現(xiàn)代設(shè)計(jì)方法學(xué)試題：隨機(jī)方向法、復(fù)合形法

、用隨機(jī)方向法法求解下問題五變量Min 2*x(l)人2+5*x(2)人2+3*x(3)+x(4)+2*x(5)人2-10S.t. 2*x(1)A2+x(2)+3*x(3)A2+5*x(4)+x(5)A2-2<03*x(1)+x(2)A2-5;x(3)+2*x(4)+3*x(5)-10<0變量下限[-10,-10,-10,-10,-10]變量上限[10,10,10,10,10]二、用隨機(jī)方向法法求解下問題四變量Minx(1)*x(2)+4*x(3)A3+3*x(1)*x(3)+5*x(4)A2+5S.t.x(1)A2+x(2)*x(3)+2*x(4)-22*x(1)-3*x(2)+4*x(3)*x(4)變量下限[-10,-9,-8,-7]變量上限[10,9,8,7]三、用隨機(jī)方向法法求解下問題三變量Min-x(1)A2-2*x(2)A3-x(3)A3-x(1)*x(2)-x(1)*x(3)+9S.t.8*x(1)+14*x(2)+7*x(3)-56x(1)A2+x(2)A2+x(3)A2-25變量下限[-10,-10,-10]變量上限[10,10,10]四、用隨機(jī)方向法法求解下問題Minx(1)A3+x(1)*x(2)+3*x(2)A2+3S.t.x(1)A2-x(2)+1x(1)+x(2)-2變量下限[-9,-9]變量上限[9,9]五、用隨機(jī)方向法法求解下問題Minx(1)A2*x(2)+x(1)*x(2)+3*x(2)+4S.t.x(1)A2-x(2)+1x(1)+x(2)-2變量下限[-9,-9]變量上限[9,9]一、用復(fù)合形法求解下問題Min2*x(l)人2+5*x(2)人4+3*x(3)+x(4)人3-10S.t.8*x(1)+14*x(2)+7*x(3)-56x(1)A2+x(2)A2+x(4)A2-25精度0.1初始點(diǎn)[0,0,0,0]變量下限[-1,-2,-3,-4]變量上限[1,2,3,4]二、用復(fù)合形法求解下問題三變量Min-x(1)A2-2*x(2)A3-x(3)A3-x(1)*x(2)-x(1)*x(3)+9S.t.8*x(1)+14*x(2)+7*x(3)-56x(1)A2+x(2)A2+x(3)A2-25精度0.1初始點(diǎn)[0,1,2]變量下限[-10,-10,-10]變量上限[10,10,10]三、用復(fù)合形法求解下問題Min4*x(1)-x(2)A3-7S.t.-x(1)-x(2)x(1)A2+x(2)A2-4精度0.1初始點(diǎn)[1,1]變量下限[-1,-1]變量上限[2,7]四、用復(fù)合形法求解下問題Min4*x(1)-x(2)A2-12S.t.-x(1)-x(2)x(1)A2+x(2)A2-25精度0.01初始點(diǎn)[2,1]變量下限[-1,-1]變量上限[2,7]五、用復(fù)合形法求解下問題Minx(1)*x(2)+4*x(3)A4+3*x(1)*x(3)+5*x(4)A2-6S.t.x(1)+8*x(3)+14*x(2)+7*x(4)-56x(1)+x(3)A4+x(2)A2+x(4)A2-25精度：0.1初始點(diǎn)：[0,0,0,0]變量下限：[-1,-2,-3,-4]變量上限：[1,2,3,4]隨機(jī)方向法答案：用隨機(jī)方向法法求解下問題五變量Min 2*x(l)人2+5*x(2)人2+3*x(3)+x(4)+2*x(5)人2-10S.t. 2*x(1)A2+x(2)+3*x(3)A2+5*x(4)+x(5)A2-2<03*x(1)+x(2)A2-5;x(3)+2*x(4)+3*x(5)-10<0變量下限[-10,-10,-10,-10,-10]變量上限[10,10,10,10,10]初始點(diǎn)x0=0.6791641.48499-1.74391-9.704734.0553迭代前后兩點(diǎn)的值之差alpha1=6.89迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.391步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.0124-0.219-0.802-0.261-0.49迭代次數(shù)為：N=1迭代后的點(diǎn)為：xmin=0.68151.443-1.896-9.7543.962迭代后點(diǎn)的值為：fxmin=17.3迭代前后兩點(diǎn)的值之差alpha1=2.6迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.19步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=-0.3630.328-0.5280.553-0.42迭代次數(shù)為：N=2迭代后的點(diǎn)為：xmin=0.5471.565-2.092-9.5493.807迭代后點(diǎn)的值為：fxmin=16.0迭代前后兩點(diǎn)的值之差alpha1=1.3迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.371步長(zhǎng)大于預(yù)先給定的誤差繼續(xù)迭代直到迭代前后兩點(diǎn)的值之差alpha1=0.0迭代前后兩點(diǎn)的值之差小于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=9.1e-3步長(zhǎng)小于預(yù)先給定的誤差總迭代次數(shù)為：N=8最優(yōu)點(diǎn)為：x=-1.103721.06571-3.87849-9.49342.37234最優(yōu)點(diǎn)的值為：fmin=-11.7578用隨機(jī)方向法法求解下問題四變量Min