进化算法程序.doc

进化算法作业 1 全局优化问题（1） ， 此问题的全局最优值。一程序(1)主函数： main.mclear all;clc;popsize=60; %种群规模chromlength=34; %二进制编码，编码精度为0.0001，所以串长l为17pc=0.7; %杂交概率pm=0.1; %变异概率t=0; %进化代数初始为0pop=initpop(popsize,chromlength); %随机产生初始种群while ty(t) newpop3(1,:)=bestindividual; %保留最佳个体 end pop=newpop3; %产生新种群endy; %每代的最佳目标函数值x1; %每代的最佳目标函数值对应的自变量x2;gy,k=min(y) %gy为全局最优值，k为最优值对应的进化代数gx1=x1(k) %全局最优值对应的自变量gx2=x2(k)plot(y) %最优值收敛曲线title(收敛性曲线);xlabel(进化代数);ylabel(函数值);axis(0,500,-1.5,1.5);(2)初始种群：initpop.mfunction pop=initpop(popsize,chromlength)pop=round(rand(popsize,chromlength); %rand随机产生0,1区间的一个小数，rand四舍五入取整end(3)计算目标函数值:：calobjvalue.mfunction objvalue =calobjvalue( pop )temp1=decodechrom(pop,1,14);temp2=decodechrom(pop,15,14);x1=-5+(10*temp1)/(pow2(14)-1); %将二值域中的数转化为变量域中的数x2=-5+(10*temp2)/(pow2(14)-1);objvalue=4*x1.2-2.1*x1.4+1/3*x1.6+x1.*x2-4*x2.2+4*x2.4; %计算目标函数enda二进制转换为十进制：decodechrom.m function temp=decodechrom(pop,spoint,length )pop1=pop(:,spoint:spoint+length-1); %按变量个数分组转换，spoint为起始点，length为一个变量的长度temp=decodebinary(pop1);endb求二进制串对应的十进制数：decodebinary.mfunction temp =decodebinary( pop)px,py=size(pop); %求pop行数和列数for i=1:py pop1(:,i)=2.(py-i).*pop(:,i);endtemp=sum(pop1,2); %每一行求和end(4)计算个体适应度：calfitvalue.mfunction fitvalue= calfitvalue( objvalue ) fitvalue=1./(1+exp(objvalue);end(5)种群中最大适应度个体及其值：best.mfunction bestindividual,bestfit = best(pop,fitvalue )px,py=size(pop);bestindividual=pop(1,:);bestfit=fitvalue(1);for i=2:px; if fitvaluebestfit bestindividual=pop(i,:); best=fitvalue(i); endendend(6)选择算子：selection.mfunction newpop1=selection(pop,fitvalue)totalfit=sum(fitvalue); %适应度和ps=fitvalue./totalfit; %单个个体被选择的概率pss=cumsum(ps); %前几项累积和px,py=size(pop);ms=sort(rand(px,1); %随机产生px个0,1之间的数，并按升序排列fitin=1;newin=1;while newin=px if(ms(newin)pss(fitin) newpop1(newin,:)=pop(fitin,:); newin=newin+1; else fitin=fitin+1; endendend(7)交叉算子：crossover.mfunction newpop2 = crossover( pop,pc )px,py=size(pop);newpop2=ones(size(pop);for i=1:2:px-1 if randpc cpoint=round(rand*py); %随机产生一个交叉位 newpop2(i,:)=pop(i,1:cpoint),pop(i+1,cpoint+1:py); %交换相邻两个个体交叉位之后的基因 newpop2(i+1,:)=pop(i+1,1:cpoint),pop(i,cpoint+1:py); else nwepop2(i,:)=pop(i,:); newpop2(i+1,:)=pop(i+1,:); endendend(8)变异算子：mutation.mfunction newpop3 = mutation( pop,pm )px,py=size(pop);newpop3=pop;for i=1:px if(randpm) mpoint=round(rand*py); %随机产生一个变异位 if mpoint=0 mpoint=1; end if (newpop3(i,mpoint)=0) %变为等为基因 newpop3(i,mpoint)=1; else