The University of Nottinghampszgxk/gxk1/presentations/20012009UNMCPGCHE.pdfgeographically close...
Transcript of The University of Nottinghampszgxk/gxk1/presentations/20012009UNMCPGCHE.pdfgeographically close...
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Balancing Conflicting Objectives for UK Football
Graham Kendall
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
"A man who dares to waste an hour of life has not discovered the value of
life"
Contents
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future Work
Charles Darwin 1809 - 1882
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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Contents
Paul Gascoigne gets booked, ruling him out of a potential world cup final
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future Work
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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George Best won 37 caps for Northern Ireland, including this match against England in May
1971
Problem Description
Football supporters and motoring organisations have called for changes in the scheduling of fixtures [over the Christmas holiday period] to prevent supporters from having to drive home from matches well into the early hours of the morning.
The Times (Sport, Football), 30th December 2005, pp 68
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Michael Owen returns to the line up at Newcastle after injury (29th April
2006)
League Structure
Four DivisionsBarclays Premiership (20 teams)Coca-Cola Championship (24 teams)Coca-Cola League One (24 teams)Coca-Cola League Two (24 teams)
Number of Matches380 (Premiership), 552 for other divisions. Total 2036
Matches to be ScheduledEach league plays a double round robin tournament. Therefore, there are no matches played between different divisions, but…..
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Pairing System
Teams are paired which means they cannot normally play at home on the same day
Typically this is due to teams which are geographically close (e.g. Manchester United/Manchester City, Sunderland/Newcastle, Liverpool/Everton/Tranmere)
Note that the pairing system operates across division boundaries
We are allowed a given number of pairing violations
Alan Shearer breaks Milburn's record, scoring his 201st Newcastle goal
(against Portsmouth)
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Pairing System
Teams are paired which means they cannot normally play at home on the same day
Typically this is due to teams which are geographically close (e.g. Manchester United/Manchester City, Sunderland/Newcastle, Liverpool/Everton/Tranmere)
Note that the pairing system operates across division boundaries
We are allowed a given number of pairing violations
Number of actual clashes from previous seasons
Season Boxing Day
New Years Day
2008-2009 10 10
2007-2008 14 10
2006-2007 14 8
2005-2006 12 14
2004-2005 10 10
2003-2004 8 14
2002-2003 10 8
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Chelsea win the Premiership for the second consecutive season (April
2006)
Geographic Constraints
There are other geographical constraints which must be adhered to
The number of London based clubs that can play at home on the same day = 6
The number of London based Premier clubs that can play at home on the same day = 3
The number of Manchester based clubs that can play at home on a the same day = 4
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Wayne Rooney makes it 4-0 - giving Manchester United the biggest League Cup Final victory in the competition's
history (2006)
Date Specific Constraints
On New Years Day and Boxing Day each team is required to play
If a team plays at home on Boxing Day they must play away on New Years Day
The same teams cannot play each other on New Years Day and Boxing Day
Paired teams cannot play each otherIn fact this is violated in the published fixtures, but we treat it as a hard constraint
The aim is to minimise the distance travelled
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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Date Specific Constraints
On New Years Day and Boxing Day each team is required to play
If a team plays at home on Boxing it must play away on New Years Day
