A Comparative Analysis of Application of Genetic Algorithm and Particle Swarm Optimization in Solving Traveling Tournament Problem (TTP)

Traveling Tournament Problem (TTP) has been a major area of research due to its huge application in developing smooth and healthy match schedules in a tournament. The primary objective of a similar problem is to minimize the travel distance for the participating teams. This would incur better quality of the tournament as the players would experience least travel; hence restore better energy level. Besides, there would be a great benefit to the tournament organizers from the economic point of view as well. A well constructed schedule, comprising of diverse combinations of the home and away matches in a round robin tournament would keep the fans more attracted, resulting in turnouts in a large number in the stadiums and a considerable amount of revenue generated from the match tickets. Hence, an optimal solution to the problem is necessary from all respects; although it becomes progressively harder to identify the optimal solution with increasing number of teams. In this work, we have described how to solve the problem using Genetic algorithm and particle swarm optimization

An instance data repository for the round-robin sports timetabling problem

The sports timetabling problem is a combinatorial optimization problem that consists of creating a timetable that defines against whom, when and where teams play games. This is a complex matter, since real-life sports timetabling applications are typically highly constrained. The vast amount and variety of constraints and the lack of generally accepted benchmark problem instances make that timetable algorithms proposed in the literature are often tested on just one or two specific seasons of the competition under consideration. This is problematic since only a few algorithmic insights are gained. To mitigate this issue, this article provides a problem instance repository containing over 40 different types of instances covering artificial and real-life problem instances. The construction of such a repository is not trivial, since there are dozens of constraints that need to be expressed in a standardized format. For this, our repository relies on RobinX, an XML-supported classification framework. The resulting repository provides a (non-exhaustive) overview of most real-life sports timetabling applications published over the last five decades. For every problem, a short description highlights the most distinguishing characteristics of the problem. The repository is publicly available and will be continuously updated as new instances or better solutions become available

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

The Traveling Tournament Problem

In this thesis we study the Traveling Tournament problem (TTP) which asks to generate a feasible schedule for a sports league such that the total travel distance incurred by all teams throughout the season is minimized. Throughout our three technical chapters a wide range of topics connected to the TTP are explored. We begin by considering the computational complexity of the problem. Despite existing results on the NP-hardness of TTP, the question of whether or not TTP is also APX-hard was an unexplored area in the literature. We prove the affirmative by constructing an L-reduction from (1,2)-TSP to TTP. To reach the desired result, we show that given an instance of TSP with a solution of cost K, we can construct an instance of TTP with a solution of cost at most 20m(m+1)cK where m = c(n-1)+1, n is the number of teams, and c > 5, c ∈ ℤ is fixed. On the other hand, we show that given a feasible schedule to the constructed TTP instance, we can recover a tour on the original TSP instance. The next chapter delves into a popular variation of the problem, the mirrored TTP, which has the added stipulation that the first and second half of the schedule have the same order of match-ups. Building upon previous techniques, we present an approximation algorithm for constructing a mirrored double round-robin schedule under the constraint that the number of consecutive home or away games is at most two. We achieve an approximation ratio on the order of 3/2 + O(1)/n. Lastly, we present a survey of local search methods for solving TTP and discuss the performance of these techniques on benchmark instances

Time Relaxed Round Robin Tournament and the NBA Scheduling Problem

This dissertation study was inspired by the National Basketball Association regular reason scheduling problem. NBA uses the time-relaxed round robin tournament format, which has drawn less research attention compared to the other scheduling formats. Besides NBA, the National Hockey League and many amateur leagues use the time-relaxed round robin tournament as well. This dissertation study is the first ever to examine the properties of general time-relaxed round robin tournaments. Single round, double round and multiple round time-relaxed round robin tournaments are defined. The integer programming and constraint programming models for those tournaments scheduling are developed and presented. Because of the complexity of this problem, several decomposition methods are presented as well. Traveling distance is an important factor in the tournament scheduling. Traveling tournament problem defined in the time constrained conditions has been well studied. This dissertation defines the novel problem of time-relaxed traveling tournament problem. Three algorithms has been developed and compared to address this problem. In addition, this dissertation study presents all major constraints for the NBA regular season scheduling. These constraints are grouped into three categories: structural, external and fairness. Both integer programming and constraint programming are used to model these constraints and the computation studies are presente

Mathematical Modeling and Optimization Approaches for Scheduling the Regular-Season Games of the National Hockey League

