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邯郸学院本科毕业论文题目全国大学生数学建模竞赛常用建模方法探讨学生柴云飞指导教师闫峰教授年级2009级本科专业数学与应用数学二级学院数学系（系、部）邯郸学院数学系2013年6月郑重声明本人的毕业论文是在指导教师闫峰的指导下独立撰写完成的．如有剽窃、抄袭、造假等违反学术道德、学术规范和侵权的行为，本人愿意承担由此产生的各种后果，直至法律责任，并愿意通过网络接受公众的监督．特此郑重声明．论文经“中国知网”论文检测系统检测，总相似比为5.80%．毕业论文作者（签名）：年月日I全国大学生数学建模竞赛常用建模方法探讨摘要全国大学生数学建模竞赛作为全国高校规模最大的基础性学科竞赛，越来越受到人们的重视，所以建模竞赛的方法也就变得尤为重要．随着竞赛的不断发展，赛题的开放性逐步增大，一道赛题可用多种解法，各种求解的算法有时会相互融合，同时也在向大规模数据处理方向发展，这就对选手的能力提出了更高的要求．由于建模方法种类众多，无法一一介绍，所以本文主要介绍了四种比较常用的数学建模竞赛方法，包括微分与差分方程建模方法、数学规划建模方法、统计学建模方法、图论方法，并结合历年赛题加以说明．关键词：数学建模竞赛统计学方法数学规划图论IICommonlyUsedModelingMethodofChinaUndergraduateMathematicalContestinModelingChaiyunfeiDirectedbyProfessorYanfengABSTRACTTheChinaundergraduatemathematicalcontestinmodelinghasbeenattentionbymoreandmorepeopleasabasicsubjectofthelargestnationalcollegecompetition.Themethodofmodelingcompetitionhasbecomemoreandmoreimportant.Openquestionsgraduallyincreasedwiththedevelopmentofcompetition.Mostofthegamescanbesolvedbylotsofsolutions.Sometimesthesemethodscanbeusedtogether.Andthereisalsoalotofdatawhichputsforwardhigherrequirementontheabilityofplayers.Themodelingmethodsistoonumeroustomention,sothisarticlemainlyfourkindsCommonlyusedmodelingmethodareintroducedthatdifferentialanddifferenceequationsmodelingmethod,Mathematicalprogrammingmodelingmethod,Statisticsmodelingmethod,graphtheoryandinterpretswithcalendaryear’stestquestions.KEYWORDS：MathematicalcontestinmodelingStatisticsmethodMathematicalprogrammingGraphtheory1目录摘要..............................................................................................................................................I英文摘要........................................................................................................................................II前言.............................................................................................................................................11微分方程与差分方程建模.........................................................................................................21.1微分方程建模..................................................................................................................21.1.1微分方程建模的原理和方法...............................................................................21.1.2微分方程建模应用实例.......................................................................................31.2差分方程建模..................................................................................................................41.2.1差分方程建模的原理和方法...............................................................................41.2.2差分方程建模应用实例.......................................................................................52数学规划建模.............................................................................................................................52.1线性规划建模的一般理论..............................................................................................62.2线性规划建模应用实例..................................................................................................73统计学建模方法.........................................................................................................................83.1聚类分析..........................................................................................................................83.1.1聚类分析的原理和方法.......................................................................................83.1.2聚类分析应用实例...............................................................................................83.2回归分析..........................................................................................................................93.2.1回归分析的原理与方法.......................................................................................93.2.2回归分析应用实例.............................................................................................104图论建模方法...........................................................................................................................104.1两种常见图论方法介绍................................................................................................114.1.1模拟退火法的基本原理.....................................................................................114.1.2最短路问题.........................................................................................................114.2图论建模应用实例........................................................................................................125小结...........................................................................................................................................13参考文献.......................................................................................................................................13致谢...........................................................................................................................................141前言全国大学生数学建模竞赛创办于1992年，每年一届，目前已成为全国高校规模最大的基础性学科竞赛，也是世界上规模最大的数学建模竞赛．参赛者需要根据题目要求，在三天时间内完成一篇包括模型假设、模型建立和求解、计算方法的设计和实现、模型结果的分析和检验、模型的改进等方面的论文．通过参加竞赛的训练和比赛，可以提高学生用数学方法解决实际问题的意识和能力，而且在培养团队精神和撰写科技论文等方面都会得到十分有益的锻