An Integrated Constraint Programming Approach to Scheduling Sports Leagues with Divisional and Round-Robin Tournaments

Previous approaches for scheduling a league with round-robin and divisional tournaments involved decomposing the problem into easier subproblems. This approach, used to schedule the top Swedish handball league Elitserien, reduces the problem complexity but can result in suboptimal schedules. This paper presents an integrated constraint programming model that allows to perform the scheduling in a single step. Particular attention is given to identifying implied and symmetry-breaking constraints that reduce the computational complexity significantly. The experimental evaluation of the integrated approach takes considerably less computational effort than the previous approach.

[1]  Gilles Pesant,et al.  A Regular Language Membership Constraint for Finite Sequences of Variables , 2004, CP.

[2]  Rasmus V. Rasmussen.  Scheduling a triple round robin tournament for the best Danish soccer league , 2008, Eur. J. Oper. Res..

[3]  Dirk Briskorn.  Sports Leagues Scheduling , 2008 .

[4]  Michael A. Trick.  Integer and Constraint Programming Approaches for Round-Robin Tournament Scheduling , 2002, PATAT.

[5]  Jean-Charles Régin,et al.  A Filtering Algorithm for Constraints of Difference in CSPs , 1994, AAAI.

[6]  Laurence A. Wolsey,et al.  Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, 4th International Conference, CPAIOR 2007, Brussels, Belgium, May 23-26, 2007, Proceedings , 2007, CPAIOR.

[7]  Timothy L. Urban,et al.  A constraint programming approach to the multiple-venue, sport-scheduling problem , 2006, Comput. Oper. Res..

[8]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[9]  Toby Walsh,et al.  Principles and Practice of Constraint Programming — CP 2001: 7th International Conference, CP 2001 Paphos, Cyprus, November 26 – December 1, 2001 Proceedings , 2001, Lecture Notes in Computer Science.

[10]  Jean-Charles Régin,et al.  Generalized Arc Consistency for Global Cardinality Constraint , 1996, AAAI/IAAI, Vol. 1.

[11]  Jean-Charles Régin.  The Symmetric Alldiff Constraint , 1999, IJCAI.

[12]  Martin Henz,et al.  Global constraints for round robin tournament scheduling , 2004, Eur. J. Oper. Res..

[13]  T. Benoist,et al.  Lagrange Relaxation and Constraint Programming Collaborative schemes for Traveling Tournament Problems , 2001 .

[14]  Edmund K. Burke,et al.  Practice and Theory of Automated Timetabling IV , 2002, Lecture Notes in Computer Science.

[15]  Michael A. Trick.  A Schedule-Then-Break Approach to Sports Timetabling , 2000, PATAT.

[16]  Edmund K. Burke,et al.  Practice and Theory of Automated Timetabling III , 2001, Lecture Notes in Computer Science.

[17]  Michael A. Trick,et al.  The timetable constrained distance minimization problem , 2006, Ann. Oper. Res..

[18]  Mikael Johansson,et al.  Constructing schedules for sports leagues with divisional and round-robin tournaments , 2014 .

[19]  Edmund K. Burke,et al.  Practice and Theory of Automated Timetabling VI, 6th International Conference, PATAT 2006, Brno, Czech Republic, August 30 - September 1, 2006, Revised Selected Papers , 2007, PATAT.

[20]  George L. Nemhauser,et al.  The Traveling Tournament Problem Description and Benchmarks , 2001, CP.

[21]  Mariusz Meszka,et al.  Round Robin Tournaments with One Bye and No Breaks in Home-Away Patterns Are Unique , 2005 .

[22]  Martin Henz,et al.  Scheduling a Major College Basketball Conference - Revisited , 2001, Oper. Res..

[23]  Laurent Perron.  Alternate Modeling in Sport Scheduling , 2005, CP.

[24]  Mark Wallace,et al.  Principles and Practice of Constraint Programming – CP 2004 , 2004, Lecture Notes in Computer Science.

[25]  Jean-Charles Régin.  Minimization of the number of breaks in sports scheduling problems using constraint programming , 1998, Constraint Programming and Large Scale Discrete Optimization.

[26]  Michael A. Trick,et al.  Round robin scheduling - a survey , 2008, Eur. J. Oper. Res..

[27]  Andrea Schaerf,et al.  Scheduling Sport Tournaments using Constraint Logic Programming , 1999, Constraints.

[28]  Celso C. Ribeiro,et al.  Scheduling the Brazilian Soccer Tournament with Fairness and Broadcast Objectives , 2006, PATAT.