RÉSUMÉ : La Ligue nationale de hockey (LNH) est une association sportive professionnelle de hockey sur glace regroupant des équipes du Canada et des États-Unis. Chaque année, la LNH dois compter sur un calendrier de haute qualité concernant des questions économiques et d'équité pour les 1230 matchs de sa saison régulière. Dans cette thèse, nous proposons le premier modèle de programmation linéaire en nombres entiers (PLNE) pour le problème de la planification de ces matchs. Basé sur la littérature scientifique en planification des horaires sportifs, et aussi sur un raisonnement pratique, nous identifions et soulignons des exigences essentielles et des préférences qui doivent être satisfaites par des calendriers de haute qualité pour la LNH. La construction de tels calendriers, tout comme la planification des horaires sportifs en général, s'avère une tâche très difficile qui doit prendre en compte des intérêts concurrents et, dans plusieurs cas, subjectifs. En particulier, les expérimentations numériques que nous décrivons dans cette étude fournissent des évidences solides suggérant qu'une approche basée sur la PLNE est actuellement incapable de résoudre des instances de taille réaliste pour le problème. Pour surmonter cet inconvénient, nous proposons ensuite un algorithme de recherche adaptative à voisinage large (ALNS) qui intègre à la fois des nouvelles stratégies et des heuristiques spécialisées provenant de la littérature scientifique. Afin de tester cette approche, nous générons plusieurs instances du problème. Toutes les instances sont basées sur les calendriers officiels de la LNH et, en particulier, utilisent les dates de matchs à domicile de chaque équipe comme des dates de disponibilité de son aréna. Dans les situations les plus difficiles, la disponibilité des arénas est rare ou est à son minimum. Dans tous les cas, en ce qui concerne les indicateurs de qualité soulevés, l'algorithme ALNS a été capable de générer des calendriers clairement meilleur que leur correspondants adoptés par la LNH. Les résultats obtenus suggèrent que notre approche pourrait certainement permettre aux gestionnaires de la LNH de trouver des calendriers de meilleur qualité par rapport à une variété de nouvelles préférences.----------ABSTRACT : The National Hockey League (NHL) is a major professional ice hockey league composed of 30 teams located throughout the United States and Canada. Every year, the NHL must rely on a high-quality schedule regarding both economic and fairness issues for the 1230 games of its regular season. In this thesis, we propose the first integer linear programming (IP) model for the problem of scheduling those games. Based both on the pertinent sports scheduling literature and on practical reasoning, we identify and point out essential requirements and preferences that should be satisfied by good NHL schedules. Finding such schedules, as many other sports scheduling problems, is a very difficult task that involves several stakeholders with many conflicting, and often subjective, interests. In fact, computational experiments that we describe in this study, provide compelling evidence that an IP approach is currently unable to solve instances of realistic size for the problem. To overcome such drawback, we propose then an Adaptive Large Neighborhood Search (ALNS) algorithm that integrates both novel strategies and specialized heuristics from the scientific literature. To test the approach, we generate instances based on past NHL schedules and on a given number of arena-available dates that are suitable for the home games of each team. In the most challenging instances, availability of arenas is scarce or at its minimum. In all cases, regarding the identified concerns, the ALNS algorithm was able to generate much better schedules than those implemented by the NHL. Results obtained suggest that our approach could certainly identify unnecessary weakness in NHL schedules, makes the NHL managers aware of better schedules with respect to different requirements, and even lead them to consider other desired features they might not have previously taken into account

English Premier League scheduling using simulated annealing

This is the first known attempt at scheduling the English Premier League (EPL), which is a NP-hard problem, in the literature. In this research an initial schedule is created using a ‘polygon’ construction method, a method which originates in graph theory. Two distinct simulated annealing metaheuristic solving methodologies are then created to improve this initial schedule. One method is based on a temperature schedule, finite epoch length and reheats while the other is based on a gradually reducing temperature schedule and non-finite epoch length. These two methods were evaluated with respect to solution quality (total penalty), reliability (variation of solution quality over numerous trials) and speed. The official schedule used by the EPL organisers was used for comparison. It was found that the first method produced comparable results, while the second produced improved results. The second method was validated over three seasons and consistently performed well. The findings in this research can be used as the maiden real-world framework and benchmark for the unsolved EPL scheduling problem in the sports scheduling literature

Solving hard industrial combinatorial problems with SAT

The topic of this thesis is the development of SAT-based techniques and tools for solving industrial combinatorial problems. First, it describes the architecture of state-of-the-art SAT and SMT Solvers based on the classical DPLL procedure. These systems can be used as black boxes for solving combinatorial problems. However, sometimes we can increase their efficiency with slight modifications of the basic algorithm. Therefore, the study and development of techniques for adjusting SAT Solvers to specific combinatorial problems is the first goal of this thesis. Namely, SAT Solvers can only deal with propositional logic. For solving general combinatorial problems, two different approaches are possible: - Reducing the complex constraints into propositional clauses. - Enriching the SAT Solver language. The first approach corresponds to encoding the constraint into SAT. The second one corresponds to using propagators, the basis for SMT Solvers. Regarding the first approach, in this document we improve the encoding of two of the most important combinatorial constraints: cardinality constraints and pseudo-Boolean constraints. After that, we present a new mixed approach, called lazy decomposition, which combines the advantages of encodings and propagators. The other part of the thesis uses these theoretical improvements in industrial combinatorial problems. We give a method for efficiently scheduling some professional sport leagues with SAT. The results are promising and show that a SAT approach is valid for these problems. However, the chaotical behavior of CDCL-based SAT Solvers due to VSIDS heuristics makes it difficult to obtain a similar solution for two similar problems. This may be inconvenient in real-world problems, since a user expects similar solutions when it makes slight modifications to the problem specification. In order to overcome this limitation, we have studied and solved the close solution problem, i.e., the problem of quickly finding a close solution when a similar problem is considered

Ant algorithm hyperheuristic approaches for scheduling problems

For decades, optimisation research has investigated methods to find optimal solutions to many problems in the fields of scheduling, timetabling and rostering. A family of abstract methods known as metaheuristics have been developed and applied to many of these problems, but their application to specific problems requires problem-specific coding and parameter adjusting to produce the best results for that problem. Such specialisation makes code difficult to adapt to new problem instances or new problems. One methodology that intended to increase the generality of state of the art algorithms is known as hyperheuristics. Hyperheuristics are algorithms which construct algorithms: using "building block" heuristics, the higher-level algorithm chooses between heuristics to move around the solution space, learning how to use the heuristics to find better solutions. We introduce a new hyperheuristic based upon the well-known ant algorithm metaheuristic, and apply it towards several real-world problems without parameter tuning, producing results that are competitive with other hyperheuristic methods and established bespoke metaheuristic techniques