数学建模竞赛技巧省名师优质课赛课获奖课件市赛课一等奖课件.ppt

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。感谢您,数学建模竞赛技巧,丁永生,东华大学信息学院,第1页,近年来获奖情况,全国二等奖,和,上海赛区一等奖,，年全国大学生数学模型竞赛,全国一等奖,和,上海赛区一等奖,，,年全国大学生数学模型竞赛,上海赛区二等奖,，年全国大学生数学模型竞赛,全国二等奖,和,上海赛区一等奖,，,年全国大学生数学模型竞赛,上海赛区二等奖,，年全国大学生数学模型竞赛,上海赛区二等奖,，年全国大学生数学模型竞赛,上海赛区二等奖,，1999年全国大学生数学模型竞赛,全国一等奖,和,上海赛区一等奖,，1998年全国大学生数学模型竞赛,第2页,近年来获奖情况,国际一等奖,，年美国大学生数学模型竞赛,国际特等奖,，,年美国大学生数学模型竞赛,国际一等奖,，年美国大学生数学模型竞赛,全国一等奖,，年全国部分高校硕士数学建模竞赛,上海市精品课程,，数学建模与数学试验，,上海市优异教学结果二等奖,，工科数学课程计算机试验教学改革与实践，,上海赛区优异教练员,，年全国大学生数学建模竞赛,第3页,近年来获奖情况,国际特等奖,，,年美国大学生数学模型竞赛,自1989年以来，取得国际特等奖中国高校未超出10所,第4页,数模小组任务分工,三个人侧重点不一样:,建模：推导数学模型，数学能力强,编程：计算机能力强,论文写作：写作能力强,第5页,竞赛时间安排,第一天：,早晨：确定题目，并查阅文件,下午：开始分析，建立初步模型,晚上：编程，得到初步计算结果,12：00 PM 休息,第二天：,早晨：得到第一个模型合理结果,下午：开始写论文，并考虑对第一个模型改进,第6页,竞赛时间安排,第二天：,晚上：得到第二个模型初步结果,12：00 PM 休息,第三天：,早晨：得到第二个模型合理结果,下午：考虑对前二个模型深入优化，得到第三个数学模型，或对前二个模型正确性进行验证,晚上：得到最终结果，完成整篇论文,第7页,论文格式规范,论文（答卷）用白色A4纸，上下左右各留出2.5cm 页边距,第一页为确保书，详细格式按要求,第二页为空白页，用于论文编号,论文题目和摘要写在第三页上,第四页开始是论文正文,论文从第三页开始编写页码，页码必须位于每页页脚中部，从“1”开始连续编号,论文不能有页眉，不能有任何可能显示答案人身份标志,第8页,论文格式规范,论文题目用3号黑体字、一级标题用4号黑体字，并居中。论文中其它汉字一律采取小4号宋体字，行距用1.5倍行距,注意：摘要在整篇论文中评阅中占有主要权重，请认真书写摘要,引用他人结果或其它公开资料（包含网上查到资料）必须按照要求参考文件表述方式在正文引用处和参考文件中均明确列出。正文引用处用“”标出，如13等。,第9页,论文格式规范,参考文件按正文中引用次序列出，其中,书籍表述方式为：,编号 作者，书名，出版地：出版社，出版年,期刊杂志论文表述方式为：,编号 作者，论文名，杂志名，卷期号：起止页码，出版年,网上资源表述方式为：,编号 作者，资源标题，网址，访问时间（年月日）,第10页,论文学作及评卷标准,论文组成部分:,1.摘要,2.问题重述,3.假设,4.建模,5.求解,6.讨论优缺点,7.模型改进,第11页,论文评卷标准,1.假设合理性,2.建模创造性,3.结果正确性,4.文字清楚程度,第12页,一定要写好。主要写三个方面：,1.处理什么问题（一句话）,2.采取什么方法（引发阅卷老师注意，不能太粗，也不能太细）,3得到什么结果（简明扼要、生动、公式要简单、必要时可采取小图表）,（一）摘 要,第13页,正 文,10页左右，公式推导放在附录中,将原问题用数学语言表示出来,重点处理问题应着重说明，把阅卷老师引导到自己思绪中，把他们看成不懂本问题读者。,（二）问题重述,第14页,最关键一步从假设开始。需要下很大功夫，简明扼要、准确清楚,1）假设太多，阅卷老师记不住。要归结出一些主要假设，普通35条，有些不是很主要假设在论文适当地方提一下,2）假设要数学化，重视逻辑性要求,3）设计好符号，使人看起来清楚,（三）假 设,第15页,说明建模思绪,有些简单事情往往是最主要东西，一定要说清楚,刚才开始原始想法，很主要,推导时，公式若很长，可放在附录中,普通要求设计,23,个模型（一个简单、再对模型进行改进，得到第二个模型，就会生动）,（四）建 模,第16页,（1）模型定性,线性或非线性,连续、离散或混合,时变或非时变,（2）模型求解,利用现成软件,自己解出来，实际意义更清楚,（五）,模型求解,第17页,（六）模型优缺点及改进,提出一些新思绪，使问题更准确、也使模型得到深入优化。,勇于讨论学生，成绩会好。,第18页,举例说明,设某生物种群在其适应环境下生存，试预测该种群数量。,第19页,普通解法,记,N,(,t,)为,t,时刻该种群数量，设该种群自然增加率为 ，则,即,假定初试时刻种群数量为N,0，,则有,于是：,第20页,模型假设,假设该环境下只有一个生物群体，或者其它生物群体不影响此生物群体生成,假定该种群自然增加率与时刻t 和时刻t 时该种群数量无关，记为,因为种群数量很大，故可设种群个体N(t)是时间连续可微函数,假定初始时刻，种群数量为,N,0,第21页,试验验证,美国战后10年人口增加,不一样时间段世界人口增加,深入改进,（1）变参数,（2）各种群共存,（3）随机模型,第22页,飓风疏散问题建模,Strategies for Escaping a Hurricanes Wrath,年美国竞赛B题,第23页,第24页,A Monumental Traffic Jam,in 1999,Traffic slowed to a standstill on Interstate I-26,which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state.,What is normally an easy two-hour drive took up to 18 hours to complete.,Many cars simply ran out of gas along the way.,Traffic leaving Columbia going northwest was moving only very slowly.,第25页,Reversal of traffic on I-26,so that both sides,including the coastal-bound lanes,have traffic headed inland from Charleston to Columbia.,Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.,The Principal Proposal,第26页,Charleston has approximately 500,000 people,Myrtle Beach has about 200,000 people,and another 250,000 people are spread out along the rest of the coastal strip,Columbia,another metro area of around 500,000 people,People in Different Cities,第27页,The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three.,Columbia does not have sufficient hotel space to accommodate the evacuees(including some coming from farther north by other routes),so some traffic continues outbound on I-26 towards Spartanburg;on I-77 north to Charlotte;and on I-20 east to Atlanta.,Others Factors,第28页,The questions that need to be addressed:,1.Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic,essentially turning the entire I-26 into one-way traffic,significantly improve evacuation traffic flow?,Construct a Model,第29页,2.In 1999,the simultaneous evacuation of the states entire coastal region was ordered.Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation,perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?,Construct a Model,第30页,3.Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these?,4.What effect would it have on evacuation flow to establish more temporary shelters in Columbia,to reduce the traffic leaving Columbia?,Construct a Model,第31页,5.In 1999,many families leaving the coast brought along their boats,campers,and motor homes.Many drove all of their cars.Under what conditions should there be restrictions on vehicle types or numbers of vehicles brought in order to guarantee timely evacuation?,Construct a Model,第32页,6.It has been suggested that in 1999 some of the coastal residents of Georgia and Florida,who were fleeing the earlier predicted landfalls of Hurricane Floyd to the south,came up I-95 and compounded the traffic problems.How big an impact can they have on the evacuation traffic flow?,Construct a Model,第33页,Requires,Clearly identify what measures of performance are used to compare strategies.,Prepare a short newspaper article,not to exceed two pages,explaining the results and conclusions of your study to the public.,第34页,(1),The interstates(e.g.,I-26,I-77,I-20)have two lanes of traffic in each direction except in the metropolitan areas where they have three,which means the traffic entering a metropolitan(such as Columbia)can be smoothly separate into the routes leaving it in most case.,(2),The normal drive takes two hours to complete from Charleston to Columbia.The average drive speed for a car on the interstate I-26,I-77,and I-20 is limited to 60-80 mph,while the one for a car on principal roads(e.g.,US501)is limited to 50-70 mph.,Assumptions,第35页,(3),Charleston has approximately 500,000 people,Myrtle Beach has about 200,000 people,and another 250,000 people are well-distributed along the rest of the coastal strip.Also,we should consider some evacuees from the coastline of Georgia and Florida in Question 6.,Assumptions,第36页,(4),Columbia has around 500,000 people.And,according to our rough search via Internet,the total number of the hotels and motels in Columbia and beyond Columbia,SC,is about 184,which can occupy around 50,000 people.Hence,Columbia does not have sufficient hotel space to accommodate the evacuees(including people coming from farther north by other routes).So,some traffic must continue outbound on I-26 towards