newpop3(i,mpoint)=0; end endend end二独立运行程序30次的结果x10.1590-0.0900-0.0888-0.0894-0.08090.07720.08760.1175-0.1578-0.0778x2-0.70160.71260.71020.64210.7120-0.6247-0.7023-0.71380.70290.7090y-1.0115-1.0316-1.0316-0.9751-1.0313-0.9763-1.0308-1.0287-1.0125-1.0310x10.0900-0.0015-0.1566-0.0888-0.0882-0.00890.10040.0766-0.0900-0.0876x2-0.7126-0.70650.71690.71260.7029-0.6931-0.7029-0.71320.71510.7102y-1.0316-0.9989-0.10147-1.0316-1.0309-0.9922-1.0303-1.0309-1.0316-1.0316x1-0.9190.07780.09060.09060.09310.09060.0906-0.0925-0.0705-0.0919x20.7126-0.7114-0.7138-0.7126-0.7816-0.7132-0.70960.71630.69860.7126y-1.0316-1.0331-1.0316-1.0316-0.9891-1.0316-1.0315-1.0315-1.0288-1.0316最好目标函数值：-1.0316 最差目标函数值：-0.9751平均目标函数值：-0.9914 标准方差：0.0286三最好的一次结果最好解：x1=0.0919 x2=-0.7126 最好值：-1.0316运行结果及收敛性曲线如下图： 运行结果 收敛性曲线（2） ， 此问题的全局最优值。一程序(1)主函数： main.mclear all;clcpopsize=40; %种群规模chromlength=28; %二进制编码，编码精度为0.001，所以串长l为14pc=0.8; %杂交概率pm=0.2; %变异概率 t=0;pop=initpop(popsize,chromlength); %随机产生初始种群while ty(t) newpop3(1,:)=bestindividual; %保留最佳个体 end pop=newpop3; %产生新种群endy; %每代的最佳目标函数值x1; %每代的最佳目标函数值对应的自变量x2;gy,k=min(y); %全局最优值gy=vpa(gy,3) %设置输出精度gx1=x1(k); %全局最优值对应的自变量x1=vpa(gx1,4)gx2=x2(k);x2=vpa(gx2,4)plot(y) %最优值收敛曲线title(收敛性曲线);xlabel(进化代数);ylabel(函数值);axis(0,500,0.2,1.5);(2)初始种群：initpop.mfunction pop=initpop(popsize,chromlength)pop=round(rand(popsize,chromlength); %rand随机产生0,1区间的一个小数，rand四舍五入取整end(3)计算目标函数值:：calobjvalue.mfunction objvalue =calobjvalue( pop )temp1=decodechrom(pop,1,14);temp2=decodechrom(pop,15,14);x1=-5+(10*temp1)/(pow2(14)-1); %将二值域中的数转化为变量域中的数x2=-5+(10*temp2)/(pow2(14)-1);objvalue=(x2-5.1/(4*pi*pi).*x1.2+5/pi.*x1-6).2+10.*(1-1/(8*pi).*cos(x1)+10; enda二进制转换为十进制：decodechrom.m function temp=decodechrom(pop,spoint,length )pop1=pop(:,spoint:spoint+length-1); %按变量个数分组转换，spoint为起始点，length为一个变量的长度temp=decodebinary(pop1);endb求二进制串对应的十进制数：decodebinary.mfunction temp =decodebinary( pop)px,py=size(pop); %求pop行数和列数for i=1:py pop1(:,i)=2.(py-i).*pop(:,i);endtemp=sum(pop1,2); %每一行求和end(4)计算个体适应度：calfitvalue.mfunction fitvalue= calfitvalue( objvalue ) fitvalue=1./(1+exp(objvalue);end(5)种群中最大适应度个体及其值：best.mfunction bestindividual,bestfit = best(pop,fitvalue )px,py=size(pop);bestindividual=pop(1,:);bestfit=fitvalue(1);for i=2:px; if fitvaluebestfit bestindividual=pop(i,:); best=fitvalue(i); endendend(6)选择算子：selection.mfunction