The thesis deals with a hard real-life school timetabling problem of a Czech secondary school. In this problem, lessons are to be allocated to classrooms while respecting various constraints such as curricula and teacher availability. We study existing approaches used for school timetabling problems and we show how to represent introduced problem in existing school timetabling software. We then present a software prototype that solves introduced problem using constraint logic programming. Related problems, such as data representation and data conversion, are discussed. Powered by TCPDF (www.tcpdf.org)

The automated timetabling and scheduling is one of the hardest problem areas. This isbecause of constraints and satisfying those constraints to get the feasible and optimizedschedule, and it is already proved as an NP Complete (1) [1]. The basic idea behind this studyis to investigate the performance of Genetic Algorithm on general scheduling problem underpredefined constraints and check the validity of results, and then having comparative analysiswith other available approaches like Tabu search, simulated annealing, direct and indirectheuristics [2] and expert system. It is observed that Genetic Algorithm is good solutiontechnique for solving such problems and later analysis will prove this argument. The programis written in C++ and analysis is done by using variation in various parameters.

The problem of timetabling events is present in various organizations such as schools, hospitals, transportation centers. The purpose of timetabling activities at a university is to ensure that all students attend their required subjects in accordance with the available resources. The set of constraints that must be considered in the design of timetables involves students, teachers and infrastructure. This study shows that acceptable solutions are generated through the application of genetic, memetic and immune system algorithms for the problem of timetabling. The algorithms are applied to real instances of the University of Mumbai in India and their results are comparable with those of a human expert. / Revisión por pares

The growing demand for railway capacity has led to high capacity consumption at times and a delay-sensitive network with insufficient robustness. The fundamental challenge is therefore to decide how to increase the robustness. To do so there is a need for accurate measures that return whether the timetable is robust or not and indicate where improvements should be made. Previously presented measures are useful when comparing different timetable candidates with respect to robustness, but less useful to decide where and how robustness should be inserted. In this paper, we focus on points where trains enter a line, or where trains are being overtaken, since we have observed that these points are critical for the robustness. The concept of critical points can be used in the practical timetabling process to identify weaknesses in a timetable and to provide suggestions for improvements. In order to quantitatively assess how crucial a critical point may be, we have defined the measure RCP (Robustness in Critical Points). A high RCP value is preferred, and it reflects a situation at which train dispatchers will have higher prospects of handling a conflict effectively. The number of critical points, the location pattern and the RCP values constitute an absolute value for the robustness of a certain train slot, as well as of a complete timetable. The concept of critical points and RCP can be seen as a contribution to the already defined robustness measures which combined can be used as guidelines for timetable constructors.

The field of automated timetabling and scheduling meeting all the requirementsthat we call constraints is always difficult task and already proved as NPComplete. The idea behind my research is to implement Genetic Algorithm ongeneral scheduling problem under predefined constraints and check the validityof results, and then I will explain the possible usage of other approaches likeexpert systems, direct heuristics, network flows, simulated annealing and someother approaches. It is observed that Genetic Algorithm is good solutiontechnique for solving such problems. The program written in C++ and analysisis done with using various tools explained in details later.

Ο χρονοπρογραμματισμός (scheduling) μπορεί να οριστεί ως το πρόβλημα εύρεσης μιας βέλτιστης σειράς για την εκτέλεση ενός πεπερασμένου συνόλου λειτουργιών, χωρίς να παραβιάζεται ένα συγκεκριμένο σύνολο κανόνων. Η παρουσα διπλωματική ασχολείται με την υλοποίηση γραφικού περιβάλλοντος για τη γραφική παρουσίαση των δεδομένων του προβλήματος χρονοπρογραμματισμου όπως αναπτύχθηκε για τον διαγώνισμό ITC07. Η διεπαφή παράγει έγκυρα (εφικτά) (για παράδειγμα δεν θα προγραμματίζονται διαφορετικές εξετάσεις στην ίδια περίοδο εφόσον έχουν κοινούς φοιτητές) προγράμματα εξεταστικής και σχεδιασμένα με γνώμονα την διευκόλυνση των φοιτητών (θα παρέχoνται δηλαδή επαρκή χρονικά διαστήματα μεταξύ των εξεταζόμενων μαθημάτων για όλους τους φοιτητές). Το κάθε πρόγραμμα που παράγεται λαμβάνει υπόψη τους εκάστοτε περιορισμούς και συγκροτεί ορθολογικά ένα κατά το δυνατόν βέλτιστο πρόγραμμα.Ο χρήστης μπορεί να τροποποιεί τα δεδομένα του προβλήματος και να ζητά την επαναϋπολογισμό του κόστους προσδοκώντας καλύτερη ποιότητα λύσης. / -

