上海海事大學-2015優(yōu)化與統(tǒng)計建模試驗模擬考查題(答案)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上精選優(yōu)質(zhì)文檔-傾情為你奉上專心-專注-專業(yè)專心-專注-專業(yè)精選優(yōu)質(zhì)文檔-傾情為你奉上專心-專注-專業(yè)上海海事大學 2014 - 2015 學年第 二 學期研究生 優(yōu)化與統(tǒng)計建模試驗 課程考查模擬題專業(yè)： 學生姓名： 學號： 要求：1.本考查為無紙化形式,要求每位研究生獨立完成,禁止和他人交流。2.請將本文件更名(原文件名學號姓名)。3.必須在本文件內(nèi)作答并緊隨相應試題后面，評閱老師只評閱本文件。4.所有問題僅限于采用本課程所學軟件: Lingo,Cplex,Spss,R進行求解. 其他方式求解將不被認可。5.作答主要內(nèi)容：Lingo,Cplex,R要求源代碼及關(guān)鍵的輸

2、出結(jié)果；Spss要求關(guān)鍵的輸出結(jié)果,一些重要的操作設置最好能加以說明。一. （共10分）線性規(guī)劃：已知線性規(guī)劃 Max z=x12x2x3 x1+x2 +2x3 12 x1+x2 x3 1 x1,x2 ,x30. 1.分別用Lingo和Cplex求解該問題；最優(yōu)解x=(0,0,0)目標函數(shù)值 02.求對偶問題； min z=12*y1+y2 y1+y2=-1; y1+y2=-2; 2*y1-y2=-1; y1,y2=0; 3.解對偶問題，試驗影子價格； y=(0,0)4.對目標函數(shù)系數(shù)，約束右邊常量進行靈敏度分析。源代碼：Lingo代碼:model:sets:ii/1.3/:x,c;jj/1.

3、2/:b;link(jj,ii):a;endsetsdata:c=-1,-2,-1;b=12 1;a=1 1 2 1 1 -1;enddatamax=sum(ii(i):x(i)*c(i);for(jj(j):sum(ii(i):a(j,i)*x(i)=b(j);Cplex代碼: /* * OPL 5.5 Model * Author: zh * Creation Date: 2015/5/19 at 10:00 */range ii=1.3;range jj=1.2;float cii=-1,-2,-1;float bjj=12,1;float ajjii=1,1,2, 1,1,-1;dva

4、r float+ xii;maximizesum(i in ii)ci*xi;subject to forall(j in jj) sum(i in ii) aji*xi= - 1; X_2 y_2 + y_3 = - 2; X_3 2 * y_2 - y_3 = - 1; END主要輸出結(jié)果LingoX( 1) 0. 1. X( 2) 0. 2. X( 3) 0. 1.Cplex最終解決方案 目標 = 0:x = 0 0 0;對偶問題輸出結(jié)果 Variable Value Reduced Cost Y_2 0. 12.00000 Y_3 0. 1.靈敏度分析Ranges in which t

5、he basis is unchanged: Objective Coefficient Ranges: Current Allowable Allowable Variable Coefficient Increase Decrease X( 1) -1. 1. INFINITY X( 2) -2. 2. INFINITY X( 3) -1. 1. INFINITY Righthand Side Ranges: Current Allowable Allowable Row RHS Increase Decrease 2 12.00000 INFINITY 12.00000 3 1. INF

6、INITY 1.二. （共15分）最短路： 已知線路網(wǎng)路如圖,兩點之間聯(lián)系上數(shù)字表示兩點間的距離。1. 求A1到A7所有最短路。共兩條：1257 1457model:sets:node/1.7/;arcs(node,node):d,x,u;!d:distance,x:0,1,u:exist or not;endsetsdata:d=0 6 2 3 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 4 0 0 0 0 0 4 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1;u=0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0

7、 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1;enddatamin=sum(arcs:d*x);!省略（i,j）!condition1: 進口路徑和出口路徑是唯一的;sum(node(i):x(1,i)=1;sum(node(i):x(i,7)=1;!condition2:進出口相同;for(node(j)|j#ne#1#and#j#ne#7:sum(node(i):x(j,i)=sum(node(i):x(i,j);!condition3:不可用路徑不顯示;for(arcs(i,j):x(i,j)=u(i,j

