Round Robin Tournament Schedule Research Articles

Multi-neighborhood simulated annealing for the sports timetabling competition ITC2021

We describe the solver that we developed for the Sports Timetabling Competition ITC2021, a three-stage simulated annealing approach, that makes use of a portfolio of six different neighborhoods. Five of these neighborhoods are taken from the literature on round-robin tournament scheduling, whereas the last one, denoted as PartialSwapTeamsPhased, is a novel contribution and it is specifically designed for the phased version of the problem. We perform a comprehensive and statistically principled tuning procedure to find the best combination of parameters for the competition instances. We dedicate specific focus to evaluate the contribution given by the new neighborhood PartialSwapTeamsPhased, which yielded better results on most phased instances. Overall, the final outcome is that the three-stage simulated annealing solver is able to find a feasible solution on 44 out of 45 instances and ranked second in both the first competition milestone and the final round. We also propose an Integer Linear Programming model implemented in CPLEX, which, unfortunately, did not produce significant results on the instances of the competition.

A new approach based on graph matching and evolutionary approach for sport scheduling problem

The Traveling Tournament Problem (TTP) is concerned with finding a double round-robin tournament schedule that minimizes the total distances traveled by the teams. It has attracted significant interest recently since a favorable TTP schedule can result in significant savings for the league. This paper proposes an original evolutionary algorithm for TTP. We first propose a quick and effective constructive algorithm to construct a Double Round Robin Tournament (DRRT) schedule with low travel cost. We then describe an enhanced genetic algorithm with a new crossover operator to improve the travel cost of the generated schedules. A new heuristic for ordering efficiently the scheduled rounds is also proposed. The latter leads to significant enhancement in the quality of the schedules. The overall method is evaluated on publicly available standard benchmarks and compared with other techniques for TTP and UTTP (Unconstrained Traveling Tournament Problem). The computational experiment shows that the proposed approach could build very good solutions comparable to other state-of-the-art approaches or better than the current best solutions on UTTP. Further, our method provides new valuable solutions to some unsolved UTTP instances and outperforms prior methods for all US National League (NL) instances.

Generating Approximate Solutions to the TTP using a Linear Distance Relaxation

In some domestic professional sports leagues, the home stadiums are located in cities connected by a common train line running in one direction. For these instances, we can incorporate this geographical information to determine optimal or nearly-optimal solutions to the n-team Traveling Tournament Problem (TTP), an NP-hard sports scheduling problem whose solution is a double round-robin tournament schedule that minimizes the sum total of distances traveled by all n teams. We introduce the Linear Distance Traveling Tournament Problem (LD-TTP), and solve it for n=4 and n=6, generating the complete set of possible solutions through elementary combinatorial techniques. For larger n, we propose a novel "expander construction" that generates an approximate solution to the LD-TTP. For n congruent to 4 modulo 6, we show that our expander construction produces a feasible double round-robin tournament schedule whose total distance is guaranteed to be no worse than 4/3 times the optimal solution, regardless of where the n teams are located. This 4/3-approximation for the LD-TTP is stronger than the currently best-known ratio of 5/3 + epsilon for the general TTP. We conclude the paper by applying this linear distance relaxation to general (non-linear) n-team TTP instances, where we develop fast approximate solutions by simply "assuming" the n teams lie on a straight line and solving the modified problem. We show that this technique surprisingly generates the distance-optimal tournament on all benchmark sets on 6 teams, as well as close-to-optimal schedules for larger n, even when the teams are located around a circle or positioned in three-dimensional space.

Traveling baseball players’ problem in Korea

We study the so-called the traveling tournament problem (TTP), to find an optimal tournament schedule. Differently from the original TTP, in which the total travel distance of all the participants is the objective function to minimize, we instead seek to maximize the fairness of the round robin tournament schedule of the Korean Baseball League. The standard deviation of the travel distances of teams is defined as the energy function, and the Metropolis Monte-Carlo method combined with the simulated annealing technique is applied to find the ground state configuration. The resulting tournament schedule is found to satisfy all the constraint rules set by the Korean Baseball Organization, but with drastically increased fairness in traveling distances.