Η παρούσα εργασία αποσκοπεί στη μελέτη του προβλήματος του χρονοπρογραμματισμού γεγονότων, την τοποθέτηση δηλαδή των γεγονότων σε υποδοχείς χρόνου και χώρου, με τη χρήση Γενετικών Αλγορίθμων. Μελετήσαμε τo πρόβλημα του χρονοπρογραμματισμού στην Εκπαίδευση και ειδικότερα σε ένα Πανεπιστήμιο, που εμφανίζεται σε δύο εκδοχές: το πρόβλημα χρονοπρογραμματισμού εξετάσεων και το πρόβλημα χρονοπρογραμματισμού διαλέξεων, καθώς και τα αντίστοιχα πειράματα και τα αποτελέσματα αυτών. Χρησιμοποιώντας το λογισμικό FET που βασίζεται στους Γενετικούς Αλγόριθμους κατασκευάσαμε χρονοδιαγράμματα για το ωρολόγιο πρόγραμμα του Μεταπτυχιακού Προγράμματος του Διατμηματικού του Πανεπιστημίου Πατρών "Μαθηματικά των Υπολογιστών και των Αποφάσεων" των τμημάτων Μαθηματικών και Μηχανικών Η/Υ και Πληροφορικής και παρουσιάσαμε τα αποτελέσματα αυτών. / The aim of this paper is the study of the timetabling problem, meaning the allocation of events in time-slots and space-slots, using Genetic Algorithms. We studied the Education Timetabling problem for a University which appears in two versions, timetabling of exams and timetabling of lectures and its corresponding experiments and results. Using the open source free software FET which is based on the Genetic Algorithms, we scheduled timetables for the weekly program of Postgraduate Program of University of Patras "Mathematics of Computers and Decision" in which participate two departments, the department of Mathematics and the department of Engineering Computing and Information Technology and we presented the results of those.

In this thesis, we present a way to model uncertainty when optimizing the UniversityTimetabling Problem. It is an NP-hard, combinatorial and highly constrained problem.In this thesis, we first propose a standardized model based on the data from MalmöUniversity. Then, we propose our extended model, which, during the creation of the solution, accounts for the probability of unexpected events to occur and changes the solution accordingly. To implement our model, we use a Particle Swarm Optimization (PSO) algorithm.In our experiments, we find problems with the algorithm converging too early.We analyze the performance of our extended model compared to the standardized model,using a benchmark devised by us, and find that it performs well, reducing the number ofconstraint violations by 32%. We then suggest further areas of research in regards to thisuncertainty model.

The University Course Timetabling Problem (UCTP) is the problem of assigning locations (lecture halls, computer rooms) and time slots (time and date) to a set of events (lectures, labs) while satisfying a number of constraints such as avoiding double-bookings. Many variants of problem formulations exist, and most realistic variants are thought to be NP-hard. A recent trend in solving hard scheduling problems lies in the application of hybrid metaheuristics, where improvements are often found by hybridizing a population-based approach with some form of local search. In this paper, an implementation of a Genetic Algorithm (GA) that solves the UCTP is hybridized with local search in the form of Tabu Search (TS). The results show significant improvements to the performance and scalability over the non-hybridized GA. Two application strategies for the TS are investigated. The first strategy performs a switch-over from the GA to the TS, while the second interleaves the two algorithms. The effectiveness of each application strategy is seen to depend on the characteristics of the individual algorithms. / Schemaläggningsproblemet UCTP (University Course Timetabling Problem) består av problemet att tilldela platser (föreläsningssalar, laborationssalar) och tidpunkter (datum och klockslag) till en mängd tillställningar (föreläsningar, laborationer) under kravet att upprätthålla en mängd restriktioner, exempelvis att undvika dubbelbokningar. Det finns många varianter av problemformuleringen och de flesta realistiska formuleringer anses ge upphov till NP-svåra optimeringsproblem. En förhållandevis ny trend för lösningsmodeller till svåra schemaläggningsproblem ligger i tillämpningen av hybrida metaheuristiker, där förbättringar ofta ses när populationsbaserade algoritmer kombineras med någon typ av lokalsökning. I denna rapport undersöks en UCTP-lösning baserad på en Genetisk Algoritm (GA) som hybridiseratsmed en lokalsökning i form av en Tabusökning (TS). Resultaten visar på signifikanta förbättringar i prestanda och skalbarhet jämfört med den icke-hybridiserade GA:n. Två appliceringsstrategier för TS undersöks. Den första strategin utgörs av att byta algoritm från GA till TS, medan den andra utgörs av att sammanfläta de två algoritmerna. Appliceringsstrategiernas effektivitet ses bero av de individuella algoritmernas egenskaper.

This thesis examines the university timetable generation problem. It begins with a discussion on the conflicting terminology used and differentiates between the terms scheduling and timetabling. This discussion integrates with an overview of the problem itself both from practical and academic perspectives. This is followed by a summary of the apparently effective timetable solution generation algorithms. The literature is then examined in detail from that perspective. This literature review is then summarised in a form to highlight the use of these different solution algorithms. A classification schema is developed and the summary of the literature presented within the framework of this schema. Trends in the research literature result from this presentation and an extrapolation to future research trends are suggested. An information system based upon the need to support timetable production and maintenance is presented. Given the very practical outcomes expected of timetable research, the information system was designed to enable the whole range of administrative functions performed by teachers to be either directly supported or readily modified to prove such support. The implementation of this particular system is given and resulting timetables are presented and discussed. The system generated manual and automated timetables and these were produced by trailing a number of objective functions. It was noted that the determination of the optimal objective function is dominated by specific individual institutional criteria. It is suggested that this would make a more than significant project for future information systems research. From the literature it is noted that the timetable generation problem, as reported time and time again in the literature, has been solved. Such claims lead to a benchmark which is proposed to enable an initial comparison of the effectiveness of proposed solutions by different researchers. The thesis then presents a summary of the work that was carried out and offers direction for future research. It is noted that despite the fifty years of research conducted into this area there exists a significant number of research avenues still to be pursued.