8、);for(arcs(i,j):bin(x(i,j);end長度：92. 求A1到A6所有最短路。僅一條：146model:sets:node/1.7/;arcs(node,node):d,x,u;!d:distance,x:0,1,u:exist or not;endsetsdata:d=0 6 2 3 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 4 0 0 0 0 0 4 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1;u=0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1

9、0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1;enddatamin=sum(arcs:d*x);!省略（i,j）!condition1: 進口路徑和出口路徑是唯一的;sum(node(i):x(1,i)=1;sum(node(i):x(i,6)=1;!condition2:進出口相同;for(node(j)|j#ne#1#and#j#ne#6:sum(node(i):x(j,i)=sum(node(i):x(i,j);!condition3:不可用路徑不顯示;for(arcs(i,j):x(i,j)=d(1);for(time(i)|i#Gt#1:x(

10、i)+s(i-1)=d(i);s(1)=x(1)+10-d(1);for(time(i)|i#gt#1:s(i)=x(i)+s(i-1)-d(i);end主要輸出結(jié)果：X( 1) 40.00000 0. X( 2) 50.00000 0. X( 3) 75.00000 0. X( 4) 25.00000 0.四. （共10分）統(tǒng)計描述性分析：對data1描述性分析: 求均值,方差,標準差,變異系數(shù),偏度,峰度,常用分位數(shù),極差,四分位差,直方圖,箱式圖,經(jīng)驗分布圖,Q_Q圖源代碼： x=c( 0.28, 0.08,-0.97, 0.42, 1.22,-1.13, 0.37,-0.14, 0.2

11、,-0.51,-0.29, 0.10,-0.14, -0.10,-0.09,-0.32, 0.38,-0.55, 0.39, 0.18,-1.00, 0.90, 0.47,-1.48, 1.13, 1.20, -1.08,-0.54, 1.63, 0.46,-1.53, 1.09, 1.26,-1.04,-0.17, 0.91, 0.16,-1.11, 0.25, 0.89,-0.46,-0.44, 0.77, 0.14,-0.87,-0.34, 0.50, 0.37,-1.19, 0.74, 0.17,-0.48, -0.16, 0.32,-0.65,-0.03,-0.20, 0.21,-0

12、.35,-0.48, 0.30, 0.02,-0.88, 0.56,-0.21, 0.06, 0.54,-1.07, 0.36, 0.90,-0.83, 0.12, 1.19,-0.42,-0.50, 0.08, 0.19,-0.89, 0.57, 0.31,-0.66, 0.39, 0.06,-0.90, 0.09, 0.39,-0.44,-0.12, 0.12,-0.56, 0.55, 0.15,-0.97, 0.88, 0.77,-1.89, 1.32, 0.95,-1.04, 0.44,-0.17, 0.01, 0.46,-0.48, -0.10,-0.21, 0.41,-0.73,-

13、0.11, 0.43,-0.12,-1.00, 0.51, 0.79,-1.34, 0.55, 1.44, -1.17,-0.17, 0.52, 0.23,-1.06, 0.35, 0.75,-0.64,-0.46, 0.69,-0.37, 0.08, 0.79, -0.82, 0.00, 0.09,-0.65, 0.12, 0.40,-1.17, 0.51, 0.57,-1.08, 0.33, 0.87,-0.59, -0.29, 1.22,-0.38,-0.51, 0.48, 0.21,-1.16, 0.85)mean(x)#均值#var(x)#方差#sd（x）#標準差#100*sd(x)

14、/mean(x)#變異系數(shù)#all.moments(x,central=TRUE, order.max=4)all.moments( x, order.max=4 )all.moments( x, absolute=TRUE, order.max=4 )skewness(x)#偏度#kurtosis(x)#峰度#max(x)-min(x)#極差#quantile(x, probs = c(0.1, 0.5, 1, 2.5, 5,0.75, 10, 50, NA)/100,type=1)y=ecdf(x)#經(jīng)驗分布圖#plot(ecdf(x),verticals=TRUE,do.p=T) #do