x(l)*x(2)+4*x(3)人3+3*x(l)*x(3)+5*x(4)人2+5S.t. x(l)人2+x(2)*x(3)+2*x(4)-22*x(1)-3*x(2)+4*x(3)*x(4)變量下限[-10,-9,-8,-7]變量上限[10,9,8,7]初始點(diǎn)x0=1.55478-1.200626.14788-1.49728迭代前后兩點(diǎn)的值之差alpha1=83.4迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.35步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=-0.7880.3270.305-0.423迭代前后兩點(diǎn)的值之差23.4迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.175步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.3590.5920.57-0.442迭代次數(shù)為：N=1迭代后的點(diǎn)為：xmin=1.492-1.3046.048-1.42迭代后點(diǎn)的值為fxmin=925.2迭代前后兩點(diǎn)的值之差alpha1=47.3迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.175步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=-0.394-0.7010.158-0.573迭代次數(shù)為：N=2迭代后的點(diǎn)為：xmin=1.582-1.1456.012-1.29迭代后點(diǎn)的值為：fxmin=909.3迭代前后兩點(diǎn)的值之差alpha1=15.9迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.228步長(zhǎng)大于預(yù)先給定的誤差繼續(xù)迭代直至迭代前后兩點(diǎn)的值之差alpha1=0.0迭代前后兩點(diǎn)的值之差小于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=7.4e-3步長(zhǎng)小于預(yù)先給定的誤差總迭代次數(shù)為：N=7最優(yōu)點(diǎn)為：2.35184-1.260324.52049-0.233025最優(yōu)點(diǎn)的值為fmin=403.703用隨機(jī)方向法法求解下問題三變量Min -x(l)人2-2*x(2)人3-x(3)人3-x(l)*x(2)-x(l)*x(3)+9S.t.8*x(1)+14*x(2)+7*x(3)-56x(1)A2+x(2)A2+x(3)A2-25變量下限[-10,-10,-10]變量上限[10,10,10]初始點(diǎn)x0=1.74038-1.72227-3.81727迭代前后兩點(diǎn)的值之差alpha1=10.5迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)0.303步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=-0.3890.4270.816迭代次數(shù)為：N=1迭代后的點(diǎn)為：xmin=1.672-1.648-3.674迭代后點(diǎn)的值為：fxmin=73.66迭代前后兩點(diǎn)的值之差alpha1=7.79迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)0.175步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.595-0.004280.804迭代次數(shù)為：N=2迭代后的點(diǎn)為：xmin=1.808-1.649-3.492迭代后點(diǎn)的值為：fxmin=66.55迭代前后兩點(diǎn)的值之差alpha1=7.11迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.228步長(zhǎng)大于預(yù)先給定的誤差繼續(xù)迭代至到迭代前后兩點(diǎn)的值之差alpha1=0.0迭代前后兩點(diǎn)的值之差小于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=9.5e-3步長(zhǎng)小于預(yù)先給定的誤差總迭代次數(shù)為：N=12最優(yōu)點(diǎn)為：x=2.210041.667913.84523最優(yōu)點(diǎn)的值為：fmin=用隨機(jī)方向法法求解下問題二變量Min