Confection de calendriers d'événements sportifs au Québec

L’automatisation de la confection de calendriers pour les ligues sportives a reçu une attention particulière au cours des dernières années puisque les ligues sportives génèrent des revenus considérables ainsi que des problèmes d’optimisation combinatoire intéressants. La Fédération Québécoise pour le Sport Étudiant (FQSE) a reçu le mandat d’organiser les championnats sportifs provinciaux scolaires, collégiaux et universitaires. Nous comparons le problème québécois qu’elle nous expose à une classe de problèmes similaires communément appelés dans la littérature traveling tournament problem, ce type de problèmes ayant pour but de minimiser la distance totale parcourue par les équipes. Nous formulons par la suite un modèle mathématique dont l’objectif est de produire des calendriers satisfaisant un nombre optimal de contraintes inédites fournies par la FQSE. La revue de littérature met en avant les différentes méthodes qui ont été utilisées pour résoudre le traveling tournament problem, mais elle nous permet aussi de constater qu’un bon nombre des contraintes du problème québécois sont originales. Pour résoudre ce problème, nous avons formulé un modèle mathématique en nombres entiers que nous résolvons à l’aide du logiciel CPLEX. Notre modèle prend en compte des variables booléennes à deux indices qui vont nous permettre de d´eterminer l’endroit où a lieu chaque rencontre, la date à laquelle chaque rencontre va se jouer et les équipes qui vont jouer à domicile, à l’extérieur ou celles qui ne vont pas jouer à chaque date. Il a été testé sur deux instances fournies par la FQSE pour le football collégial et universitaire pour lesquelles nous avons pu facilement générer des calendriers optimaux. Une extension du modèle est ensuite proposée pour prendre en compte la distance parcourue pour chaque équipe. Ce nouveau modèle utilise des variables booléennes à deux et trois indices, le rendant ainsi plus intéressant que les modèles que nous avons pu trouver dans la littérature. Le modèle développé est capable de prendre en compte toutes les contraintes que nous avons pu rencontrer dans la littérature, mais il est aussi capable de traiter ensemble un bon nombre de contraintes originales. La flexibilité du modèle rend ses applications éventuelles nombreuses étant donné que des contraintes supplémentaires peuvent facilement être rajoutées en autant qu’elles s’écrivent comme une combinai- son linéaire des variables du modèle.---------- ABSTRACT Several sport federations are confronted with the problem of tournament scheduling. The Fédération Québcoise du Sport Étudiant (FQSE) has the mandate to organize championship tournaments at the school, college and university levels in the province of Quebec and we have been asked to help them in scheduling their tournaments. We first compare their problem to a class of similar instances commonly known as the traveling tournament problem (TTP). In the TTP, the objective is to minimize the total traveled distance for all teams. Then we formulate a mathematical model for the problem in Quebec where the objective is to produce schedules with an optimal number of satisfied constraints. The constraints we consider are all given by the FQSE and the literature review shows that many of them are new. After having described in the literature review the different methods that have been used for solving the TTP, we propose an integer programming model and use CPLEX to solve it. The mathematical model uses boolean variables with two indices which indicate where and when each game is to take place, and which teams play at home, away or do not play in each round. The mathematical model has been tested on two instances given by the FQSE for college and university football. For both of them we can easily generate optimal schedules. In the last section, an extended model is presented to take into account the traveled distance for each team. This model uses boolean variables with two or three indices, which makes it more interesting when compared with what can be found in the literature. Our model is able to take into account the different types of constraints we have seen in the literature, but it can also handle a good number of original constraints. Its flexibility makes it easy to apply to several sport scheduling problems: we can add any constraint that can be written as a linear combination of the variables of the model. The main restriction is due to the fact that the more constraints a problem has, the more difficult it gets. In that case, a good solution would be to develop a heuristic algorithm

Mathematical modeling and tabu search heuristic for the traveling tournament problem

As professional sports have become big businesses all over the world, many researches with respect to sports scheduling problem have been worked over the last two decades. The traveling tournament problem (TTP) is defined as minimizing total traveling distance for all teams in the league. In this study, a mathematical model for the TTP is presented. This model is formulated using an integer programming (IP). In order to solve practical problems with large size of teams, a tabu search heuristic is suggested. Also, the concepts of alternation and intimacy were introduced for effective neighborhood search. Experiments with several instances are tested to evaluate their performances. It was shown that the proposed heuristic shows good performances with computational efficiency.ope

Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast