Optimization of The Best Line-up in Football using Binary Integer Programming Model
Keywords:
Sport, football, football Line-up, football formations, optimization, binary linear programming, binary integer programmingAbstract
This paper aims to find the formation with the best line-up of the Liverpool FC football team in the English Premier League in the 2020/2021 season. Researchers used binary integer programming (BIP) modeling to determine optimum solutions. The data used for this optimization is the rating value of the players recorded in the performance data from the previous matches. The optimum result of this problem is the selection of variables that are valued at 1, namely {x_1, x_4, x_6, x_8, x_21, x_28, x_34, x_37, and x_39} for formations 4-3-3 with a maximum value of 82.47, and variables {x_1, x_6, x_7, x_8, x_11, x_14, x_16, x_29, x_31, x_32, andx_42} for 4-2-3-1 formations with a maximum value of 80.04. The 4-3-3 formation is more effective because it has a higher maximum rating than the 4-2-3-1 formation. 4-3-3 formation is an attacking formation with a higher intensity of attack and faster than 4-2-3-1 formation that tends to defend moderately.References
P. S. Bradley, “The effect of playing formation on high-intensity running and technical profiles in English FA premier League soccer matches,†J. Sports Sci., vol. 29, no. 8, pp. 821–830, 2011, doi: 10.1080/02640414.2011.561868.
C. Carling, “Influence of opposition team formation on physical and skill-related performance in a professional soccer team,†Eur. J. Sport Sci., vol. 11, no. 3, pp. 155–164, 2011, doi: 10.1080/17461391.2010.499972.
P. Tierney, “Match play demands of 11 versus 11 professional football using Global Positioning System tracking: Variations across common playing formations,†Hum. Mov. Sci., vol. 49, pp. 1–8, 2016, doi: 10.1016/j.humov.2016.05.007.
R. Aquino, “Comparisons of ball possession, match running performance, player prominence and team network properties according to match outcome and playing formation during the 2018 FIFA World Cup,†Int. J. Perform. Anal. Sport, vol. 19, no. 6, pp. 1026–1037, 2019, doi: 10.1080/24748668.2019.1689753.
R. Aquino, “Effects of competitive standard, team formation and playing position on match running performance of Brazilian professional soccer players,†Int. J. Perform. Anal. Sport, vol. 17, no. 5, pp. 695–705, 2017, doi: 10.1080/24748668.2017.1384976.
S. Dobson, “Optimizing strategic behaviour in a dynamic setting in professional team sports,†Eur. J. Oper. Res., vol. 205, no. 3, pp. 661–669, 2010, doi: 10.1016/j.ejor.2010.01.024.
K. Tamura, “Win-stay lose-shift strategy in formation changes in football,†EPJ Data Sci., vol. 4, no. 1, pp. 1–19, 2015, doi: 10.1140/epjds/s13688-015-0045-1.
K. He, “Formation optimization of RoboCup3D soccer robots using delaunay triangulation network,†Proc. 30th Chinese Control Decis. Conf. CCDC 2018, pp. 224–229, 2018, doi: 10.1109/CCDC.2018.8407135.
T. Ge, “An analysis on the effectiveness of cooperation in a soccer team,†15th Int. Conf. Comput. Sci. Educ. ICCSE 2020, pp. 787–794, 2020, doi: 10.1109/ICCSE49874.2020.9202386.
R. Beal, “Optimising game tactics for football,†Proc. Int. Jt. Conf. Auton. Agents Multiagent Syst. AAMAS, vol. 2020, pp. 141–149, 2020, [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85096654096&origin=inward.
J. Pan, “Mixed binary integer programming formulations for the reentrant job shop scheduling problem,†Comput. Oper. Res., vol. 32, no. 5, pp. 1197–1212, 2005, doi: 10.1016/j.cor.2003.10.004.
R. Corrêa, “Online coordination of directional overcurrent relays using binary integer programming,†Electr. Power Syst. Res., vol. 127, pp. 118–125, 2015, doi: 10.1016/j.epsr.2015.05.017.
J. Wong, “Base station placement in indoor wireless systems using binary integer programming,†IEE Proc. Commun., vol. 153, no. 5, pp. 771–778, 2006, doi: 10.1049/ip-com:20050013.
J. Brey, “Using AHP and binary integer programming to optimize the initial distribution of hydrogen infrastructures in Andalusia,†Int. J. Hydrogen Energy, vol. 37, no. 6, pp. 5372–5384, 2012, doi: 10.1016/j.ijhydene.2011.08.040.
M. Ziaee, “Mixed binary integer programming formulations for the flow shop scheduling problems. A case study: ISD projects scheduling,†Appl. Math. Comput., vol. 185, no. 1, pp. 218–228, 2007, doi: 10.1016/j.amc.2006.06.092.
N. Balouchzahi, “Optimal road side units placement model based on binary integer programming for efficient traffic information advertisement and discovery in vehicular environment,†IET Intell. Transp. Syst., vol. 9, no. 9, pp. 851–861, 2015, doi: 10.1049/iet-its.2014.0051.
J. Gholamnejad, “Using chance constrained binary integer programming in optimising long term production scheduling for open pit mine design,†Trans. Institutions Min. Metall. Sect. A Min. Technol., vol. 116, no. 2, pp. 58–66, 2007, doi: 10.1179/174328607X191074.
F. S. Hillier and G. J. Lieberman, Introduction to operations research. McGraw-Hill Science, Engineering & Mathematics, 1995.
Published
Issue
Section
Authors who publish with this journal agree to the following terms:
With the receipt of the article by Editorial Board of the International Journal of Global Operations Research (IJGOR) and it was decided to be published, then the copyright regarding the article will be diverted to IJGOR
International Journal of Global Operations Research (IJGOR) hold the copyright regarding all the published articles and has the right to multiply and distribute the article under Creative Commons Atribusi 4.0 Internasional.
Copyright tranfer statement the author to the journal is done through filling out the copyright transfer form by author. The form can be downloaded HERE.
