Scheduling sport tournaments using constraint logic programming

We tackle the problem of scheduling the matches of a round robin tournament for a sport league. We formally define the problem, state its computational complexity, and present a solution algorithm using a two-step approach. The first step is the creation of a tournament pattern and is based on known graph-theoretic results. The second one is a constraint-based depth-first branch and bound procedure that assigns actual teams to numbers in the pattern. The procedure is implemented using the finite domain library of the constraint logic programming language eclipse. Experimental results show that, in practical cases, the optimal solution can be found in reasonable time, despite the fact that the problem is NP-complete

A flexible mathematical model for the planning and designing of a sporting fixture by considering the assignment of referees

Indexación: Scopus.This paper deals with the problems faced with the designing and planning of a sporting fixture considering correct referee assignments. A non-linear binary program model is proposed to solve the problems, which aims to minimize the sums of the differences that exist between the requirements of each match and the quality of the referee assigned achieving the design of the most adequate referee for each match. The efficiency of the proposed model is proved using some real data obtained from various fixtures for sports such as soccer, volleyball, and basketball. The mathematical model is solved by using CPLEX 12.7.0., which allows the automatic linearization of the problems. The results obtained demonstrate the efficiency of the proposed methodology for tackling problems, as well as its extension to other sporting disciplines, which require a similar type of planning. Similarly, given the robust nature of the proposed model, it is possible to implement other objective functions in accordance with the requirements of each league. © 2019 by the authors; licensee Growing Science, Canada.http://growingscience.com/beta/ijiec/2960-a-flexible-mathematical-model-for-the-planning-and-designing-of-a-sporting-fixture-by-considering-the-assignment-of-referees.htm

The restricted group draw problem in sports tournaments: a detailed case study

Many sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Since finding an allocation of the teams that satisfies the established criteria is non-trivial, UEFA has adopted a procedure based on a random draw assisted by the computer to indicate the group(s) available for the drawn team. It is shown how this mechanism is connected to generating permutations, and a straightforward modification is proposed to increase the excitement of the draw. The consequences of draw restrictions are investigated through the case study of the European Qualifiers to the 2022 FIFA World Cup. We assess the probability of an obscure situation that threatens the transparency of the draw and quantify the departure of the UEFA mechanism from an evenly distributed random draw among all feasible allocations.Comment: 18 pages, 4 figures, 2 table

A hybrid constraint-based programming approach to design a sports tournament scheduling

We investigate the problem of sports tournament scheduling as reflected in the quality of tournament schedule in University Utara Malaysia (UUM). The background of the sports tournament problems that inefficiency of the human scheduler, time-consuming task and unfairness among the athletes that need to be solved gives direction and motivation in investigating the problem of scheduling the sports tournament. Subsequently,previous work related to the problem is discussed. Thus, we present an innovative hybrid of a constraint-based algorithm and a neighbourhood search, which is an exploration into alternative and improved methodology in the problem of sports tournament scheduling with special multiple constraints. A scheduling system is then developed. As a result, fair distribution of break or rest times and game venues among the competing teams are achieved in our objectives. The sports tournament scheduling system assists and improves the sports events management through high quality schedule as compared with the current human scheduler, which consider rest period, day and time preferences and venue availability. Thus, this sophisticated algorithm provides the feasible, optimum, efficient and quick solution

A modified migrating bird optimization for university course timetabling problem

University course timetabling problem is a dilemma which educational institutions are facing due to various demands to be achieved in limited resources. Migrating bird optimization (MBO) algorithm is a new meta-heuristic algorithm which is inspired by flying formation of migrating birds. It has been applied successfully in tackling quadratic assignment problem and credit cards fraud detection problem. However, it was reported that MBO will get stuck in local optima easily. Therefore, a modified migrating bird optimization algorithm is proposed to solve post enrolment-based course timetabling. An improved neighbourhood sharing mechanism is used with the aim of escaping from local optima. Besides that, iterated local search is selected to be hybridized with the migrating bird optimization in order to further enhance its exploitation ability. The proposed method was tested using Socha’s benchmark datasets. The experimental results show that the proposed method outperformed the basic MBO and it is capable of producing comparable results as compared with existing methods that have been presented in literature. Indeed, the proposed method is capable of addressing university course timetabling problem and promising results were obtained

A flexible mathematical model for the planning and designing of a sporting fixture by considering the assignment of referees

This paper deals with the problems faced with the designing and planning of a sporting fixture considering correct referee assignments. A non-linear binary program model is proposed to solve the problems, which aims to minimize the sums of the differences that exist between the requirements of each match and the quality of the referee assigned achieving the design of the most adequate referee for each match. The efficiency of the proposed model is proved using some real data obtained from various fixtures for sports such as soccer, volleyball, and basketball. The mathematical model is solved by using CPLEX 12.7.0., which allows the automatic linearization of the problems. The results obtained demonstrate the efficiency of the proposed methodology for tackling problems, as well as its extension to other sporting disciplines, which require a similar type of planning. Similarly, given the robust nature of the proposed model, it is possible to implement other objective functions in accordance with the requirements of each league

CONJURE: automatic generation of constraint models from problem specifications

Funding: Engineering and Physical Sciences Research Council (EP/V027182/1, EP/P015638/1), Royal Society (URF/R/180015).When solving a combinatorial problem, the formulation or model of the problem is critical tothe efficiency of the solver. Automating the modelling process has long been of interest because of the expertise and time required to produce an effective model of a given problem. We describe a method to automatically produce constraint models from a problem specification written in the abstract constraint specification language Essence. Our approach is to incrementally refine the specification into a concrete model by applying a chosen refinement rule at each step. Any nontrivial specification may be refined in multiple ways, creating a space of models to choose from. The handling of symmetries is a particularly important aspect of automated modelling. Many combinatorial optimisation problems contain symmetry, which can lead to redundant search. If a partial assignment is shown to be invalid, we are wasting time if we ever consider a symmetric equivalent of it. A particularly important class of symmetries are those introduced by the constraint modelling process: modelling symmetries. We show how modelling symmetries may be broken automatically as they enter a model during refinement, obviating the need for an expensive symmetry detection step following model formulation. Our approach is implemented in a system called Conjure. We compare the models producedby Conjure to constraint models from the literature that are known to be effective. Our empirical results confirm that Conjure can reproduce successfully the kernels of the constraint models of 42 benchmark problems found in the literature.Publisher PDFPeer reviewe

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

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