newpop1=selection(pop,fitvalue)totalfit=sum(fitvalue); %适应度和ps=fitvalue./totalfit; %单个个体被选择的概率pss=cumsum(ps); %前几项累积和px,py=size(pop);ms=sort(rand(px,1); %随机产生px个0,1之间的数，并按升序排列fitin=1;newin=1;while newin=px if(ms(newin)pss(fitin) newpop1(newin,:)=pop(fitin,:); newin=newin+1; else fitin=fitin+1; endendend(7)交叉算子：crossover.mfunction newpop2 = crossover( pop,pc )px,py=size(pop);newpop2=ones(size(pop);for i=1:2:px-1 if randpc cpoint=round(rand*py); %随机产生一个交叉位 newpop2(i,:)=pop(i,1:cpoint),pop(i+1,cpoint+1:py); %交换相邻两个个体交叉位之后的基因 newpop2(i+1,:)=pop(i+1,1:cpoint),pop(i,cpoint+1:py); else nwepop2(i,:)=pop(i,:); newpop2(i+1,:)=pop(i+1,:); endendend(8)变异算子：mutation.mfunction newpop3 = mutation( pop,pm )px,py=size(pop);newpop3=pop;for i=1:px if(randpm) mpoint=round(rand*py); %随机产生一个变异位 if mpoint=0 mpoint=1; end if (newpop3(i,mpoint)=0) %变为等为基因 newpop3(i,mpoint)=1; else newpop3(i,mpoint)=0; end endend end二独立运行程序30次的结果x13.1253.1453.1283.1453.1413.1243.1253.1453.1453.125x22.2852.2652.5002.2652.2762.2902.3052.2652.2732.287y0.3990.3980.4450.3980.3980.3990.4000.3980.3980.399x13.1253.1253.1453.1403.1083.1463.1113.1653.1453.145x22.2652.2872.2652.2652.5002.2762.5002.1872.2702.265y0.4000.3990.3980.3980.4430.3980.4430.4050.3980.398x13.1223.1253.1253.1423.1343.1253.1253.1433.1413.125x22.2842.2862.2852.2742.2862.3442.2852.2752.2762.288y0.4000.3990.3990.3980.3980.4020.3990.3980.3980.399最好目标函数值：0.398 最差目标函数值：0.445平均目标函数值：0.403 标准方差：1.886e-004三最好的一次结果最好解：x1=3.145 x2=2.265最好值：0.398运行结果及收敛性曲线如下图： 运行结果 收敛性曲线（3） ，此问题的全局最优值。本题采用十进制编码方式，与二进制编码方式相比较，效率不如二进制，但程序相比简单一些。多次运行，自变量去平均值可得到最好结果。一程序(1)主函数： main.mclear all;clcpopsize=40; %种群规模chromlength=10; %变量个数，十进制编码pc=0.8; %杂交概率pm=0.1; %变异概率t=0; %进化代数 pop=initpop(popsize,chromlength); %初始种群while ty(t) newpop3(1,:)=bestindividual; %保留最佳个体 end pop=newpop3; %产生新种群endy; %每代的最佳目标函数值x; %每代的最佳目标函数值对应的自变量gy,k=min(y) %gy为全局最优值，k为最优值对应的进化代数x=x(k,:) %全局最优值对应的自变量plot(y) %最优值收敛曲线 title(收敛性曲线);xlabel(进化代数);ylabel(函数值);axis(0,5000,0,1);(2)初始种群：initpop.mfunction pop=initpop(popsize,chromlength)pop=-100+200.*rand(popsize,chromlength); %随机产生-100,100之间的数end(3)计算目标函数值:：calobjvalue.mfunction objvalue =calobjvalue( pop )px,py=size(pop);for i=1:py x(:,i)=pop(:,i);endobjvalue=sum(x.