摘要单循环赛是一种全面而公平的竞赛机制，赛程安排的恰当与否，在很大程度上影响比赛的结果。本文主要针对单循环赛的最优赛程安排方案建立相应的数学模型，给出最优赛程的安排方案。对于问题一，通过直接拼凑的方法得出符合题目要求的关于5支队伍的赛程安排：(A,B),(C,D),(A,E),(B,C),(D,E),(A,C),(B,D),(C,E),(A,D),(B,E)。对于问题二，则是通过参赛队伍数与各队每两场比赛中间相隔的场次数的上限之间的数量关系，列出相应的不等式，解不等式得即为问题二的结果，并通过MATLAB软件编程验证。针对问题三，我们建立了1号位置固定逆时针轮转法模型，基于参赛队数的奇偶性的算法差异，通过MATLAB软件编程求出部分结果如下：参赛队伍为8支时的赛程安排：(1,5),(2,6),(3,7),(4,8),(1,6),(5,7),(2,8),(3,4),(1,7),(6,8),(5,4),(2,3),(1,8),(7,4),(6,3),(5,2),(1,4),(8,3),(7,2),(6,5),(1,3),(4,2),(8,5),(7,6),(1,2),(3,5),(4,6),(8,7).针对问题四，通过各间隔场次与平均相隔场次的偏差(整个赛程相隔场次数的最大偏差,球队之间相隔场次的最大偏差)来度量各队每场比兩赛相隔场次的“均匀性”，进而衡量问题三所求赛程的优劣。检验结果：计算8支队伍的赛程得,；计算9支队伍的赛程得,。结果表明,问题三所得的两个赛程都达到了、下界。关键词：单循环赛；数学模型；MATLAB；逆时针轮转法AbstractSingleroundrobinisacomprehensiveandfaircompetitionmechanism,andscheduleanappropriateornot,toagreatextent,affecttheresultofthegame.ThisarticlemainlyaimsattheoptimalscheduleofthesingleroundrobinschemetoestablishthecorrespondingMathematicalmodelofoptimalschedulearrangementschemeisgiven.Forquestionone,itisconcludedthatconformtotherequirementsofthesubjectbyusingthemethodofdirectlytopiecetogethertheteamconsistsofabout5schedule:(A,B),(C,D),(A,E),(B,C),(D,E),(A,C),(B,D),(C,E),(A,D),(B,E).Forquestiontwo,itisthroughtheQuantitativerelationshipbetweenthenumberoftheteamsnandtheupperlimitrofeverytwogamesbyalltheteams,liststhecorrespondinginequalities，inequalityintoistheresultsofthequestion2，thenverifyitbyMATLABsoftwareprogramming.Forquestionthree,weestablishedthemodelno.1positionfixedcounterclockwiserotationmethod,basedontheparityofthecompetingteamsnumberdifferencealgorithm,throughtheMATLABsoftwareprogrammingandthepartresultsareasfollows:Teamsofeightschedule:(1,5),(2,6),(3,7),(4,8),(1,6),(5,7),(2,8),(3,4),(1,7),(6,8),(5,4),(2,3),(1,8),(7,4),(6,3),(5,2),(1,4),(8,3),(7,2),(6,5),(1,3),(4,2),(8,5),(7,6),(1,2),(3,5),(4,6),(8,7).Forquestionfour,itisthroughthedeviationbetweentheeveryintervalnumberandtheaverageintervalnumber(ThewholeSchedule’sintervalnumbermaximumdeviationandintervalnumbermaximumdeviationbetweentheteams)measuringteamsseparatedbysessioneverytwogames"uniformity",Andthenmeasuringtheprosandconsoftheschedulewhichworkedoutbytheproblemthree.Theinspectionresults：Computing8teamconsistsoftheschedule，,；Computing9teamconsistsoftheschedule，,.Theresultsshowthatthetwoschedulewhichworkedoutbytheproblemthreehasreachedand’slowerbound.Keywords：Singleroundrobin;Mathematicalmodel;MATLAB;Counterclockwiserotationmethod目录第一章前言...............................................................................................................11.1数学建模介绍...............................................................................................11.2单循环赛介绍...............................................................................................21.3MATLAB的介绍.........................................................................................21.4本文研究内容与章节安排........................
