Presentation is loading. Please wait.

Presentation is loading. Please wait.

Optimization problems in sports 1/55 Celso C. Ribeiro Joint work with S. Urrutia, A.Duarte, T. Noronha, E.H. Haeusler, R. Melo, A.Guedes, F. Costa, S.

Similar presentations


Presentation on theme: "Optimization problems in sports 1/55 Celso C. Ribeiro Joint work with S. Urrutia, A.Duarte, T. Noronha, E.H. Haeusler, R. Melo, A.Guedes, F. Costa, S."— Presentation transcript:

1 Optimization problems in sports 1/55 Celso C. Ribeiro Joint work with S. Urrutia, A.Duarte, T. Noronha, E.H. Haeusler, R. Melo, A.Guedes, F. Costa, S. Martins, R. Capua et al. Optimization Problems in Sports

2 Optimization problems in sports Motivation Optimization in sports is a field of increasing interest: – Traveling tournament problem – Playoff elimination – Tournament scheduling – Referee assignment Regional amateur leagues in the US (baseball, basketball, soccer): hundreds of games every weekend in different divisions 2/55

3 Optimization problems in sports 3/55 Motivation Sports competitions involve many economic and logistic issues Multiple decision makers: federations, TV, teams, security authorities,... Conflicting objectives: – Maximize revenue (attractive games in specific days) – Minimize costs (traveled distance) – Maximize athlete performance (time to rest) – Fairness (avoid playing all strong teams in a row) – Avoid conflicts (teams with a history of conflicts playing at the same place)

4 Optimization problems in sports 4/55 Motivation Professional sports: – Millions of fans – Multiple agents: organizers, media, fans, players, security forces,... – Big investments: Belgacom TV: €12 million per year for soccer broadcasting rights Baseball US: > US$ 500 millions Basketball US: > US$ 600 millions – Main problems: maximize revenues, optimize logistic, maximize fairness, minimize conflicts, etc.

5 Optimization problems in sportsLa Havana, March /91 Taxi driver the night before: “the only fair solution is that San Lorenzo and Boca play at Tigre’s, Boca and Tigre at San Lorenzo's, and Tigre and San Lorenzo at Boca’s, but these guys never do the right thing!” If San Lorenzo would have won the first two games, the tournament would have been decided and the third game would have no importance!

6 Optimization problems in sports 6/55 Fairness issues: “The International Rugby Board (IRB) has admitted the World Cup draw was unfairly stacked against poorer countries so tournament organisers could maximise their profits.” (2003)

7 Optimization problems in sports 7/55 Motivation Amateur sports: – Different problems and applications – Thousands of athletes – Athletes pay for playing – Large number of simultaneous events – Amateur leagues do not involve as much money as professional leagues but, on the other hand, amateur competitions abound

8 Optimization problems in sports Motivation In a single league in California there might be up to 500 soccer games in a weekend, to be refereed by hundreds of certified referees MOSA (Monmouth & Ocean Counties Soccer Association) League (NJ): boys & girls, ages 8-18, six divisions per age/gender group, six teams per division: 396 games every Sunday (US$ 40 per ref; U$ 20 per linesman, two linesmen) 8/55

9 Optimization problems in sports 9/55 Optimization problems in sports Examples: – Qualification/elimination problems – Tournament scheduling – Referee assignment – Tournament planning (teams? dates? rules?) – League assignment (which teams in each league?) – Player selection – Carry-over minimization – Practice assignment –... – Optimal strategies for curling!

10 Optimization problems in sports 10/55 Qualification/elimination problems How all this work started in Team managers, players, fans and the press are often eager to know the chances of a team to be qualified for the playoffs of a given competition Press often makes false announcements based on unclear forecasts that are often biased and wrong (“any team with 54 points will qualify”)

11 Optimization problems in sports 11/55 Qualification/elimination problems Two basic approaches: – Probabilistic model + simulation (abound in the sports press, journalists love but do not understand: “Probability that Estudiantes wins is 14,87%”; “Probability that Fluminense will be downgraded next year is 1%”) – Number of points to qualify: ìnteger programming application, doctorate thesis of Sebastián Urrutia (“easy” only in the last round!)

