双峰和多峰函数最大值的遗传算法求解.doc

【自动充值】百度文库财富值充值 双峰和多峰函数最大值的遗传算法求解摘 要 本文利用基本遗传算法的思路寻找双峰或多峰函数的最大值，选择采用轮盘选择方法；交叉采用单点交叉，交叉位置随机，交叉概率取0.20；变异概率0.005。经多次运行，求得最大值。停止法则为循环最大遗传代数为止到。的编程环境为Matlab6.5。关键字 遗传算法 多峰函数遗传算法是一种通用性非常强，计算性能非常好的算法，解决类似X.*sin(10*pi*X)+2.0这样的多峰函数的最大值采用遗传算法似乎是最好的算法。所以本问题采用遗传算法来解决，也是对遗传算法编程的一次练习。函数Y=X.*sin(10*pi*X)+2.0 在-1 2区间上的图像如下：Y=X.*sin(10*pi*X)+2.0 在-1 2区间上的图像本程序最大遗传代数为200，个体数目为50，采用二进制编码，基因长度为30。运算结果：best_Y =3.8503index =106X =1.8506各代最大值情况见下图（蓝点为第一代初始值，红色三角为各代最大值）每一代计算过程如下表：Index各代Y最大值各代X值各代Y平均值1.00003.63781.64671.79822.00003.63781.64671.82533.00003.63771.64671.79934.00003.63771.64671.80835.00003.63771.64671.85906.00003.63931.64691.91937.00003.63931.64691.86098.00003.63921.64691.85309.00003.63921.64691.882910.00003.59871.83371.815511.00003.59871.83371.851812.00003.55141.83211.824613.00003.55141.83211.851014.00003.35701.46211.744015.00003.35701.46211.806616.00003.35701.46211.751517.00003.35701.46211.810718.00003.35701.46211.785719.00003.35701.46211.729720.00003.35701.46211.684321.00003.35661.46221.732722.00003.35661.46221.844023.00003.52081.83121.888824.00003.52081.83121.876925.00003.52111.83121.877826.00003.52111.83121.883927.00003.35831.46211.914328.00003.35831.46211.878329.00003.35741.46211.941630.00003.49931.63691.957531.00003.49931.63691.899732.00003.49931.63691.936133.00003.39991.45911.867534.00003.39841.45921.808435.00003.43181.63401.928736.00003.46291.63531.909937.00003.46291.63531.864638.00003.46301.63531.812639.00003.46301.63531.880740.00003.48041.66511.883841.00003.48041.66511.854642.00003.48041.66511.964543.00003.52381.66311.926844.00003.05731.88101.855745.00003.05731.88101.921346.00003.05731.88101.902047.00003.05711.88101.825248.00003.44751.44871.892649.00003.44841.44901.969850.00003.44841.44901.989751.00003.44841.44901.971452.00002.85030.85211.914553.00002.85030.85211.917054.00002.85791.22471.950155.00002.85030.85211.913456.00003.72481.86231.887257.00003.72481.86231.882058.00003.72421.86231.860959.00003.72421.86231.960960.00003.12411.87961.945761.00003.12411.87961.966362.00003.43531.44611.958663.00003.43561.44611.934564.00003.77121.85991.976665.00003.77731.85952.004766.00003.77731.85951.958767.00003.47481.87111.963168.00003.70911.83802.042769.00003.70901.83802.019970.00003.82741.84552.072071.00003.74381.83972.073872.00003.74301.83962.025573.00003.74381.83972.028874.00003.62731.86632.006375.00003.77601.85962.020476.00003.78501.85902.152377.00003.78501.85902.144478.00003.78501.85902.115879.00003.84291.84772.115780.00003.84291.84771.962381.00003.84291.84771.962082.00003.84301.84771.941683.00003.84301.84771.852784.00003.84301.84772.000585.00003.84301.84772.022686.00003.84301.84772.084687.00003.84301.84772.039988.00003.84271.84772.042489.00003.84271.84772.024790.00003.84291.85342.089891.00003.84291.85342.071592.00003.84291.85342.091693.00003.35251.87431.966994.00003.35251.87432.020695.00003.35251.87432.018396.00003.36501.87402.019197.00003.84041.85382.057898.00003.83911.85402.012099.00003.83911.85401.9769100.00003.83911.85402.0035101.00003.85021.85072.0710102.00003.85021.85072.0570103.00003.85021.85072.0683104.00003.85021.85072.0826105.00003.85021.85072.0440106.00003.85031.85062.0487107.00003.85031.85062.0244108.00003.85031.85062.0568109.00003.85031.85062.1176110.00003.85031.85062.0873111.00003.85031.85062.1207112.00003.85031.85