數(shù)學(xué)建模競(jìng)賽論文寫作ppt課件市公開課金獎(jiǎng)市賽課一等獎(jiǎng)?wù)n件

數(shù)學(xué)建模競(jìng)賽論文寫作丁永生東華大學(xué)信息學(xué)院第1頁(yè)第1頁(yè)近年來獲獎(jiǎng)情況20美國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，國(guó)際特等獎(jiǎng)20全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，上海賽區(qū)二等獎(jiǎng)20美國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，國(guó)際一等獎(jiǎng)20全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，全國(guó)二等獎(jiǎng)和上海賽區(qū)一等獎(jiǎng)20全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，上海賽區(qū)二等獎(jiǎng)年全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，上海賽區(qū)二等獎(jiǎng)1999年全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，上海賽區(qū)二等獎(jiǎng)1998年全國(guó)大學(xué)生數(shù)學(xué)模型競(jìng)賽，全國(guó)一等獎(jiǎng)和上海賽區(qū)一等獎(jiǎng)第2頁(yè)第2頁(yè)數(shù)模小組任務(wù)分工三個(gè)人側(cè)重點(diǎn)不同:建模：推導(dǎo)數(shù)學(xué)模型，數(shù)學(xué)能力強(qiáng)編程：計(jì)算機(jī)能力強(qiáng)論文寫作：寫作能力強(qiáng)第3頁(yè)第3頁(yè)競(jìng)賽時(shí)間安排第一天：早晨：擬定題目，并查閱文獻(xiàn)下午：開始分析，建立初步模型晚上：編程，得到初步計(jì)算結(jié)果12：00PM休息第二天：早晨：得到第一個(gè)模型合理結(jié)果下午：開始寫論文，并考慮對(duì)第一個(gè)模型改進(jìn)第4頁(yè)第4頁(yè)競(jìng)賽時(shí)間安排第二天：晚上：得到第二個(gè)模型初步結(jié)果12：00PM休息第三天：早晨：得到第二個(gè)模型合理結(jié)果下午：考慮對(duì)前二個(gè)模型進(jìn)一步優(yōu)化，得到第三個(gè)數(shù)學(xué)模型，或?qū)η岸€(gè)模型正確性進(jìn)行驗(yàn)證晚上：得到最后結(jié)果，完畢整篇論文第5頁(yè)第5頁(yè)論文格式規(guī)范論文（答卷）用白色A4紙，上下左右各留出2.5cm頁(yè)邊距第一頁(yè)為確保書，詳細(xì)格式按要求第二頁(yè)為空白頁(yè)，用于論文編號(hào)論文題目和摘要寫在第三頁(yè)上第四頁(yè)開始是論文正文論文從第三頁(yè)開始編寫頁(yè)碼，頁(yè)碼必須位于每頁(yè)頁(yè)腳中部，從“1”開始連續(xù)編號(hào)論文不能有頁(yè)眉，不能有任何也許顯示答案人身份標(biāo)志第6頁(yè)第6頁(yè)論文格式規(guī)范論文題目用3號(hào)黑體字、一級(jí)標(biāo)題用4號(hào)黑體字，并居中。論文中其它中文一律采用小4號(hào)宋體字，行距用1.5倍行距注意：摘要在整篇論文中評(píng)閱中占有主要權(quán)重，請(qǐng)認(rèn)真書寫摘要引用別人結(jié)果或其它公開資料（包括網(wǎng)上查到資料）必須按照要求參考文獻(xiàn)表述方式在正文引用處和參考文獻(xiàn)中均明確列出。正文引用處用“[]”標(biāo)出，如[1][3]等。