12 Optimization problems in sports 12/55 Qualification/elimination problems How many points a team should make to: … be sure of finishing among the p teams in the first positions? (sufficient condition for play-offs qualification) … have a chance of finishing among the p teams in the first positions? (necessary condition for play-offs qualification): – Integer programming model determines the maximum number K of points a team can make such as that p other teams can still make more than K points. – Team must win K+1 points to qualify.

13 Optimization problems in sports 13/55 Tournament scheduling Timetabling is the major area of applications: game scheduling is a difficult task, involving different types of constraints, logistic issues, multiple objectives, and several decision makers Round robin schedules: – Every team plays each other a fixed number of times – Every team plays once in each round – Single (SRR) or double (DRR) round robin – Mirrored DRR: two phases with games in same order

14 Optimization problems in sports 14/55 Tournament scheduling Problems: – Minimize distance (costs) – Minimize breaks (fairness and equilibrium, every two rounds there is a game in the city) – Balanced tournaments (even distribution of fields used by the teams: n teams, n/2 fields, SRR with n-1 games/team, 2 games/team in n/2-1 fields and 1 in the other) – Minimize carry over effect (maximize fairness, polygon method)

15 Optimization problems in sports Polygon method Example: “polygon method” for n=6 1 st round

16 Optimization problems in sports Example: “polygon method” for n=6 2 nd round Polygon method

17 Optimization problems in sports Example: “polygon method” for n=6 3 rd round Polygon method

18 Optimization problems in sports Example: “polygon method” for n=6 4 th round Polygon method

19 Optimization problems in sports Example: “polygon method” for n=6 5 th round Polygon method

20 Optimization problems in sports 20/55 1-factorizations Factor of a graph G=(V, E): subgraph G’=(V,E’) with E’  E 1-factor: all nodes have degree equal to 1 Factorization of G=(V,E): set of edge- disjoint factors G 1 =(V,E 1 ),..., G p =(V,E p ), such that E 1 ...  E p =E 1-factorization: factorization into 1- factors Oriented factorization: orientations assigned to edges

21 Optimization problems in sports 21/ factorizations Example: 1-factorization of K 6

22 Optimization problems in sports 22/55 Oriented 1-factorization of K

23 Optimization problems in sports 23/55 SRR tournament: – Each node of K n represents a team – Each edge of K n represents a game – Each 1-factor of K n represents a round – Each ordered 1-factorization of K n represents a feasible schedule for n teams – Edge orientations define teams playing at home – Dinitz, Garnick & McKay, “There are 526,915,620 nonisomorphic one- factorizations of K 12 ” (1995) 1-factorizations

24 Optimization problems in sports 24/55 Distance minimization problems Whenever a team plays two consecutive games away, it travels directly from the facility of the first opponent to that of the second Maximum number of consecutive games away (or at home) is often constrained Minimize the total distance traveled (or the maximum distance traveled by any team) This was never the Brazilian problem!

25 Optimization problems in sports 25/55 Distance minimization problems Methods: – Metaheuristics: simulated annealing, iterated local search, hill climbing, tabu search, GRASP, genetic algorithms, ant colonies – Integer programming – Constraint programming – IP/CP column generation – CP with local search

26 Optimization problems in sports 26/55 Break minimization problems There is a break whenever a team has two consecutive home games (or two consecutive away games) Break minimization is somehow opposed to distance minimization

27 Optimization problems in sports 27/55 Predefined timetables/venues Given a fixed timetable, find a home- away assignment minimizing breaks/distance: – Metaheuristics, constraint programming, integer programming Given a fixed venue assignment for each game, find a timetable minimizing breaks/distance: – Melo, Urrutia & Ribeiro 2007 (JoS); Costa, Urrutia & Ribeiro 2008 (PATAT): ILS metaheuristic – Chilean soccer tournament – Table tennis in Germany

28 Optimization problems in sports 28/55 Decomposition methods Nemhauser & Trick 1998: 1. Find home-away patterns 2. Create an schedule for place holders consistent with a subset of home-away patterns 3. Assign teams to place holders Order in which the above tasks are tackled may vary depending on the application

29 Optimization problems in sports 29/55 Mirrored traveling tournament problem – Typical structure of LA soccer tournaments – GRASP+ILS heuristic – Best benchmark results for some time Brazilian professional basketball tournament – “Nova liga” (Oscar e Hortênsia) Referee assignment in amateur leagues – Bi-objective problem Applications of metaheuristics