15、.p是邏輯變量=FALSE表示不畫點處的記號#x=seq(-2,2,0.01)#lines(x,pnorm(x,mean(x),sd(x),col=red)hist(x)#直方圖#boxplot(x)#箱式圖#boxplot(x,horizontal=T);qqnorm(x,pch=+,ylab=,main=)#q-q圖#qqline(x, col = 2)主要輸出結(jié)果： mean(x)1 -0. var(x)1 0. x=c(1,2,3) all.moments(x,central=TRUE, order.max=4)1 1. 0. 0. 0. 0. all.moments( x, orde

16、r.max=4 )1 1. 2. 4. 12. 32. all.moments( x, central=TRUE, order.max=4 )1 1. 0. 0. 0. 0. all.moments( x, absolute=TRUE, order.max=4 )1 1. 2. 4. 12. 32. skewness(x)1 0 kurtosis(x)1 1.5 quantile(x, probs = c(0.1, 0.5, 1, 2, 5, 10, 50, NA)/100,type=1)0.1% 0.5% 1% 2% 5% 10% 50% 1 1 1 1 1 1 2 NA y=ecdf(x)

17、 plot(ecdf(x),verticals=TRUE,do.p=T) #do.p是邏輯變量=FALSE表示不畫點處的記號 #x=seq(-2,2,0.01) #lines(x,pnorm(x,mean(x),sd(x),col=red) #boxplot(x) #boxplot(x,horizontal=T); qqnorm(x,pch=+,ylab=,main=) qqline(x, col = 2)五. （共10分）回歸分析：對data6中經(jīng)漂吟霉素處理數(shù)據(jù)用指數(shù)增長模型非線性回歸1. 寫出回歸表達式，獲得回歸的檢驗結(jié)論；y1=192.095(1-exp(-11.385x)2. 比較M

18、ichaelis-Menten回歸，哪一個效果好，為什么？用R語言兩者求解系數(shù)顯著度差距不大，回歸效果差不多。見后面回歸檢驗結(jié)果。(用SPSS比較R2值, Michaelis-Menten R2=0.96126, 而指數(shù)模型, R2=0.90144, 因而前者回歸效果好)3. 畫出回歸效果圖像。源代碼x=c(0.02 , 0.06, 0.11, 0.22, 0.56, 1.10);#底物濃度#y1=c(76, 47, 97, 107, 123, 139, 159, 152, 191, 201, 207, 200);#反應速度處理#xx=c(0.02 , 0.02 , 0.06, 0.06, 0

19、.11, 0.11, 0.22, 0.22, 0.56, 0.56, 1.10, 1.10);x=xx;y=y1;plot(x,y,pch=8); z=nls(ySSmicmen(x,Vm,K);#Michaelis-Menten模型summary(z);z=nls(ybeta1*(1-exp(-beta2*x),start=list(beta1 = 195, beta2=0.4);#混合反應模型summary(z);points(x,fitted(z),pch=e,col=red);#在前面最后一個plot，作圖基礎上添加擬合值主要輸出結(jié)果回歸檢驗輸出：Michaelis-Menten模型代

20、碼：Formula: y SSmicmen(x, Vm, K)Parameters: Estimate Std. Error t value Pr(|t|) Vm 2.127e+02 6.947e+00 30.615 3.24e-11 *K 6.412e-02 8.281e-03 7.743 1.57e-05 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1Residual standard error: 10.93 on 10 degrees of freedomNumber of iterations to convergence: 0 Ac

21、hieved convergence tolerance: 1.93e-06指數(shù)模型代碼：Formula: y beta1 * (1 - exp(-beta2 * x)Parameters: Estimate Std. Error t value Pr(|t|) beta1 192.095 8.176 23.495 4.42e-10 *beta2 11.385 1.628 6.992 3.75e-05 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1Residual standard error: 17.44 on 10 degrees of f