x(l)人3+x(l)*x(2)+3*x(2)人2+3S.t. x(1)A2-x(2)+1x(l)+x(2)-2精度0.001變量下限[-9,-9]變量上限[9,9]初始點(diǎn)x0=0.1412791.54096迭代前后兩點(diǎn)的值之差alpha1=0.193649迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.024745步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.533261-0.845951迭代次數(shù)為迭代后的點(diǎn)為：xmin=0.1506111.52616迭代后點(diǎn)的值為：fxmin=10.2208迭代前后兩點(diǎn)的值之差alpha1=0.123471迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.0175步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.9945250.104495迭代前后兩點(diǎn)的值之差alpha1=0.05851迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差步長(zhǎng)alpha2=0.02275步長(zhǎng)大于預(yù)先給定的誤差迭代前后兩點(diǎn)的值之差alpha1=0.0迭代前后兩點(diǎn)的值之差小于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=7.3e-4一直迭代直到步長(zhǎng)小于預(yù)先給定的誤差總迭代次數(shù)為：N=11最優(yōu)點(diǎn)為：x=-0.4329691.03513最優(yōu)點(diǎn)的值為：fmin=5.68515用隨機(jī)方向法法求解下問題Minx(l)人2*x(2)+x(l)*x(2)+3*x(2)+4S.t. x(1)A2-x(2)+1x(l)+x(2)-2精度0.1變量下限[-9,-9]變量上限[9,9]初始點(diǎn)x0=-0.9794482.63363迭代前后兩點(diǎn)的值之差alpha1=11.2836迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=2.47487步長(zhǎng)大于預(yù)先給定的誤差單位化后的隨機(jī)方向：dir=0.6350250.772491迭代前后兩點(diǎn)的值之差alpha1=4.70335迭代前后兩點(diǎn)的值之差大于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=1.75步長(zhǎng)大于預(yù)先給定的誤差一直迭代直到迭代前后兩點(diǎn)的值之差alpha1=0.0迭代前后兩點(diǎn)的值之差小于預(yù)先給出的誤差rHLZ步長(zhǎng)alpha2=0.084步長(zhǎng)小于預(yù)先給定的誤差總迭代次數(shù)為：N=2最優(yōu)點(diǎn)為：x=1.05662-0.635285最優(yōu)點(diǎn)的值為：fmin=0.71復(fù)合形法答案第一題初始復(fù)合形X=[0,0.0645661,-0.214631,0.942999,0.373276][0,-0.882432,-1.90058,-1.77227,0.877731][0,2.67738,1.02862,-0.298057,0.900245][0,3.25155,2.69737,0.659762,1.81532]滿足約束的初始復(fù)合形X=[0,0.0645661,-0.214631,0.942999,0.373276][0,-0.882432,-1.90058,-1.77227,0.877731][0,2.67738,1.02862,-0.298057,0.900245][0,3.25155,2.69737,0.659762,1.81532]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0,0.373276,0.0645661,0.942999,-0.214631][0,0.877731,-0.882432,-1.77227,-1.90058][0,0.900245,2.67738,-0.298057,1.02862][0,1.81532,3.25155,0.659762,2.69737]各頂點(diǎn)與中心點(diǎn)的均方根SumF=43.37繼續(xù)迭代去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.34521,-0.444242,0.819892,1.43166]迭代次數(shù)：反射后點(diǎn)矩陣：X=[0,0.373276,0.0645661,0.942999,1.073][0,0.877731,-0.882432,-1.77227,1.449][0,0.900245,2.67738,-0.298057,0.548545][0,1.81532,3.25155,0.659762,-0.213765]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0,0.373276,1.073,0.0645661,0.942999][0,0.877731,1.449,-0.882432,-1.77227][0,0.900245,0.548545,2.67738,-0.298057][0,1.81532,-0.213765,3.25155,0.659762]各頂點(diǎn)與中心點(diǎn)的均方根SumF=28.44繼續(xù)迭代去