30 Optimization problems in sports 30/55 Referee assignment MOSA (Monmouth & Ocean Counties Soccer Association) League (NJ): boys & girls, ages 8-18, six divisions per age/gender group, six teams per division: 396 games every Sunday (US$ 40 per referee; U$ 20 per linesman, two linesmen) Problem: assign referees to games Duarte, Ribeiro & Urrutia (PATAT 2006, LNCS 2007) Referee assignment involves many constraints and multiple objectives

31 Optimization problems in sports 31/55 Referee assignment Possible constraints: – Different number of referees may be necessary for each game – Games require referees with different levels of certification: higher division games require referees with higher skills – A referee cannot be assigned to a game where he/she is a player – Timetabling conflicts and traveling times

32 Optimization problems in sports 32/55 Referee assignment Possible constraints (cont.): – Referee groups: cliques of referees that request to be assigned to the same games (relatives, car pools, no driver’s licence) Hard links Soft links – Number of games a referee is willing to referee – Traveling constraints – Referees that can officiate games only at a certain location or period of the day

33 Optimization problems in sports 33/55 Referee assignment Possible objectives: – Difference between the target number of games a referee is willing to referee and the number of games he/she is assigned to – Traveling/idle time between consecutive games – Number of inter-facility travels – Number of games assigned outside his/her preferred time-slots or facilities – Number of violated soft links

34 Optimization problems in sports 34/55 Referee assignment Three-phase heuristic approach 1.Greedy constructive heuristic 2.ILS-based repair heuristic to make the initial solution feasible (if necessary): minimization of the number of violations 3.ILS-based procedure to improve a feasible solution

35 Optimization problems in sports 35/55 Referee assignment Improvement heuristic (hybridization of exact and approximate algorithms): – After each perturbation, instead of applying a local search to both facilities involved in this perturbation, solve a MIP model associated with the subproblem considering all refereeing slots and referees corresponding to these facilities (“MIP it!”) Matheuristics’2012: Fourth International Workshop on Model- Based Metaheuristics – Angra dos Reis, September 16-21, 2012 –

36 Optimization problems in sports 36/55 Referee assignment Bi-criteria version Objectives: 1.minimize the sum over all referees of the absolute value of the difference between the target and the actual number of games assigned to each referee 2.minimize the sum over all referees of the total idle time between consecutive games Metaheuristics for multi-criteria combinatorial optimization problems: –Relatively new field with many applications –Search for Pareto frontier (efficient solutions)

37 Optimization problems in sports 37/55 Referee assignment Exact approach: dichotomic method 50 games and 100 referees

38 Optimization problems in sports 38/55 Referee assignment

39 Optimization problems in sports 39/55 Referee assignment

40 Optimization problems in sports 40/55 Referee assignment

41 Optimization problems in sports 41/55 Mirrored traveling tournament problem – Typical structure of LA soccer tournaments Brazilian professional basketball tournament – Nova liga (Oscar e Hortênsia) Referee assignment in amateur leagues – Bi-objective problem Practice assignment (R. Capua’s doctorate thesis) Carry-over minimization problem – Hard non-linear optimization integer problem Applications of metaheuristics

42 Optimization problems in sports 42/55 Carry-over effects Team B receives a carry-over effect (COE) due to team A if there is a team X that plays A in round r and B in round r+1

43 Optimization problems in sports 43/55 Carry-over effects Team B receives a carry-over effect (COE) due to team A if there is a team X that plays A in round r and B in round r+1 Team A receives COE due to B Team G receives COE due to D Team A receives COE due to E

44 Optimization problems in sports 44/55 Carry-over effects SRRT and carry-over effects matrix (COEM) RRT COE matrix

45 Optimization problems in sports 45/55 Carry-over effects SRRT and carry-over effects matrix (COEM) RRT COE Matrix Suppose B is a very strong competitor: then, five times A will play an opponent that is tired or wounded due to meeting B before

46 Optimization problems in sports 46/55 Carry-over effects value COE matrix COEM DG = 3 COEM FH = 2

47 Optimization problems in sports 47/55 Carry-over effects value COE Matrix Minimize!!! COEM DG = 3 COEM FH = 2

48 Optimization problems in sports 48/55 Carry-over effects Karate-Do competitions Groups playing round-robin tournaments – Pan-american Karate-Do championship – Brazilian classification for World Karate-Do championship Open weight categories – Physically strong contestants may fight weak ones – One should avoid that a competitor benefits from fighting (physically) tired opponents coming from matches against strong athletes

