上海海事大学-2015优化与统计建模试验模拟考查题(答案)

1、精选优质文档-倾情为你奉上精选优质文档-倾情为你奉上专心-专注-专业专心-专注-专业精选优质文档-倾情为你奉上专心-专注-专业上海海事大学 2014 - 2015 学年第 二 学期研究生 优化与统计建模试验 课程考查模拟题专业： 学生姓名： 学号： 要求：1.本考查为无纸化形式,要求每位研究生独立完成,禁止和他人交流。2.请将本文件更名(原文件名学号姓名)。3.必须在本文件内作答并紧随相应试题后面，评阅老师只评阅本文件。4.所有问题仅限于采用本课程所学软件: Lingo,Cplex,Spss,R进行求解. 其他方式求解将不被认可。5.作答主要内容：Lingo,Cplex,R要求源代码及关键的输

2、出结果；Spss要求关键的输出结果,一些重要的操作设置最好能加以说明。一. （共10分）线性规划：已知线性规划 Max z=x12x2x3 x1+x2 +2x3 12 x1+x2 x3 1 x1,x2 ,x30. 1.分别用Lingo和Cplex求解该问题；最优解x=(0,0,0)目标函数值 02.求对偶问题； min z=12*y1+y2 y1+y2=-1; y1+y2=-2; 2*y1-y2=-1; y1,y2=0; 3.解对偶问题，试验影子价格； y=(0,0)4.对目标函数系数，约束右边常量进行灵敏度分析。源代码：Lingo代码: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代码: /* * 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主要输出结果LingoX( 1) 0. 1. X( 2) 0. 2. X( 3) 0. 1.Cplex最终解决方案 目标 = 0:x = 0 0 0;对偶问题输出结果 Variable Value Reduced Cost Y_2 0. 12.00000 Y_3 0. 1.灵敏度分析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： 已知线路网路如图,两点之间联系上数字表示两点间的距离。1. 求A1到A7所有最短路。共两条：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: 进口路径和出口路径是唯一的;sum(node(i):x(1,i)=1;sum(node(i):x(i,7)=1;!condition2:进出口相同;for(node(j)|j#ne#1#and#j#ne#7:sum(node(i):x(j,i)=sum(node(i):x(i,j);!condition3:不可用路径不显示;for(arcs(i,j):x(i,j)=u(i,j

8、);for(arcs(i,j):bin(x(i,j);end长度：92. 求A1到A6所有最短路。仅一条：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: 进口路径和出口路径是唯一的;sum(node(i):x(1,i)=1;sum(node(i):x(i,6)=1;!condition2:进出口相同;for(node(j)|j#ne#1#and#j#ne#6:sum(node(i):x(j,i)=sum(node(i):x(i,j);!condition3:不可用路径不显示;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主要输出结果：X( 1) 40.00000 0. X( 2) 50.00000 0. X( 3) 75.00000 0. X( 4) 25.00000 0.四. （共10分）统计描述性分析：对data1描述性分析: 求均值,方差,标准差,变异系数,偏度,峰度,常用分位数,极差,四分位差,直方图,箱式图,经验分布图,Q_Q图源代码： 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）#标准差#100*sd(x)

14、/mean(x)#变异系数#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)#极差#quantile(x, probs = c(0.1, 0.5, 1, 2.5, 5,0.75, 10, 50, NA)/100,type=1)y=ecdf(x)#经验分布图#plot(ecdf(x),verticals=TRUE,do.p=T) #do

15、.p是逻辑变量=FALSE表示不画点处的记号#x=seq(-2,2,0.01)#lines(x,pnorm(x,mean(x),sd(x),col=red)hist(x)#直方图#boxplot(x)#箱式图#boxplot(x,horizontal=T);qqnorm(x,pch=+,ylab=,main=)#q-q图#qqline(x, col = 2)主要输出结果： 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是逻辑变量=FALSE表示不画点处的记号 #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）回归分析：对data6中经漂吟霉素处理数据用指数增长模型非线性回归1. 写出回归表达式，获得回归的检验结论；y1=192.095(1-exp(-11.385x)2. 比较M

18、ichaelis-Menten回归，哪一个效果好，为什么？用R语言两者求解系数显著度差距不大，回归效果差不多。见后面回归检验结果。(用SPSS比较R2值, Michaelis-Menten R2=0.96126, 而指数模型, R2=0.90144, 因而前者回归效果好)3. 画出回归效果图像。源代码x=c(0.02 , 0.06, 0.11, 0.22, 0.56, 1.10);#底物浓度#y1=c(76, 47, 97, 107, 123, 139, 159, 152, 191, 201, 207, 200);#反应速度处理#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);#混合反应模型summary(z);points(x,fitted(z),pch=e,col=red);#在前面最后一个plot，作图基础上添加拟合值主要输出结果回归检验输出：Michaelis-Menten模型代

20、码：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指数模型代码：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指数回归效果图六. （共15分）主成分分析：对data7 进行主成分分析，1. 要求获得载荷矩阵，主成分得分矩阵，碎石图；2. 各主成分命名。各企业总效应大小的综合指标y1y1=0.32113x1+0.29516x2+0.38912x3+0.38472x4+0.37955x5+0.37087x6+0.31996x7+0.35546x8Spss主要输出结果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）时间序列分析：data2,3作时间序列分析(数据横着读)(要求用R语言)1. ARIMA模型的最佳参数data2 AR(3) data3 AR(2)2. 模型的检验3. 往后预测至少六期4. 画图源代码: data2代码：par(mfrow=c(1,1)#library(tseries)#无效命令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)#起始时间和结束时间#acf(z)pacf(z)x - ari

32、ma(z,order=c(3,0,0)tsdiag(x)#3个图的出现#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、产生新序列已设置后面plot格式pred.mod=z-x$residuals#计算拟和值par(mfrow=c(1,1)plot(zt,col=green,lwd=2,xlab=,ylab=)#实值与预测值lines(pred.mod,col=green,lwd=2)#拟和值lines(z,col=red,lwd=2)#实值data3代码：par(mfrow=c(1,1)#library(tseries)#无效命令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任务无人做； 最小耗时数为：z=29+20+32+24=105 源代码：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主要输出结果：X( 1, 1) 0. 0. X( 1, 2) 0. 0. X( 1, 3) 0. 0. X( 1, 4) 0. 0. X(