062.0535113.00003.85031.85062.0841114.00003.85021.85032.1926115.00003.76371.84082.1121116.00003.76361.84082.0932117.00003.76361.84081.9732118.00003.76371.84081.9570119.00003.76361.84081.9336120.00003.76361.84081.9575121.00003.72801.83891.8549122.00003.72801.83891.9322123.00003.72801.83891.9030124.00003.72801.83891.9238125.00003.72801.83891.9764126.00003.72801.83892.0212127.00003.72821.83891.9752128.00003.72821.83891.9498129.00003.73301.83911.8933130.00003.73301.83911.8934131.00003.59331.83351.8165132.00003.59331.83351.8368133.00003.30531.82541.8050134.00003.24491.25381.7433135.00003.24491.25381.7819136.00002.84990.85251.7336137.00002.84990.85251.7512138.00002.84990.85251.7261139.00002.84990.85251.7688140.00003.25291.62801.8543141.00003.63191.65541.8755142.00003.63191.65541.8593143.00003.61441.65731.8239144.00003.62301.65641.8335145.00003.62301.65641.8621146.00003.62291.65641.8524147.00003.31861.67111.9152148.00003.19851.46961.9109149.00003.70831.86312.0110150.00003.70831.86311.9662151.00003.62671.86631.9461152.00003.62671.86632.0019153.00003.62671.86631.9808154.00003.62671.86631.9828155.00003.62671.86631.9835156.00003.65501.86531.9858157.00003.65501.86532.0047158.00003.65501.86532.0711159.00003.65321.86532.0025160.00003.65321.86532.0074161.00003.84661.84862.0899162.00003.84661.84862.0768163.00003.84661.84862.0675164.00003.84171.85362.0655165.00003.84171.85362.0244166.00003.49291.63661.9715167.00003.60631.65801.9138168.00003.44331.66671.9892169.00003.43811.66691.9848170.00003.43811.66691.9934171.00003.43811.66691.9868172.00003.79241.84262.0324173.00003.43791.66692.0047174.00003.43791.66692.0191175.00003.43791.66691.9246176.00003.43801.66691.9055177.00003.43801.66691.9284178.00003.60891.64352.0184179.00003.60901.64351.9541180.00003.84521.85291.9973181.00003.60931.64351.9780182.00003.60931.64351.9613183.00003.60961.64351.9650184.00003.35411.43901.9575185.00003.42771.45631.9087186.00003.15211.23811.9247187.00003.45031.45041.9454188.00002.89891.47921.9066189.00002.88221.61841.9284190.00003.42281.66751.9520191.00003.43051.66721.9905192.00003.43051.66721.9467193.00003.33651.87471.9122194.00003.16941.23931.8371195.00003.85031.85061.9073196.00003.81471.85681.9294197.00003.85011.85022.0429198.00003.81471.85681.9125199.00003.81521.85671.9703200.00003.81521.85672.0873201.00003.81821.85652.0715评价：由于此程序为循环完指定代数后才结束，并且算不是绝对收敛的，所以会出现后面的一些最大值反而比前面的小的情况，而且显得没有规律。此程序运行时间很短，1秒左右，性能不错。可以输出也可看出此程序收敛速度实际上有点快。双峰函数不必讨论了。本程序文件名为：SGA.m子函数：bs2rv.m 二进制转换10进制函数程序源代码如下：function SGA()%简单遗传算法程序解决多峰函数的最值问题Maxgen=200; %最大遗传代数NIND=50; %个体数目gen_len=30; %基因长度FieldD=-1,2;%区域描述cross_probability=0.20;%交叉概率mutate_probability=0.005;%变异概率fun=variable.*sin(10*pi*variable)+2.0;%目标函数%subplot(2,1,1);fplot(fun,FieldD);%画出目标函数曲线hold on%生成初始种群Chrom=round(rand(NIND,gen_len); %生成二维01数组Chrom_real=bs2rv(Chrom,FieldD) %二进制转换成十进制数%计算目标函数值Obj=Chrom_real.*sin(10*pi*Chrom_real)+2.0%绘制初始值点plot(Chrom_real,Obj,*);%绘制当前最大值的点ma(1,3)=1;ma(1,2) index=max(Obj);ma(1,3)=Chrom_real(index);plot(ma(1,3),ma(1,2),);%种群平均值ma(1,4)=mean(Obj);%开始遗传计算for gen=1:Maxgen %计算适应度 sumObj=sum(Obj);%所有个体的目标函数值之和 fitness=Obj/sumObj;%每个个体的选择概率 fitness2=fitness(1);%累计概率 %选择 numof=length(fitness); %计算累计概率fitness2 for j=2:numof fitness2(j)=fitness(j)+fitness2(j-1);%计算累计概率 end %轮盘选择 tempChrom=Chrom;%储存一个原始的个体值 index=1; for k=1:NIND fo