Spartanburg;on I-77 north to Charlotte;and on I-20 west to Atlanta.,Assumptions,第37页,(5),There are several tropical cyclone guidance models available to the NHC and CPHC forecasters for the hurricane season.These models range in complexity from simple statistical models to three-dimensional primitive equation models.According to their models,we assume that the National Hurricane Center(NHC)in Miami,Florida can issue 72 hour tropical cyclone track and intensity forecasts.Also,hurricanes are possible in the specified area of the WATCH,usually within 36 hours,and are expected in the specified area of the WARNING,usually within 24 hours.,Assumptions,第38页,(6)Evacuees traveling on I-26 in the normal westbound lanes of travel will be allowed to exit at all interchanges between Charleston and Columbia.Evacuees traveling in the reversed lanes of travel will be allowed to exit at most,but not all,interchanges.,Assumptions,第39页,10,9,6,5,4,3,2,1,11,T,S,x,1,x,2,x,3,x,4,x,5,x,7,x,6,x,8,x,9,x,10,x,11,x,12,x,14,x,15,x,13,8,7,x,16,S Super source,1(,V,1,)Hilton Head,2(,V,2,)Charleston,3(,V,3,)Myrtle Beach,4(,V,4,)The crossover point,between I-95 and I-26,5(,V,5)The crossover point,between I-95 and I-20,6(,V,6,)Columbia,7(,V,7,)Hotels in Columbia,8(,V,8,)Temporary shelters in Columbia,9(,V,9,)Atlanta,10(,V,10,)Spartanburg,11(,V,11,)Charlotte,T Super sink,Fig.1.The traffic network of the main routes of evacuation.,第40页,The Maximum Flow Problem,The objective function for Questions 1,to 6 except Question 2:,The constraint conditions:,第41页,The Maximum Flow Problem,The objective function for Questions 2:,The constraint conditions:,第42页,Evacuees from Sources,(Hilton Head,Charleston,and Myrtle Beach),We should first deal with the 250,000 people well distributing along the rest of the coastal strip,and divide them into three sources.,Then we must consider two cases in our algorithms:(1)Non-consideration of the some of the coastal residents of Georgia and Florida came up I-95;(2)Consideration of some of the coastal residents of Georgia and Florida came up I-95.,第43页,The Famous,Golden Section,Method,=500,000+125,000=625,000,=200,000+,I-95:,I-26:,US501:,(case 2),第44页,The Impact of,Temporary Shelters,The flow of entering Columbia and that of staying at and outgoing Columbia should be equal to:,-I-26 westbound traffic to Columbia,-I-20 westbound traffic to Columbia,-I-26 westbound traffic leaving Columbia,-I-20 westbound traffic leaving Columbia,-I-77 northbound traffic leaving Columbia,-In hotels and motels in Columbia,-In established temporary shelters in Columbia,第45页,The Performance Measure,of Traffic Flow,The traffic flow to be an important performance measure,Flow=,第46页,Simulation Results and,Model Testing,Five different strategies according to Questions 1 to 5 considering two cases:,(1)Non-consideration of the some of the coastal residents of Georgia and Florida came up I-95;,(2)Consideration of some of the coastal residents of Georgia and Florida came up I-95,which is Question 6.,第47页,Q:Under what conditions does the plan for turning the two coastal-bound lanes of I-26 into