*x,2);end (4)计算个体适应度：calfitvalue.mfunction fitvalue= calfitvalue( objvalue )fitvalue=1./objvalue;end (5)种群中最大适应度个体及其值：best.mfunction bestindividual,bestfit = best(pop,fitvalue )px,py=size(pop);bestindividual=pop(1,:);bestfit=fitvalue(1);for i=2:px; if fitvaluebestfit bestindividual=pop(i,:); best=fitvalue(i); endendend(6)选择算子：selection.mfunction newpop1=selection(pop,fitvalue)totalfit=sum(fitvalue); %适应度和if(fitvalue=0)newpop1=pop;elseps=fitvalue./totalfit; %单个个体被选择的概率pss=cumsum(ps); %前几项累积和px,py=size(pop);ms=sort(rand(px,1); %随机产生px个0,1之间的数，并按升序排列fitin=1;newin=1;while newin=px if(ms(newin)pss(fitin) newpop1(newin,:)=pop(fitin,:); newin=newin+1; else fitin=fitin+1; endendend end (7)交叉算子：crossover.mfunction newpop2 = crossover( pop,pc )px,py=size(pop);newpop2=ones(size(pop);for i=1:2:px-1 for j=1:py if randpc a=rand(); newpop2(i,j)=a*pop(i,j)+(1-a)*pop(i+1,j); %算数交叉 newpop2(i+1,j)=a*pop(i+1,j)+(1-a)*pop(i,j); else newpop2(i,j)=pop(i,j); newpop2(i+1,j)=pop(i+1,j); end endendend(8)变异算子：mutation.mfunction newpop3 = mutation( pop,pm )px,py=size(pop);newpop3=pop;for i=1:px %每一个点以概率pm变为等为基因 for j=1:py if(randpm) r=-100+200*rand; while(r=pop(i,j) r=-100+200*rand; end newpop3(i,j)=r; else newpop3(i,j)=pop(i,j); endend end二独立运行程序30次的结果y0.00420.00740.00800.00790.00680.00630.00200.00750.00990.0120x10.0460-0.02490.0108-0.0224-0.00670.02150.00340.00350.01190.0266x2-0.02640.02500.0188-0.04310.02220.0071-0.0184-0.02620.03020.0388x30.00780.00800.0316-0.00300.0058-0.0311-0.0080-0.0134-0.0382-0.0416x4-0.0184-0.0097-0.0386-0.0285-0.0167-0.02960.01560.03570.01050.0216x5-0.0160-0.0454-0.03320.00060.0169-0.0556-0.0127-0.00300.0545-0.0067x6-0.0024-0.04910.0108-0.0498-0.0467-0.00140.0000-0.03030.02760.0243x7-0.0131-0.0180-0.0048-0.0332-0.03280.0144-0.02340.0512-0.0366-0.0260x8-0.0051-0.01350.0227-0.01100.0069-0.00570.0131-0.00670.0440-0.0310x9-0.01930.0275-0.03690.03040.04390.02200.0079-0.0392-0.0153-0.0710x10-0.01120.01510.0405-0.0111-0.0204-0.01030.02080.02530.0053-0.0162y0.00940.01110.01090.00480.00660.00480.00710.00550.01120.0072x1-0.0343-0.02180.0301-0.0309-0.0319-0.00370.01860.01660.0626-0.0349x20.0310-0.0030-0.0368-0.0271-0.03120.03380.0354-0.03020.0089-0.0115x30.04240.0329-0.01880.00490.0214-0.0293-0.00980.0069-0.0098-0.0193x4-0.04150.0392-0.05440.00740.01290.00370.05140.03100.0039-0.0151x50.03240.0198-0.0236-0.0042-0.0133-0.01610.0116-0.0228-0.02070.0090x60.04790.0330-0.0581-0.01110.0103-0.0379-0.00300.0224-0.03440.0076x7-0.0012-0.04270.0313-0.04180.02490.0027-0.04360.0204-0.05040.0340x80.0065-0.0231-0.00070.01580.0049-0.02050.0243-0.02320.0350-0.0466x9-0.0063-0.0452-0.01120.02960.03800.0092-0.00960.00500.0408-0.0173x10-0.01880.0454-0.0168-0.0058-0.0406-0.0226