The same teams cannot play each other on New Years Day and Boxing Day
Paired teams cannot play each otherIn fact this is violated in the published fixtures, but we treat it as a hard constraint
The aim is to minimise the distance travelled
• Analysis of previous seasons fixtures and meetings with the Football League have shown that this is the case
• Not like TSP or TTP as we cannot minimise the overall distance travelled (throughout the entire season)
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2002-2003 2003-2004
2005-20062004-2005
Maps of Premier League Clubs
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Division 1: 2004-2005
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Division 1: 2004-2005
153 Miles (Plymouth to
Cardiff)
405 Miles(Plymouth to Sunderland)
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niversity of Nottingham
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Contents
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future WorkGordon Banks saves a “certain”
headed goal from Pele
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Bobby Charlton: Then and Now
Solution Methodology (JORS)
Two-stage algorithm
Depth-first searchProduces two fixtures for each division, one for Boxing Day and one for New Years Day (i.e. eight sets of fixtures)
Local SearchOperates across divisions in order to resolve clashes
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Nottingham Forest Football Ground
Results (JORS)Published Fixtures Generated Fixtures
Season 2005-2006
Boxing DayTotal Distance 4295 3049
Clashes 12 10
New Years DayTotal Distance 6336 3868
Clashes 14 10
Season 2004-2005
Boxing DayTotal Distance 4563 3725
Clashes 10 10
New Years DayTotal Distance 5122 3059
Clashes 10 10
Season 2003-2004
Boxing DayTotal Distance 3872 2859
Clashes 8 8
New Years DayTotal Distance 4296 3500
Clashes 14 14
Season 2002-2003
Boxing DayTotal Distance 3827 2839
Clashes 10 10
New Years DayTotal Distance 3964 3201
Clashes 8 8
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Bobby Moore in 1966
Results (JORS)Season Total
Distance for
Published Fixtures
Total Distance for Generated Fixtures
Distance Saving Number of Pair Clashes for Published Fixtures
Number of Pair Clashes for Generated Fixtures
2005-2006 10631 6917 3714 (34.94%)
26 20
2004-2005 9685 6784 2901 (29.95%)
20 20
2003-2004 8168 6359 1809 (22.15%)
22 22
2002-2003 7791 6020 1751 (22.47%)
18 18
Kendall G. Scheduling English Football Fixtures Over Holiday Periods. (2008) Journal of the Operational Research Society, 59(6), pages 743-755 (http://dx.doi.org/10.1057/palgrave.jors.2602382)
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Contents
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future Work
“Are you blind ref?”
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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© Graham Kendall (not to be distributed or used without permission)
Revised Methodology
Stamford Bridge: Chelsea’s home ground
Two-stage algorithm
CPLEXProduces Boxing Day fixtures and New Years Day fixtures at the same time.
Simulated AnnealingOperates across divisions in order to resolve clashes
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Revised MethodologySearch Phase
Season Division Stage 1a Stage 1b Local Search
2005-06
Barclays Premiership 5 <1 <5
Coca-Cola Championship 823 <1 <5
Coca-Cola League One 149 <1 <5
Coca-Cola League 2 148 <1 <5
2004-05
Barclays Premiership 4 <1 <5
Coca-Cola Championship 993 <1 <5
Coca-Cola Lauge One 222 <1 <5
Coca-Cola League 2 401 <1 <5
2003-04
Barclays Premiership 8 <1 <5
Coca-Cola Championship 891 <1 <5
Coca-Cola Lauge One 157 <1 <5
Coca-Cola League 2 218 <1 <5
2002-03
Barclays Premiership 3 <1 <5
Coca-Cola Championship 1023 <1 <5
Coca-Cola Lauge One 874 <1 <5
Coca-Cola League 2 26 <1 <5
• Times in minutes
• Large differences, but generally expensive
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Revised Methodology
Two-stage algorithmCPLEXSimulated Annealing
• Produces optimal solutions for the relaxed problem for each division.
• We create fixtures for boxing day and news years day at the same time (cf DFS, where we ran the DFS for each day).
• Significant improvements on speed.