第7頁(yè)第7頁(yè)論文格式規(guī)范參考文獻(xiàn)按正文中引用順序列出，其中書籍表述方式為：[編號(hào)]作者，書名，出版地：出版社，出版年期刊雜志論文表述方式為：[編號(hào)]作者，論文名，雜志名，卷期號(hào)：起止頁(yè)碼，出版年網(wǎng)上資源表述方式為：[編號(hào)]作者，資源標(biāo)題，網(wǎng)址，訪問時(shí)間（年月日）第8頁(yè)第8頁(yè)論文學(xué)作及評(píng)卷原則論文構(gòu)成部分:1.摘要2.問題重述3.假設(shè)4.建模5.求解6.討論優(yōu)缺點(diǎn)7.模型改進(jìn)第9頁(yè)第9頁(yè)論文評(píng)卷原則1.假設(shè)合理性2.建模創(chuàng)造性3.結(jié)果正確性4.文字清楚程度第10頁(yè)第10頁(yè)一定要寫好。主要寫三個(gè)方面：1.處理什么問題（一句話）2.采用什么辦法（引起閱卷老師注意，不能太粗，也不能太細(xì)）3.得到什么結(jié)果（簡(jiǎn)明扼要、生動(dòng)、公式要簡(jiǎn)樸、必要時(shí)可采用小圖表）（一）摘要第11頁(yè)第11頁(yè)正文10頁(yè)左右，公式推導(dǎo)放在附錄中將原問題用數(shù)學(xué)語言表示出來重點(diǎn)處理問題應(yīng)著重闡明，把閱卷老師引導(dǎo)到自己思緒中，把他們當(dāng)作不懂本問題讀者。（二）問題重述第12頁(yè)第12頁(yè)最關(guān)鍵一步從假設(shè)開始。需要下很大功夫，簡(jiǎn)明扼要、準(zhǔn)確清楚1）假設(shè)太多，閱卷老師記不住。要?dú)w結(jié)出一些主要假設(shè)，普通3~5條，有些不是很主要假設(shè)在論文適當(dāng)?shù)胤教嵋幌?）假設(shè)要數(shù)學(xué)化，注重邏輯性要求3）設(shè)計(jì)好符號(hào)，使人看起來清楚（三）假設(shè)第13頁(yè)第13頁(yè)闡明建模思緒有些簡(jiǎn)樸事情往往是最主要東西，一定要說清楚剛剛開始原始想法，很主要推導(dǎo)時(shí)，公式若很長(zhǎng)，可放在附錄中普通要求設(shè)計(jì)2~3個(gè)模型（一個(gè)簡(jiǎn)樸、再對(duì)模型進(jìn)行改進(jìn)，得到第二個(gè)模型，就會(huì)生動(dòng)）（四）建模第14頁(yè)第14頁(yè)（1）模型定性線性或非線性連續(xù)、離散或混合時(shí)變或非時(shí)變（2）模型求解利用現(xiàn)成軟件自己解出來，實(shí)際意義更清楚（五）模型求解第15頁(yè)第15頁(yè)（六）模型優(yōu)缺點(diǎn)及改進(jìn)提出一些新思緒，使問題更準(zhǔn)確、也使模型得到進(jìn)一步優(yōu)化。敢于討論學(xué)生，成績(jī)會(huì)好。第16頁(yè)第16頁(yè)舉例闡明設(shè)某生物種群在其適應(yīng)環(huán)境下生存，試預(yù)測(cè)該種群數(shù)量。第17頁(yè)第17頁(yè)普通解法記N(t)為t時(shí)刻該種群數(shù)量，設(shè)該種群自然增長(zhǎng)率為，則即假定初試時(shí)刻種群數(shù)量為N0，則有于是：第18頁(yè)第18頁(yè)模型假設(shè)假設(shè)該環(huán)境下只有一個(gè)生物群體，或者其它生物群體不影響此生物群體生成假定該種群自然增長(zhǎng)率與時(shí)刻t和時(shí)刻t時(shí)該種群數(shù)量無關(guān)，記為由于種群數(shù)量很大，故可設(shè)種群個(gè)體N(t)是時(shí)間連續(xù)可微函數(shù)假定初始時(shí)刻，種群數(shù)量為N0第19頁(yè)第19頁(yè)試驗(yàn)驗(yàn)證美國(guó)戰(zhàn)后人口增加不同時(shí)間段世界人口增加深入改進(jìn)（1）變參數(shù)（2）各種群共存（3）隨機(jī)模型第20頁(yè)第20頁(yè)颶風(fēng)疏散問題建模StrategiesforEscapingaHurricane’sWrath