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.377711,0.361074,1.03154,1.21327]迭代次數(shù)：N=2壓縮后點(diǎn)矩陣：X=[0,0.186638,0.536502,0.0322831,0.4715][0,0.438866,0.724498,-0.441216,-0.886134][0,0.450122,0.274272,1.33869,-0.149029][0,0.907658,-0.106883,1.62577,0.329881]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0,0.186638,0.536502,0.4715,0.0322831][0,0.438866,0.724498,-0.886134,-0.441216][0,0.450122,0.274272,-0.149029,1.33869][0,0.907658,-0.106883,0.329881,1.62577]各頂點(diǎn)與中心點(diǎn)的均方根SumF=3.384繼續(xù)迭代直到各頂點(diǎn)與中心點(diǎn)的均方根SumF=9.8e-3各頂點(diǎn)與中心點(diǎn)的均方根小于精度，停止迭代總迭代次數(shù)為：N=60最優(yōu)點(diǎn)為：x=0.89830.1781-5.119-4.915最優(yōu)點(diǎn)的值為：fmin=-142.5第二題初始復(fù)合形X=[0,-3.05477,-6.03661,3.88808][1.0,-8.15705,3.4454,-4.86431][2.0,-7.04301,-1.36978,-9.80483]滿足約束的初始復(fù)合形X=[0,-1.52739,-3.0183,1.94404][1.0,-3.57852,2.2227,-1.93215][2.0,-2.52151,0.315112,-3.90241]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[-3.0183,0,1.94404,-1.52739][2.2227,1.0,-1.93215,-3.57852][0.315112,2.0,-3.90241,-2.52151]各頂點(diǎn)與中心點(diǎn)的均方根SumF=70.32不滿足約束條件繼續(xù)迭代去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[-0.358088,0.430183,-0.529101]迭代次數(shù)：1反射后點(diǎn)矩陣：X=[-3.0183,0,1.94404,0.386755][2.2227,1.0,-1.93215,2.98373][0.315112,2.0,-3.90241,0.740061]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.386755,-3.0183,0,1.94404][2.98373,2.2227,1.0,-1.93215][0.740061,0.315112,2.0,-3.90241]各頂點(diǎn)與中心點(diǎn)的均方根SumF=50.78去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[-0.877183,2.06881,1.01839]迭代次數(shù)：N=2反射后點(diǎn)矩陣：X=[0.386755,-3.0183,0,-1.75777][2.98373,2.2227,1.0,3.31763][0.740061,0.315112,2.0,2.55432]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[-1.75777,0.386755,-3.0183,0][3.31763,2.98373,2.2227,1.0][2.55432,0.740061,0.315112,2.0]各頂點(diǎn)與中心點(diǎn)的均方根SumF=38.29不滿足約束條件繼續(xù)迭代去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[-1.46311,2.84135,1.20316]迭代次數(shù)：N=3反射后點(diǎn)矩陣：X=[-1.75777,0.386755,-3.0183,-2.3951][3.31763,2.98373,2.2227,4.0143][2.55432,0.740061,0.315112,0.695581]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[-2.3951,-1.75777,0.386755,-3.0183][4.0143,3.31763,2.98373,2.2227][0.695581,2.55432,0.740061,0.315112]各頂點(diǎn)與中心點(diǎn)的均方根SumF=46.06不滿足約束條件繼續(xù)迭代直到各頂點(diǎn)與中心點(diǎn)的均方根SumF=8.7e-3各頂點(diǎn)與中心點(diǎn)的均方根小于精度，停止迭代總迭代次數(shù)為：N=54最優(yōu)點(diǎn)為：x=-1.2994.79-0.6106最優(yōu)點(diǎn)的值為：fmin=-206.783第三題初始復(fù)合形X=[1.0,0.172003,-0.544159