22、reedomNumber of iterations to convergence: 19 Achieved convergence tolerance: 4.533e-06指數(shù)回歸效果圖六. （共15分）主成分分析：對data7 進行主成分分析，1. 要求獲得載荷矩陣，主成分得分矩陣，碎石圖；2. 各主成分命名。各企業(yè)總效應大小的綜合指標y1y1=0.32113x1+0.29516x2+0.38912x3+0.38472x4+0.37955x5+0.37087x6+0.31996x7+0.35546x8Spss主要輸出結(jié)果Communalities InitialExtractionVAR0

23、00011.000.812VAR000021.000.907VAR000031.000.984VAR000041.000.989VAR000051.000.988VAR000061.000.988VAR000071.000.709VAR000081.000.801Extraction Method: Principal Component Analysis.Total Variance ExplainedComponentInitial EigenvaluesExtraction Sums of Squared Loadings Total% of VarianceCumulative %To

24、tal% of VarianceCumulative %16.13776.70876.7086.13776.70876.70821.04213.02789.7341.04213.02789.7343.4365.44995.184 4.2202.75597.938 5.1521.89999.837 6.009.11099.948 7.003.03799.985 8.001.015100.000 Extraction Method: Principal Component Analysis.Component Matrix(a) Component 12VAR00001.796.424VAR000

25、02.731.610VAR00003.964-.235VAR00004.953-.285VAR00005.940-.323VAR00006.919-.379VAR00007.793.284VAR00008.881.160Extraction Method: Principal Component Analysis.a 2 components extracted.Component Score Coefficient Matrix Component 12VAR00001.130.407VAR00002.119.585VAR00003.157-.225VAR00004.155-.273VAR0

26、0005.153-.310VAR00006.150-.364VAR00007.129.272VAR00008.143.154Extraction Method: Principal Component Analysis.七. （共15分）時間序列分析：data2,3作時間序列分析(數(shù)據(jù)橫著讀)(要求用R語言)1. ARIMA模型的最佳參數(shù)data2 AR(3) data3 AR(2)2. 模型的檢驗3. 往后預測至少六期4. 畫圖源代碼: data2代碼：par(mfrow=c(1,1)#library(tseries)#無效命令x0=c(1000.7, 571.9, 573.6, 368.3

27、, 146.6, 114.8, 122.3,389.1, 571.2, 647.6, 754.3, 1030.2, 733.8, 541.4,436.2, 250.9, 136.9, 453.9, 838.1, 1273.1, 1209.6,979, 797.9, 417.3, 367.4, 84.1, 237.8, 1110,1852.4, 1511.1, 1017.6, 817.1, 461.5, 273.6, 122,289.2, 994.4, 1584.3, 1570.9, 1417.3, 1078.7, 799,720.5, 562.8, 492, 255.2, 192.2, 76.

28、7, 48.8,81.1, 173.7, 408, 540.4, 516.6, 569.6, 506.9,337.3, 120.6, 97.7, 30.4, 0, 17, 59.4,146.3, 167.2, 424.8, 549.7, 492.7, 360.7, 287.3,188.1, 79.1, 48, 21.5, 102.5, 198.8, 435.3,596.5, 769.8, 804.3, 851.8, 573.7, 330.3, 102.3,158.9, 682.3, 1457.4, 1659.3, 1237.8, 1029.8, 758.3,441.6, 290.3, 128.

29、1, 180, 480.7, 738, 1181.5,1491.8, 1150.4, 798.4, 774, 650.5, 468.3, 246.8,80.5, 51.6, 273.3, 657.7, 1126, 1148.3, 926,709.3, 528.2, 563.4, 365.7, 195.5, 87.1, 447.5,886.8, 1669.3, 1334.4, 1220, 795.5, 535.8, 204.9,135.8, 147.3, 40.5, 71.5, 387.2, 651, 715.8,764.4, 761.4, 625.9, 304.5, 156.6, 81, 75

30、.2,84.6, 427.5, 875.6, 1019.2, 936.1, 767.6, 501.4,314.9, 320.6, 145.3, 113.5, 32.9, 60.3, 292.6,503.4, 761.6, 646.3, 744.4, 582.5, 526.6, 223,68.4, 43.1, 17.3, 115.1, 568.4, 684.8, 1246.7,966.9, 763.3, 451.7, 313.6, 170.9, 69.3, 200.6,531.7, 766.7, 828.5, 933.5, 779.6, 428, 254.7,133.7, 67.9, 104.6