年美國(guó)競(jìng)賽B題第21頁(yè)第21頁(yè)第22頁(yè)第22頁(yè)AMonumentalTrafficJamin1999TrafficslowedtoastandstillonInterstateI-26,whichistheprincipalroutegoinginlandfromCharlestontotherelativelysafehavenofColumbiainthecenterofthestate.Whatisnormallyaneasytwo-hourdrivetookupto18hourstocomplete.Manycarssimplyranoutofgasalongtheway.TrafficleavingColumbiagoingnorthwestwasmovingonlyveryslowly.第23頁(yè)第23頁(yè)ReversaloftrafficonI-26,sothatbothsides,includingthecoastal-boundlanes,havetrafficheadedinlandfromCharlestontoColumbia.TrafficreversalonprincipalroadsleadinginlandfromMyrtleBeachandHiltonHeadisalsoplanned.ThePrincipalProposal第24頁(yè)第24頁(yè)Charlestonhasapproximately500,000peopleMyrtleBeachhasabout200,000people,andanother250,000peoplearespreadoutalongtherestofthecoastalstripColumbia,anothermetroareaofaround500,000peoplePeopleinDifferentCities第25頁(yè)第25頁(yè)Theinterstateshavetwolanesoftrafficineachdirectionexceptinthemetropolitanareaswheretheyhavethree.Columbiadoesnothavesufficienthotelspacetoaccommodatetheevacuees(includingsomecomingfromfarthernorthbyotherroutes),sosometrafficcontinuesoutboundonI-26towardsSpartanburg;onI-77northtoCharlotte;andonI-20easttoAtlanta.OthersFactors第26頁(yè)第26頁(yè)Thequestionsthatneedtobeaddressed:1.Underwhatconditionsdoestheplanforturningthetwocoastal-boundlanesofI-26intotwolanesofColumbia-boundtraffic,essentiallyturningtheentireI-26intoone-waytraffic,significantlyimproveevacuationtrafficflow?ConstructaModel第27頁(yè)第27頁(yè)2.In1999,thesimultaneousevacuationofthestate'sentirecoastalregionwasordered.Wouldtheevacuationtrafficflowimproveunderanalternativestrategythatstaggerstheevacuation,perhapscounty-by-countyoversometimeperiodconsistentwiththepatternofhowhurricanesaffectthecoast?ConstructaModel第28頁(yè)第28頁(yè)3.SeveralsmallerhighwaysbesidesI-26extendinlandfromthecoast.Underwhatconditionswoulditimproveevacuationflowtoturnaroundtrafficonthese?4.WhateffectwouldithaveonevacuationflowtoestablishmoretemporarysheltersinColumbia,toreducethetrafficleavingColumbia?ConstructaModel第29頁(yè)第29頁(yè)5.In1999,manyfamiliesleavingthecoastbroughtalongtheirboats,campers,andmotorhomes.Manydrovealloftheircars.Underwhatconditionsshouldthereberestrictionsonvehicletypesornumbersofvehiclesbroughtinordertoguaranteetimelyevacuation?ConstructaModel第30頁(yè)第30頁(yè)6.Ithasbeensuggestedthatin1999someofthecoastalresidentsofGeorgiaandFlorida,whowerefleeingtheearlierpredictedlandfallsofHurricaneFloydtothesouth,cameupI-95andcompoundedthetrafficproblems.Howbiganimpactcantheyhaveontheevacuationtrafficflow?ConstructaModel第31頁(yè)第31頁(yè)RequiresClearlyidentifywhatmeasuresofperformanceareusedtocomparestrategies.Prepareashortnewspaperarticle,nottoexceedtwopages,explainingtheresultsandconclusionsofyourstudytothepublic.第32頁(yè)第32頁(yè)(1)