CPLEX
Barclays Premiers
hip
Coca-Cola
Championship
Coca-Cola
League One
Coca-Cola
League 2
2005-06 677 / 4 948 / 5 1156 / 4 1369 / 42004-05 888 / 6 1104 / 5 1394 / 4 1357 / 52003-04 917 / 4 1331 / 4 1277 / 4 1224 / 52002-03 737 / 3 1301 / 3 1297 / 4 1217 / 6
Objective value / time for CPLEX in seconds
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Revised MethodologyTwo-stage algorithm
CPLEXSimulated Annealing
Comparison of run times for SA and Local Search (seconds)
Gary Lineker scoring against Paraguay in 1986
Season Simulated Annealing
Local Search
2008-2009 195 34
2007-2008 222 28
2006-2007 205 33
2005-2006 210 32
2004-2005 196 31
2003-2004 201 29
2002-2003 207 33
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Revised Methodology
Season Published Fixtures
Kendall, 2008
Best Result
Number of Pair Clashes for Published Fixtures
Number of Pair Clashes for Generated Fixtures
2008-09 9312 - 5564 20 20
2007-08 8544 - 5366 24 22
2006-07 8439 - 5713 22 22
2005-06 10631 6917 6020 26 24
2004-05 9685 6784 5838 20 20
2003-04 8168 6359 6006 22 22
2002-03 7791 6040 5547 18 18
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Contents
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future Work20th Dec 2007: Sunderland double
their lead and Kenwyne Jones celebrates
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Pairing System
Teams are paired which means they cannot normally play at home on the same day
Typically this is due to teams which are geographically close (e.g. Manchester United/Manchester City, Sunderland/Newcastle, Liverpool/Everton/Tranmere)
Note that the pairing system operates across division boundaries
We are allowed a given number of pairing violations
Number of actual clashes from previous seasons
Season Boxing Day
New Years Day
2008-2009 10 10
2007-2008 14 10
2006-2007 14 8
2005-2006 12 14
2004-2005 10 10
2003-2004 8 14
2002-2003 10 8
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2002-2003
5550
5600
5650
5700
5750
5800
5850
0 5 10 15 20 25
Min
Min
Clashes Min20 556418 557416 573618 558116 579016 5809
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2003-2004
5300
5400
5500
5600
5700
5800
5900
6000
6100
0 5 10 15 20 25
Min
Min
Clashes Min22 546420 541218 551116 588720 555018 555916 589818 559216 588616 6028
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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2004-2005
5300
5400
5500
5600
5700
5800
5900
0 5 10 15 20 25
Min
Min
Clashes Min20 536518 534516 581218 544316 564516 5810
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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2005-2006
5000
5200
5400
5600
5800
6000
6200
0 5 10 15 20 25 30
Min
Min
Clashes Min26 523424 533522 524020 533418 548116 604124 517122 530820 546018 559516 602722 533520 533418 560816 614620 550018 552816 588418 571316 603216 6084
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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2006-2007
5600
5700
5800
5900
6000
6100
6200
6300
0 5 10 15 20 25
Min
Min
Clashes Min22 571320 573518 587216 611020 572118 571416 619518 576216 589416 6071
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2007-2008
52005300540055005600570058005900600061006200
0 5 10 15 20 25 30
Min
Min
Clashes Min24 536622 540320 542518 569016 590522 537020 532118 562516 596120 534018 561616 610118 553616 609116 5951
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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2008-2009
5550
5600
5650
5700
5750
5800
5850
0 5 10 15 20 25
Min
Min
Clashes Min20 556418 557416 573618 558116 579016 5809
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
The U
niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
2004-2005
5300
5400
5500
5600
5700
5800
5900
0 5 10 15 20 25
Min
Min
Clashes Min20 536518 534516 581218 544316 564516 5810
t-test Analysis (Statistically Different?)
10-10 10-8 10-6 8-10 8-8 6-10
10-10 X No Yes Yes Yes Yes
10-8 X Yes No Yes Yes
10-6 X Yes No No
8-10 X Yes Yes
8-8 X No
6-10 X
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2005-2006
5000
5200
5400
5600
5800
6000
6200
0 5 10 15 20 25 30
Min
Min
Clashes Min26 523424 533522 524020 533418 548116 604124 517122 530820 546018 559516 602722 533520 533418 560816 614620 550018 552816 588418 571316 603216 6084
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2005-2006t-test Analysis (Statistically Different?)