-0.0055-0.0363-0.0030-0.0384y0.00420.00740.00800.00790.00680.00630.00200.00750.00990.0094x10.0460-0.02490.0108-0.0224-0.00670.02150.00340.00350.0119-0.0343x2-0.02640.0250-0.0188-0.04310.02220.0071-0.0184-0.02620.03020.0310x30.00780.00800.0316-0.00300.0058-0.031-0.0080-0.0134-0.03820.0424x4-0.0184-0.0097-0.0386-0.0285-0.0167-0.02960.01560.03570.0105-0.0415x5-0.0160-0.0454-0.03320.00060.0169-0.0556-0.0127-0.00300.05450.0324x6-0.0024-0.04910.0108-0.0498-0.0467-0.00140.0000-0.03030.02760.0479x7-0.0131-0.0180-0.0048-0.0332-0.03280.0144-0.02340.0512-0.0366-0.0012x8-0.0051-0.01350.0277-0.01100.0069-0.00570.0131-0.00670.04400.0065x9-0.01930.0275-0.03690.03040.04390.02200.0079-0.0329-0.0153-0.0063x10-0.01120.01510.0405-0.0111-0.0204-0.01030.02080.0253-0.0053-0.0188最好目标函数值：0.0020 最差目标函数值：0.0120平均目标函数值：0.0073 标准方差：6.3099e-006三最好的一次结果最好解：x1=0.0034 x2=-0.0184 x3=-0.0080 x4=0.0156 x5=-0.0127 x6=0.0000 x7=-0.0234 x8=0.0131 x9=0.0079 x10=0.0208最好值：0.0020运行结果及收敛性曲线如下图： 运行结果 收敛性曲线2 组合优化问题多背包问题 ，测试算例： 100, 220, 90, 400, 300, 400, 205, 120, 160, 580, 400, 140, 100, 1300, 650;.最优值为： 4015一程序(1)主函数： main.mclear all;clcc=100 220 90 400 300 400 205 120 160 580 400 140 100 1300 650;A=8 24 13 80 70 80 45 15 28 90 130 32 20 120 40 8 44 13 100 100 90 75 25 28 120 130 32 40 160 40 3 6 4 20 20 30 8 3 12 14 40 6 3 20 5 5 9 6 40 30 40 16 5 18 24 60 16 11 30 25 5 11 7 50 40 40 19 7 18 29 70 21 17 30 25 5 11 7 55 40 40 21 9 18 29 70 21 17 30 25 0 0 1 10 4 10 0 6 0 6 32 3 0 70 10 3 4 5 20 14 20 6 12 10 18 42 9 12 100 20 3 6 9 30 29 20 12 12 10 30 42 18 18 110 20 3 8 9 35 29 20 16 15 10 30 42 20 18 120 20;b=550;700;130;240;280;310;110;205;260;275;popsize=20; %种群规模chromlength=15; %变量个数pc=0.9; %杂交概率pm=0.2; %变异概率t=0;pop=initpop(popsize,chromlength); %随机产生初始种群while t500 %迭代次数 t=t+1; pop=repair(pop,A,b,c); %修补算子，修补不满足约束的解 objvalue=calobjvalue(pop,c); %计算目标函数值 fitvalue=calfitvalue(objvalue); %计算适应度 bestindividual,bestfit=best(pop,fitvalue); %最近个体及其适应度值 x(t,:)=bestindividual; %最佳个体 y(t)=sum(c.*bestindividual); %计算最佳个体的目标函数值 newpop1=selection(pop,fitvalue); %选择算子 newpop2=crossover(newpop1,pc); %交叉算子 newpop3=mutation(newpop2,pm); %变异算子 objvalue1=calobjvalue(newpop3(1,:),c); if objvalue11&y(t)b(i) %判断每一约束，当不满足约束时，将该背包中利润密度最小的物资拿出 ty,I=min(t(i,:); pop(k,I)=0; t(i,I)=Inf; end endendend(4)计算目标函数值:：calobjvalue.mfunction objvalue =calobjvalue( pop,c)px,py=size(pop);for i=1:px objvalue(i)=sum(c.*pop(i,:);endend(5)计算个体