Theinterstates(e.g.,I-26,I-77,I-20)havetwolanesoftrafficineachdirectionexceptinthemetropolitanareaswheretheyhavethree,whichmeansthetrafficenteringametropolitan(suchasColumbia)canbesmoothlyseparateintotheroutesleavingitinmostcase.(2)

ThenormaldrivetakestwohourstocompletefromCharlestontoColumbia.TheaveragedrivespeedforacarontheinterstateI-26,I-77,andI-20islimitedto60-80mph,whiletheoneforacaronprincipalroads(e.g.,US501)islimitedto50-70mph.Assumptions第33頁(yè)第33頁(yè)(3)

Charlestonhasapproximately500,000people,MyrtleBeachhasabout200,000people,andanother250,000peoplearewell-distributedalongtherestofthecoastalstrip.Also,weshouldconsidersomeevacueesfromthecoastlineofGeorgiaandFloridainQuestion6.Assumptions第34頁(yè)第34頁(yè)(4)

Columbiahasaround500,000people.And,accordingtoourroughsearchviaInternet,thetotalnumberofthehotelsandmotelsinColumbiaandbeyondColumbia,SC,isabout184,whichcanoccupyaround50,000people.Hence,Columbiadoesnothavesufficienthotelspacetoaccommodatetheevacuees(includingpeoplecomingfromfarthernorthbyotherroutes).So,sometrafficmustcontinueoutboundonI-26towardsSpartanburg;onI-77northtoCharlotte;andonI-20westtoAtlanta.Assumptions第35頁(yè)第35頁(yè)(5)

ThereareseveraltropicalcycloneguidancemodelsavailabletotheNHCandCPHCforecastersforthehurricaneseason.Thesemodelsrangeincomplexityfromsimplestatisticalmodelstothree-dimensionalprimitiveequationmodels.Accordingtotheirmodels,weassumethattheNationalHurricaneCenter(NHC)inMiami,Floridacanissue72hourtropicalcyclonetrackandintensityforecasts.Also,hurricanesarepossibleinthespecifiedareaoftheWATCH,usuallywithin36hours,andareexpectedinthespecifiedareaoftheWARNING,usuallywithin24hours.Assumptions第36頁(yè)第36頁(yè)(6)EvacueestravelingonI-26inthenormalwestboundlanesoftravelwillbeallowedtoexitatallinterchangesbetweenCharlestonandColumbia.Evacueestravelinginthereversedlanesoftravelwillbeallowedtoexitatmost,butnotall,interchanges.Assumptions第37頁(yè)第37頁(yè)10965432111TSx1x2x3x4x5x7x6x8x9x10x11x12x14x15x1387x16S—Supersource1(V1)—HiltonHead2(V2)—Charleston3(V3)—MyrtleBeach4(V4)—ThecrossoverpointbetweenI-95andI-265(V5)—ThecrossoverpointbetweenI-95andI-206(V6)—Columbia7(V7)—HotelsinColumbia8(V8)—TemporarysheltersinColumbia9(V9)—Atlanta10(V10)—Spartanburg11(V11)—CharlotteT—SupersinkFig.1.Thetrafficnetworkofthemainroutesofevacuation.第38頁(yè)第38頁(yè)TheMaximumFlowProblem

TheobjectivefunctionforQuestions1to6exceptQuestion2:Theconstraintconditions:第39頁(yè)第39頁(yè)TheMaximumFlowProblem

TheobjectivefunctionforQuestions2:Theconstraintconditions:第40頁(yè)第40頁(yè)EvacueesfromSources

