it deals with finite domains, it has well-defined interfaces between basic building blocks and supports good debugging facilities. The implemented timetable was based on the existing, currently used, timetables at the School of Informatics at out university. It integrates constraints concerning room and period availability.

Abstract. The construction of course timetables for academic institutions is a very difficult problem with a lot of constraints that have to be respected and a huge search space to be explored, even if the size of the problem input is not significantly large, due to the exponential number of the possible feasible timetables. On the other hand, the problem itself does not have a widely approved definition, since different variations of it are faced by different departments. However, there exists a set of entities and constraints among them which are common to every possible instantiation of the timetabling problem. In this paper, we present a model of this common core in terms of Ilog Solver, a constraint programming object-oriented C++ library, and we show the way this model may be extended to cover the needs of a specific academic unit. 1

In the paper we discuss the implementation of a genetic based algorithm that is used to produce timetables for a small school. A problem specific chromosome representation and the use of a repair algorithm after the genetic operators avoid searching through illegal timetables. We also tested the use of different fitness functions and present results obtained with our prototype timetabling system implemented in C. 1. Introduction The school-timetabling problem is basically the assignment of weekly lessons to time periods. Existing solutions are either difficult to use or lead to inadequate solutions. Our objective is to develop a program that can easily be used in a typical school and allowing user interaction and modification of parameter settings. In section 2 we discuss the class-teachertimetabling problem in more detail. The genetic algorithm (G.A.), chromosome representation and the cost and fitness functions are explained in section 3. Section 4 presents the genetic operators an...

This paper considers the use of discrete Hopfield neural networks for solving school timetabling problems. Two alternative formulations are provided for the problem: a standard Hopfield-Tank approach, and a more compact formulation which allows the Hopfield network to be competitive with swapping heuristics. It is demonstrated how these formulations can lead to different results. The Hopfield network dynamics are also modified to allow it to be competitive with other metaheuristics by incorporating controlled stochasticities. These modifications do not complicate the algorithm, making it possible to implement our Hopfield network in hardware. The neural network results are evaluated on benchmark data sets and are compared to results obtained using greedy search, simulated annealing and tabu search.

. The construction of course timetables for academic institutions is a very difficult problem with a lot of constraints that have to be respected and a huge search space to be explored, even if the size of the problem input is not significantly large, due to the exponential number of the possible feasible timetables. On the other hand, the problem itself does not have a widely approved definition, since different variations of it are faced by different departments. However, there exists a set of entities and constraints among them which are common to every possible instantiation of the timetabling problem. In this paper, we present a model of this common core in terms of a constraint programming objectoriented C++ library, namely the Ilog Solver, and we show the way this model may be extended to cover the needs of a specific academic unit, the Department of Informatics of the University of Athens. The exploration of the relevant search space, in order to find solutions of ...

Abstract. One of the most significant problems in the training centers is presenting an exam timetabling due to enrolled subjects for each student with maximum spread between exams. In this paper, a special mathematical programming model is presented which its purpose is to minimize interference of the time period of each exam for each student. It is too difficult and even impossible to optimally solve the above problem in a reasonable computational time. Thus, an evolutionary computing, for example genetic algorithm, is used as one of the stochastic search methods for solving an exam timetabling problem. The problem is considered as the assignment of facilities (i. e., exam subject) to the specific locations (i. e., positions). In other word, the exam subjects are assigned within time periods to its optimal position. 1