Les modèles mathématiques et des méthodes fondées sur l'approche métaheuristique pour résoudre les problèmes d'établissement des horaires

Mathematical models and methods based on metaheuristic approach for timetabling problem

• Auteur / Autrice : Maqsood Ahmad
• Direction : Michel Gourgand, Christophe Caux
• Type : Thèse de doctorat
• Discipline(s) : Informatique
• Date : Soutenance le 15/11/2013
• Etablissement(s) : Clermont-Ferrand 2
• Ecole(s) doctorale(s) : École doctorale des sciences pour l'ingénieur (Clermont-Ferrand)
• Partenaire(s) de recherche : Laboratoire : Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
• Jury : Président / Présidente : Abdelhakim Artiba
• Jury : Examinateurs / Examinatrices : Michel Gourgand, Christophe Caux, Alain Quilliot
• Jury : Rapporteurs / Rapporteuses : Ameur Soukhal, Gülgün Alpan

Mots clés

Mots clés contrôlés

Métaheuristiques

Budgets temps

Mots clés libres

Timetabling

Optimisation combinatoire

Modélisation mathématique

Méta heuristiques

Algorithme mémétique

Recherche tabou

Timetabling problem

Combinatorial optimization

Mathematical modeling

Resource constrained project scheduling problem

Metaheuristics

Memetic algorithm

Tabu search

Honey bee mating

Résumé

Résumé indisponible.

In this thesis we have concerned ourselves with university timetabling problems both course timetabling and examination timetabling problems. Most of the timetabling problems are computationally NP-complete problems, which means that the amount of computation required to find solutions increases exponentially with problem size. These are idiosyncratic nature problems, for example different universities have their own set of constraints, their own definition of good timetable, feasible timetable and their own choice about the use of constraint type (as a soft or hard constraint). Unfortunately, it is often the case that a problem solving approach which is successfully applied for one specific problem may not become suitable for others. This is a motivation, we propose a generalized problem which covers many constraints used in different universities or never used in literature. Many university timetabling problems are sub problems of this generalized problem. Our proposed algorithms can solve these sub problems easily, moreover constraints can be used according to the desire of user easily because these constraints can be used as reference to penalty attached with them as well. It means that give more penalty value to hard constraints than soft constraint. Thus more penalty value constraints are dealt as a hard constraint by algorithm. Our algorithms can also solve a problem in two phases with little modification, where in first phase hard constraints are solved. In this work we have preferred and used two phase technique to solve timetabling problems because by using this approach algorithms have broader search space in first phase to satisfy hard constraints while not considering soft constraints at all. Two types of algorithms are used in literature to solve university timetabling problem, exact algorithms and approximation algorithms. Exact algorithms are able to find optimal solution, however in university timetabling problems exact algorithms constitute brute-force style procedures. And because these problems have the exponential growth rates of the search spaces, thus these kinds of algorithms can be applied for small size problems. On the other side, approximation algorithms may construct optimal solution or not but they can produce good practically useable solutions. Thus due to these factors we have proposed approximation algorithms to solve university timetabling problem. We have proposed metaheuristic based techniques to solve timetabling problem, thus we have mostly discussed metaheuristic based algorithms such as evolutionary algorithms, simulated annealing, tabu search, ant colony optimization and honey bee algorithms. These algorithms have been used to solve many other combinatorial optimization problems other than timetabling problem by modifying a general purpose algorithmic framework. We also have presented a bibliography of linear integer programming techniques used to solve timetabling problem because we have formulated linear integer programming formulations for our course and examination timetabling problems. We have proposed two stage algorithms where hard constraints are satisfied in first phase and soft constraints in second phase. The main purpose to use this two stage technique is that in first phase hard constraints satisfaction can use more relax search space because in first phase it does not consider soft constraints. In second phase it tries to satisfy soft constraints when maintaining hard constraints satisfaction which are already done in first phase. (...)