(HiltonHead,Charleston,andMyrtleBeach)Weshouldfirstdealwiththe250,000peoplewelldistributingalongtherestofthecoastalstrip,anddividethemintothreesources.Thenwemustconsidertwocasesinouralgorithms:(1)Non-considerationofthesomeofthecoastalresidentsofGeorgiaandFloridacameupI-95;(2)ConsiderationofsomeofthecoastalresidentsofGeorgiaandFloridacameupI-95.第41頁(yè)第41頁(yè)TheFamous

GoldenSection

Method=500,000+125,000=625,000=200,000+I-95:I-26:US501:(case2)第42頁(yè)第42頁(yè)TheImpactofTemporarySheltersTheflowofenteringColumbiaandthatofstayingatandoutgoingColumbiashouldbeequalto:--I-26westboundtraffictoColumbia--I-20westboundtraffictoColumbia--I-26westboundtrafficleavingColumbia--I-20westboundtrafficleavingColumbia--I-77northboundtrafficleavingColumbia--InhotelsandmotelsinColumbia--InestablishedtemporarysheltersinColumbia第43頁(yè)第43頁(yè)ThePerformanceMeasureofTrafficFlow

ThetrafficflowtobeanimportantperformancemeasureFlow=第44頁(yè)第44頁(yè)SimulationResultsandModelTesting

FivedifferentstrategiesaccordingtoQuestions1to5consideringtwocases:(1)Non-considerationofthesomeofthecoastalresidentsofGeorgiaandFloridacameupI-95;(2)ConsiderationofsomeofthecoastalresidentsofGeorgiaandFloridacameupI-95,whichisQuestion6.第45頁(yè)第45頁(yè)Q:Underwhatconditionsdoestheplanforturningthetwocoastal-boundlanesofI-26intotwolanesofColumbia-boundtraffic,essentiallyturningtheentireI-26intoone-waytraffic,significantlyimproveevacuationtrafficflow?A:StrategyI第46頁(yè)第46頁(yè)Q:SeveralsmallerhighwaysbesidesI-26extendinlandfromthecoast.Underwhatconditionswoulditimproveevacuationflowtoturnaroundtrafficonthese?A:StrategyII第47頁(yè)第47頁(yè)StrategyIII

Q:WhateffectwouldithaveonevacuationflowtoestablishmoretemporarysheltersinColumbia,toreducethetrafficleavingColumbia?

第48頁(yè)第48頁(yè)StrategyIV

Q:In1999,manyfamiliesleavingthecoastbroughtalongtheirboats,campers,andmotorhomes.Manydrovealloftheircars.Underwhatconditionsshouldthereberestrictionsonvehicletypesornumbersofvehiclesbroughtinordertoguaranteetimelyevacuation?

第49頁(yè)第49頁(yè)Table1.TheStrategiescomparisonleavingthecoasttoColumbia.

Performancemeasuresoftrafficflow(cars/hour)StrategyIStrategyIIStrategyIIIStrategyIVTheFlowonI-26Case14327.54496.85048.85770.1Case23854.43823.15049.55770.8TheFlowonUS501toI-20Case11920224022402560Case21920224022402560TheFlowonI-95Case1330.6356.5385.7440.8Case2945.6992.91193.71364.2第50頁(yè)第50頁(yè)StrategyV

Q:In1999,thesimultaneousevacuationofthestate'sentirecoastalregionwasordered.Wouldtheevacuationtrafficflowimproveunderanalternativestrategythatstaggerstheevacuation,perhapscounty-by-countyoversometimeperiodconsistentwiththepatternofhowhurricanesaffectthecoast?第51頁(yè)第51頁(yè)Table2.ThecomparisonofevacuatingtimesbetweenusingStrategyVcombinedwithStrategyItoIVandusingonlyStrategyItoIVStrategyIIIIIIIVCompletingsimultaneouslyCase1108.457172.216966.964961.8984Case2121.796878.136674.490563.8862Escapingcounty-by-countyCase1105.400866.191661.065755.8962Case2112.337972.769069.131956.5233第52頁(yè)第52頁(yè)SensitivityAnalysis

Twoimportantimpliedfactorstoaffecttheperformanceofthe