31、, 432.7, 956.8, 1372.8, 1314.6,1065, 813.4, 569.7, 367.2, 195.9, 115.1, 397.1,1110.1, 1798.1, 1634.4, 1621.4, 1007.1, 837.1, 376.9,166.2, 52.9, 455.4, 1700.5, 2278.2, 2215.1, 1905,1347.3, 646.8, 451.2, 334.7, 122.4, 180.7)x0z=ts(x0,frequency=1,start=c(1742),end=c(1957)#起始時間和結(jié)束時間#acf(z)pacf(z)x - ari

32、ma(z,order=c(3,0,0)tsdiag(x)#3個圖的出現(xiàn)#fore.mod-predict(object =x, n.ahead = 12, se.fit = TRUE) fore.modforevalue=c( 275.1532, 324.2066 ,456.2553, 562.3887, 644.3462 ,663.5609, 639.0554, 581.7076 ,521.1731, 474.8483 ,455.7449, 462.8644)x00=c(x0,forevalue)zt=ts(x00,frequency=1,start=c(1742),end=c(1969)#

33、產(chǎn)生新序列已設置后面plot格式pred.mod=z-x$residuals#計算擬和值par(mfrow=c(1,1)plot(zt,col=green,lwd=2,xlab=,ylab=)#實值與預測值lines(pred.mod,col=green,lwd=2)#擬和值lines(z,col=red,lwd=2)#實值data3代碼：par(mfrow=c(1,1)#library(tseries)#無效命令x0=c(580.38, 581.86, 580.97, 580.8, 579.79, 580.39, 580.42, 580.82, 581.4, 581.32, 581.44,

34、581.68, 581.17, 580.53, 580.01, 579.91, 579.14, 579.16, 579.55, 579.67, 578.44, 578.24, 579.1, 579.09, 579.35, 578.82, 579.32, 579.01, 579, 579.8, 579.83, 579.72, 579.89, 580.01, 579.37, 578.69, 578.19, 578.67, 579.55, 578.92, 578.09, 579.37, 580.13, 580.14, 579.51, 579.24, 578.66, 578.86, 578.05, 5

35、77.79, 576.75, 576.75, 577.82, 578.64, 580.58, 579.48, 577.38, 576.9, 576.94, 576.24, 576.84, 576.85, 576.9, 577.79, 578.18, 577.51, 577.23, 578.42, 579.61, 579.05, 579.26, 579.22, 579.38, 579.1, 577.95, 578.12, 579.75, 580.85, 580.41, 579.96, 579.61, 578.76, 578.18, 577.21, 577.13, 579.1, 578.25, 5

36、77.91, 576.89, 575.96, 576.8, 577.68, 578.38, 578.52, 579.74, 579.31, 579.89, 579.96)x0z=ts(x0,frequency=1,start=c(1875),end=c(1972)acf(z)pacf(z)x - arima(z,order=c(2,0,0)tsdiag(x)fore.modB；乙-D；丙-E；丁-A；C任務無人做； 最小耗時數(shù)為：z=29+20+32+24=105 源代碼：model:sets:i0/1.9/;links(i0,i0):x,a,c;endsetsdata:a=0 0 0 0 1

37、 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;c=0 0 0 0 25 29 31 42 37 0 0 0 0 39 38 26 20 33 0 0 0 0 34 27 28 40 32 0 0 0 0 24 42 36 23 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;enddatamin=sum(links: x*c);for(i0(i)|i#le#4:sum(i0(j)|j#ge#5:x(i,j)=1); for(i0(i)|i#Ge#5#and#i#ne#9:sum(i0(j)|j#le#4:x(j,i)=1);sum(i0(j)|j#le#4:x(j,9)=1;x(1,5)=0;for(links:bin(x);end主要輸出結(jié)果：X( 1, 1) 0. 0. X( 1, 2) 0. 0. X( 1, 3) 0. 0. X( 1, 4) 0. 0. X(