][1.0,1.18573,2.17687]滿足約束的初始復(fù)合形[1.0,0.172003,0.0209213][1.0,1.18573,1.63487]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.0209213,0.172003,1.0][1.63487,1.18573,1.0]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.096462,1.4103]迭代次數(shù)：N=1反射后點(diǎn)矩陣：X=[0.0209213,0.172003,0.0287486][1.63487,1.18573,1.44105]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.0209213,0.0287486,0.172003][1.63487,1.44105,1.18573]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.0248349,1.53796]迭代次數(shù)：N=2反射后點(diǎn)矩陣：X=[0.0209213,0.0287486,0.00232658][1.63487,1.44105,1.59183]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.0209213,0.00232658,0.0287486][1.63487,1.59183,1.44105]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.011624,1.61335]繼續(xù)迭代直至各頂點(diǎn)與中心點(diǎn)的均方根SumF=0.092各頂點(diǎn)與中心點(diǎn)的均方根小于精度，停止迭代總迭代次數(shù)為：N=7最優(yōu)點(diǎn)為：0.018551.995最優(yōu)點(diǎn)的值為：fmin=-14.8713第四題X=[2.0,0.124167,0.305122][1.0,0.0489177,-0.267895]滿足約束的初始復(fù)合形X=[2.0,0.124167,0.683603][1.0,0.0489177,0.128282]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.124167,0.683603,2.0][0.0489177,0.128282,1.0]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.403885,0.0885999]迭代次數(shù)：N=1反射后點(diǎn)矩陣：[0.124167,0.683603,0.284268][0.0489177,0.128282,0.0202973]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.124167,0.284268,0.683603][0.0489177,0.0202973,0.128282]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.204218,0.0346075]迭代次數(shù)：N=2反射后點(diǎn)矩陣：X=[0.124167,0.284268,0.0545875][0.0489177,0.0202973,0.00536885]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0.0545875,0.124167,0.284268][0.00536885,0.0489177,0.0202973]去掉壞點(diǎn)的復(fù)合形中心點(diǎn)px=[0.0893774,0.0271433]繼續(xù)迭代直至各頂點(diǎn)與中心點(diǎn)的均方根

SumF=4.6e-3各頂點(diǎn)與中心點(diǎn)的均方根小于精度，停止迭代總迭代次數(shù)為：N=6最優(yōu)點(diǎn)為：x=0.00012230.03064最優(yōu)點(diǎn)的值為：fmin=-12.0004第五題初始復(fù)合形X=[0,0.229254,-0.529266,-0.00742223,0.94215][0,-1.95608,-0.207921,[0,0.439562,0.416149,[0,-1.95608,-0.207921,[0,0.439562,0.416149,[0,2.31784,-3.50879,滿足約束的初始復(fù)合形0.569261,1.38549]-1.67241,0.036]2.69645,-1.769][0,0.229254,-0.529266,-0.00742223,0.94215][0,-1.95608,-0.207921,[0,0.439562,0.416149,[0,-1.95608,-0.207921,[0,0.439562,0.416149,0.569261,1.38549]-1.67241,0.036][0,2.31784,-3.50879,2.69645,-1.769][0,2.31784,-3.50879,2.69645,-1.769]按照函數(shù)值從小到大排序的復(fù)合形Xsorted=[0,0.94215,0.229254,-0.529266,-0.00742223][0,1.38549,-1.95