12-14 12-12 12-10 12-8 12-6 12-4 10-14 10-12 10-10 10-8 10-6 8-14 8-12 8-10 8-8 6-14 6-12 6-10 4-14 4-12 2-14
12-14 X No No Yes Yes Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes
12-12 X No Yes Yes Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes
12-10 X No Yes Yes No No Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes
12-8 X Yes Yes Yes Yes No Yes Yes No No Yes Yes No Yes Yes Yes Yes Yes
12-6 X Yes Yes Yes No No Yes Yes Yes No Yes Yes No Yes No Yes Yes
12-4 X Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes Yes Yes
10-14 X No Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes
10-12 X Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes
10-10 X No Yes No No No Yes No No Yes Yes Yes Yes
10-8 X Yes Yes Yes No Yes No No Yes Yes Yes Yes
10-6 X Yes Yes Yes No Yes Yes No Yes No No
8-14 X No Yes Yes Yes Yes Yes Yes Yes Yes
8-12 X Yes Yes Yes Yes Yes Yes Yes Yes
8-10 X Yes No No Yes Yes Yes Yes
8-8 X Yes Yes No Yes No No
6-14 X No Yes Yes Yes Yes
6-12 X Yes Yes Yes Yes
6-10 X Yes No No
4-14 X Yes Yes
4-12 X No
2-14 X
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2006-2007
5600
5700
5800
5900
6000
6100
6200
6300
0 5 10 15 20 25
Min
Min
Clashes Min22 571320 573518 587216 611020 572118 571416 619518 576216 589416 6071
t-test Analysis (Statistically Different?)14-8 14-6 14-4 14-2 12-8 12-6 12-4 10-8 10-6 8-8
14-8 X No Yes Yes No No Yes No Yes Yes14-6 X Yes Yes No No Yes No Yes Yes14-4 X Yes Yes No Yes No Yes Yes14-2 X Yes Yes No Yes No Yes12-8 X Yes Yes No Yes Yes12-6 X Yes No Yes Yes12-4 X Yes No Yes10-8 X Yes Yes10-6 X No8-8 X
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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© Graham Kendall (not to be distributed or used without permission)
2008-2009
5550
5600
5650
5700
5750
5800
5850
0 5 10 15 20 25
Min
Min
Clashes Min20 556418 557416 573618 558116 579016 5809
t-test Analysis (Statistically Different?)
10-10 10-8 10-6 8-10 8-8 6-10
10-10 X No Yes No Yes Yes
10-8 X Yes No Yes Yes
10-6 X Yes No No
8-10 X Yes Yes
8-8 X No
6-10 X
Graham Kendall, 20th Jan 2009, UNMC – Sports Scheduling
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niversity of Nottingham
© Graham Kendall (not to be distributed or used without permission)
Contents
• Problem Definition
• Previous results (JORS)
• CPLEX vs DFS
• Multi-objective (clashes vs distance)
• “Suggesting” maximum distance
• Future Work
Maradonna
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Season 2002-2003
League 1
246 Miles
153 Miles
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Experimental Setup
• Simulated Annealing (as before)
• Suggested Maximum Distance•{500, 250, 180, 160, 140, 120, 100}
• Weighted•{4, 20, 100, 5000}
22nd Dec 2007: Nicklas Bendtner heads in the winner seconds after
coming on as a substitute
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2002-2003 (weight = 4)
5200
5300
5400
5500
5600
5700
5800
5900
6000
6100
6200
0 100 200 300 400 500 600
Maximum Distance Miles
500 6106250 5566200 5463180 5683160 5356140 5432120 5326100 5459
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2002-2003 (weight = 20)
5000
5200
5400
5600
5800
6000
6200
6400
6600
0 100 200 300 400 500 600
Maximum Distance Miles
500 6382250 5659200 5866180 5450160 5271140 5341120 5204100
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2002-2003 (weight = 100)Maximum Distance Miles
500 5516250 6242200 5434180 5599160 5491140 5370120 5250100
5200
5400
5600
5800
6000
6200
6400
0 100 200 300 400 500 600
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2002-2003 (weight = 5000)Maximum Distance Miles
500 5495250 5949200 5600180 5352160 5357140 5423120100
5300
5400
5500
5600
5700
5800
5900
6000
0 100 200 300 400 500 600
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Season 2002-2003
League 1153 Miles
119 Miles
10th Feb 2007: Darius Henderson scores from the penalty spot
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Season 2002-2003
The only stats so far
•30 runs
•Maximum Miles = 160
•Weights = {4, 5000}
•Results are statistically significant
27th Oct 2007: Wayne Rooney scores for the eighth time in seven games for
club and country
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Future Research Directions
Carry out further analysisRun full set of experiments for all divisions/seasonsContact FA/Police
Produce a 4-fixture scheduleUse this as a start for generating fixtures for the complete season.
Wembley Stadium
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Questions/Discussion