49 Optimization problems in sports 49/55 Carry-over effects value Find a schedule with minimum COEV – RRT distributing the carry-over effects as evenly as possible among the teams New problem: weighted COEV – minimization problem – min-max problem Non-linear integer optimization problem Hard for IP approaches

50 Optimization problems in sports 50/55 Carry-over effects In case you don’t believe in the relevance of the problem, google “Alanzinho” and check Youtube and Wikipedia: – Played at Flamengo, America RJ, Gama, Stabaek (Norway), Trabzonspor (Turkey) Also relevant in tournaments with an odd number of teams, to avoid that the same team always play against another team coming from a bye (residual effect of polygon method) (College Basketball in Alabama)

51 Optimization problems in sports Applications of exact methods (IP) Improved algorithm and formulation for the Chilean soccer tournament 46/55

52 Optimization problems in sports Applications of exact methods (IP) Projeto CBF – Tabela do Campeonato Brasileiro de Futebol (A e B) – Projeto inicialmente desenvolvido com a TV Globo (2006) e posteriormente encampado pela Diretoria de Competições da CBF (2008) – 40 critérios (restrições) diferentes: aspectos esportivos, técnicos, geográficos, financeiros, logísticos, de equilíbrio e de segurança – Otimizar público, audiência e renda de publicidade; otimizar clássicos em finais de semana; etc. 47/55

53 Optimization problems in sports Applications of exact methods (IP) Projeto CBF – Solução exata por programação inteira – Tabelas oficiais adotadas em 2009, 2010 e 2011 vêm sendo extremamente equilibradas – Usuário escolhe entre diversas tabelas e refina sucessivamente a melhor solução – A cada ano, novas exigências: Calendário apertado em 2010 levou à maximização dos clássicos aos domingos Efeito “mala branca” levou a marcar os clássicos regionais para as rodadas finais em /55

54 Optimization problems in sports 49/55 Kendall, Knust, Ribeiro & Urrutia (C&OR, 2010): “Scheduling in sports: An annotated bibliography” Nurmi, Goossens, Bartsch, Bonomo, Briskorn, Duran, Kyngäs, Marenco, Ribeiro, Spieksma, Urrutia & Wolf-Yadlin (IAENG Transactions, 2010): “A framework for scheduling professional sports leagues” Ribeiro & Urrutia (Interfaces, to appear): “Scheduling the Brazilian soccer tournament: Solution approach and practice” Ribeiro (ITOR, to appear): “Sports scheduling: Problems and applications” ITOR is now indexed by ISI (will appear in JCR in 2012) Some recent references

55 Optimization problems in sports 55/55 Sports timetabling in professional leagues worldwide: – Basketball: USA (College), New Zealand – Baseball: MLB (USA) (also referee assignment) – Soccer: Austria, Costa Rica, Germany, Brazil, Chile, Denmark, The Netherlands, Japan – Volleyball: Argentina – Rugby: World Cup – Hockey: NHL (USA/Canada), Finland – “American” football: NFL (USA) (unclear status in some cases: real-life vs real-data apps.) Perspectives and concluding remarks

56 Optimization problems in sports 56/55 However, old technologies might also be useful… Perspectives and concluding remarks

57 Optimization problems in sports

58 58/55 Fair and balanced schedules for all teams are a major issue for attractiveness and confidence in the outcome of any tournament. Few professional leagues have adopted optimization software to date: – Due not only to the difficulty of the problem and to some fuzzy requirements that can hardly be described and formulated, but also to the resistance of teams and leagues that are often afraid of using new tools that break with the past and introduce modern techniques in sports management. Perspectives and concluding remarks

59 Optimization problems in sports 59/55 Operations Research has certainly proved its usefulness in sports management: – Besides the quality of the schedules found, the main advantages of the optimization systems are its ease of use and the construction of alternative schedules, making it possible for the organizers to compare and select the most attractive schedule from among different alternatives, contemplating distinct goals. Perspectives and concluding remarks

60 Optimization problems in sportsLa Havana, March /91


Download ppt "Optimization problems in sports 1/55 Celso C. Ribeiro Joint work with S. Urrutia, A.Duarte, T. Noronha, E.H. Haeusler, R. Melo, A.Guedes, F. Costa, S."

Similar presentations


Ads by Google