two lanes of Columbia-bound traffic,essentially turning the entire I-26 into one-way traffic,significantly improve evacuation traffic flow?,A:,Strategy I第48页,Q:Several smaller highways besides I-26 extend inland from the coast.Under what conditions would it improve evacuation flow to turn around traffic on these?,A:,Strategy II,第49页,Strategy III,Q:What effect would it have on evacuation flow to establish more temporary shelters in Columbia,to reduce the traffic leaving Columbia?,第50页,Strategy IV,Q:In 1999,many families leaving the coast brought along their boats,campers,and motor homes.Many drove all of their cars.Under what conditions should there be restrictions on vehicle types or numbers of vehicles brought in order to guarantee timely evacuation?,第51页,Table 1.The Strategies comparison,leaving the coast to Columbia.,Performance measures of traffic flow(cars/hour),Strategy I,Strategy II,Strategy III,Strategy IV,The Flow on I-26,Case 1,4327.5,4496.8,5048.8,5770.1,Case 2,3854.4,3823.1,5049.5,5770.8,The Flow on US501 to I-20,Case 1,19202240,2240,2560,Case 2,1920,2240,2240,2560,The Flow on I-95,Case 1,330.6,356.5,385.7,440.8,Case 2,945.6,992.9,1193.7,1364.2,第52页,Strategy V,Q:In 1999,the simultaneous evacuation of the states entire coastal region was ordered.Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation,perhaps county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?,第53页,Table 2.The comparison of evacuating times between using Strategy V combined with Strategy I to IV and using only Strategy I to IV,Strategy,I,II,III,IV,Completing simultaneously,Case 1,108.4571,72.2169,66.9649,61.8984,Case 2,121.7968,78.1366,74.4905,63.8862,Escaping county-by-county,Case 1,105.4008,66.1916,61.0657,55.8962,Case 2,112.3379,72.7690,69.1319,56.5233,第54页,Sensitivity Analysis,Two important implied factors to affect the performance of the entire network:,The accommodation capacity in Columbia,and,The evacuees from Georgia and Florida came up I-95.,第55页,Strengths and Limitations,Discussions and Conclusions,Others,第56页,Fig.2.The traffic flow on I-26 changing with the time period of predicted landfall of hurricane,resulting in different regions of the strategies(I to IV)to be carried out.,第57页,Fig.3.The minimum total required traffic flow changing with the time period of predicted landfall of hurricane,resulting in different regions of the strategies(I to IV)to be carried out.,第58页,Fig.4.The comparison of maximum traffic flow by evacuating county-by-county(Strategy V combined with Strategies I to IV)and in a simultaneous way(using only Strategies I to IV).,第59页,Fig.5.The influence of evacuees accommodated in Columbia on the traffic flow on I-26,resulting in different regions of the strategies(I to III)to be carried out.,第60页,Fig6.The impacts of evacuees from Georgia and Florida on the traffic flow on I-26,resulting in different regions of the strategies(I to IV)to be carried out.,第61页,Fig.7.The impacts of evacuees from Georgia and Florida on the traffic flow on I-95,resulting in different regions of the strategies(I to IV)to be carried out.,第62页,Thanks!,The End,第63页,