Round Robin Tournament Scheduling with Arbitrary Competitors: A Novel Divide and Conquer Approach

Round Robin Tournament Scheduling with Arbitrary Competitors: A Novel Divide and Conquer Approach

A heuristic for minimizing weighted carry-over effects in round robin tournaments

The carry-over effects value is one of the various measures one can consider to assess the quality of a round robin tournament schedule. We introduce and discuss a new, weighted variant of the minimum carry-over effects value problem. The problem is formulated by integer programming and an algorithm based on the hybridization of the Iterated Local Search metaheuristic with a multistart strategy is proposed. Numerical results are presented.

Maximizing breaks and bounding solutions to the mirrored traveling tournament problem

We investigate the relation between two aspects of round robin tournament scheduling problems: breaks and distances. The distance minimization problem and the breaks maximization problem are equivalent when the distance between every pair of teams is equal to 1. We show how to construct schedules with a maximum number of breaks for some tournament types. The connection between breaks maximization and distance minimization is used to derive lower bounds to the mirrored traveling tournament problem and to prove the optimality of solutions found by a heuristic for the latter.

Minimizing Travels by Maximizing Breaks in Round Robin Tournament Schedules

Abstract We investigate the relation between two aspects of round robin tournament scheduling problems: breaks and distances. We show that the breaks maximization problem and the distance minimiza- tion problem are equivalent for a new class of uniform problem instances. This relation is used to prove the optimality of solutions found by a heuristic to the mirrored traveling tournament problem. The uniform instances solved to optimality are the largest solved to date and shed some light on the complexity of this problem.

Scheduling the Italian Football League: an ILP-based approach

Scheduling the Italian Major Football League (the so-called “Serie A”) consists in finding for that league a double round robin tournament schedule that takes into account both typical requirements such as conditions on home-away matches and specific requests of the Italian Football Association such as twin-schedules for teams belonging to the same home-town. In this paper, we present a solution procedure able to derive feasible schedules that are also balanced with respect to additional cable televisions requirements. This procedure adapts the recent approach by Nemhauser and Trick to schedule a College Basketball Conference that considers however only half of the teams involved here. The proposed procedure is divided into three phases: phase 1 generates a pattern set respecting the cable televisions requirements and several other constraints; phase 2 produces a feasible round robin schedule compatible with the above pattern set; finally, phase 3 generates the actual calendar assigning the teams to the patterns. The procedure allows to generate within short time several different reasonable calendars satisfying the cable television companies requirements and satisfying various other operational constraints while minimizing the total number of violations on the home-away matches conditions.

Global constraints for round robin tournament scheduling

In the presence of side-constraints and optimization criteria, round robin tournament problems are hard combinatorial problems, commonly tackled with tree search and branch-and-bound optimization. Recent results indicate that constraint-based tree search has crucial advantages over integer programming-based tree search for this problem domain by exploiting global constraint propagation algorithms during search. In this paper, we analyze arc-consistent propagation algorithms for the global constraints “all-different” and “one-factor” in the domain of round robin tournaments. The best propagation algorithms allow us to compute all feasible perfectly mirrored pattern sets with minimal breaks for intermural tournaments of realistic size, and to improve known lower bounds for intramural tournaments balanced with respect to carry-over effects.

Diagonal and Pandiagonal Tournament Latin Squares

A tournament latin square T = [tij] is a latin square satisfying the additional requirement tij = k implies tik = j. A tournament latin square can be used for round robin tournament scheduling by interpreting tij = k as a match at round i between team j and team k. We show that the necessary and sufficient conditions for the respective existence of diagonal and pandiagonal tournament latin squares are the same as for ordinary diagonal and pandiagonal latin squares.