编辑器里面没有MATLAB选项，所以我为了注释更清楚，用的是//，大家不要被误解了呀，算法看代码就好了

1 免疫算法的精髓

生物免疫系统：动态性免疫、自适应免疫免疫算法-保证信息的无害性、有效、抵御垃圾信息

2 理解免疫算法

生物名词对应计算机抗原要解决的问题抗原识别问题识别抗体最优解抗体增加利用遗传算法产生新的最优解记忆细胞产生抗体联想过去的成功淋巴细胞分化优良解或者记忆能力的保持细胞抑制候选解的消除

3 免疫算法原理

遗传算法的交叉和变异有一定的盲目性，容易早熟收敛，因此引入免疫算法，对遗传算法全局搜索的过程进行一定强度的干预，提高算法的效率。

4 MatLab代码详解

首先要进行初始化种群 %D是维度，NP是种群数目，XMin是取值下限，XMax是取值上限 function pOp = InitialPop(D,NP,XMin,XMax) pOp = rand(D,NP)*(XMax-XMin)+XMin; end 然后计算一下初始种群的抗原和抗体的亲和度，这里和遗传算法的适应度很像，其实就是函数的值 //计算函数的值 func Eval = EvalFunc(x) Eval = 5*sin(x(1)*x(2))+x(1)*x(1)+x(2)*x(2); end //计算抗体和抗原之间的亲和度 func MSLL = EvalMSLL() for np = 1:NP MSLL(np) = EvalFunc(f(:,np)); end end 然后免疫算法比较独特就是引入了个体的浓度，这样可以保证他的全局搜索性，因为浓度高的个体的数目会被抑制，这样不会在一个局部解反复搜索。 //计算个体浓度 for np = 1:NP for j=1:NP nd(j) = sqrt(sum((f(:,np)-f(:,j)).^2)); if nd(j)<detas //detas=0.2;相似度阈值 nd(j) = 1; else nd(j) = 0; end end ND(j) = sum(nd)/NP; end //计算个体的激励度 //alfa和belta都是激励度的系数 //浓度高的个体被抑制，与抗原亲和度高的个体被激励 MSLL = alfa*MSLL — belta*ND; 按照激励度对个体进行排序 [SortMSLL,Index] = sort(MSLL); Sortf = f(:,Index);

-免疫循环

while gen<G for i=1:NP/2 a = Sortf(:,i); Na = repmat(a,1,Nc1);//Nc1是复制的个数，本来a是2*1的，复制以后Na变成了2*5 end deta = deta0/gen; //变异操作 for j = 1:Nc for ii = 1:D if rand<pm Na(ii,j) = Na(ii,j)+(rand-0.5)*deta; end //边界条件处理 if (Na(ii,j)<XMin) | (Na(ii,j)>XMax) Na(ii,j) = rand*(XMax-XMin)+XMin; end end end Na(:,1) = Sortf(:,i); //保留亲和度最高的个体 for j = a:Nc1 NaMSLL(j) = func2(Na(:,j)); end [NaSortMSLL,Index] = sort(NaMSLL); aMSLL(i) = NaSortMSLL(1); NaSortf = Na(:,Index); af(:,i) = NaSortf(:,1); end 免疫种群激励度 for np = 1:NP/2 for j = 1:NP/2 nda(j) = sqrt(sum((af(:,np)-af(:,j)).^2)); if nda(j) <detas nda(j) = 1; else nda(j) = 0; end end aND(np) = sum(nda)/NP/2; end aMSLL = alfa*aMSLL - belta*aND;

-种群刷新

bf = rand(D,NP/2)*(XMax-XMin)+XMin; for i=1:NP/2 bMSLL(np) = func2(bf(:,np)) end 免疫种群与新种群合并 f1 = [af,bf]; MSLL1 = [aMSLL,MSLL]; [SortMSLL,Index] = sort(MSLL); Sortf = f1(:,Index); gen = gen + 1; trace(gen) = func2(Sortf(:,1));

奉上源码

上面是我自己在CDSN上敲的，代码编辑还不是很舒服，肯定会有一些错误，所以把源码给大家贴在这里，其实算法分步骤去理解也没那么难，奥里给。

%%%%%%%%%%%%%%%%%免疫算法求函数极值%%%%%%%%%%%%%%%%%%%% %%智能算法专题设计 shiyan42.m % 蚁群算法求解函数极值问题 % 2020/10/22 %%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%% clear all; %清除所有变量 close all; %清图 clc; %清屏 D=2; %免疫个体维数 NP=50; %免疫个体数目 Xs=4; %取值上限 Xx=-4; %取值下限 G=200; %最大免疫代数 pm=0.7; %变异概率 alfa=2; %激励度系数 belta=1; %激励度系数 detas=0.2; %相似度阈值 gen=0; %免疫代数 Ncl=5; %克隆个数 deta0=0.5*Xs; %邻域范围初值 %%%%%%%%%%%%%%%%%%%%%%%初始种群%%%%%%%%%%%%%%%%%%%%%%%% f=rand(D,NP)*(Xs-Xx)+Xx; for np=1:NP MSLL(np) = func2(f(:,np)); end %%%%%%%%%%%%%%%%%计算个体浓度和激励度%%%%%%%%%%%%%%%%%%% for np=1:NP for j=1:NP nd(j) = sum(sqrt((f(:,np)-f(:,j)).^2)); if nd(j)<detas nd(j)=1; else nd(j)=0; end end ND(np)=sum(nd)/NP; end MSLL = alfa*MSLL - belta*ND; %%%%%%%%%%%%%%%%%%%激励度按升序排列%%%%%%%%%%%%%%%%%%%%%% [SortMSLL,Index] = sort(MSLL); Sortf = f(:,Index); %%%%%%%%%%%%%%%%%%%%%%%%免疫循环%%%%%%%%%%%%%%%%%%%%%%%% while gen<G for i=1:NP/2 %%%%%%%%选激励度前NP/2个体进行免疫操作%%%%%%%%%%% a = Sortf(:,i); Na = repmat(a,1,Ncl); deta = deta0/gen; for j = 1:Ncl for ii = 1:D %%%%%%%%%%%%%%%%%变异%%%%%%%%%%%%%%%%%%% if rand<pm Na(ii,j) = Na(ii,j)+(rand-0.5)*deta; end %%%%%%%%%%%%%%边界条件处理%%%%%%%%%%%%%%% if (Na(ii,j)>Xs) | (Na(ii,j)<Xx) Na(ii,j) = rand * (Xs-Xx)+Xx; end end end Na(:,1)=Sortf(:,i); %保留克隆源个体 %%%%%%%%%%克隆抑制，保留亲和度最高的个体%%%%%%%%%% for j=1:Ncl NaMSLL(j) = func2(Na(:,j)); end [NaSortMSLL,Index]=sort(NaMSLL); aMSLL(i) =NaSortMSLL(1); NaSortf=Na(:,Index); af(:,i)=NaSortf(:,1); end %%%%%%%%%%%%%%%%%%%%免疫种群激励度%%%%%%%%%%%%%%%%%%% for np=1:NP/2 for j=1:NP/2 nda(j)=sum(sqrt((af(:,np)-af(:,j)).^2)); if nda(j)<detas nda(j)=1; else nda(j)=0; end end aND(np)=sum(nda)/NP/2; end aMSLL = alfa*aMSLL- belta*aND; %%%%%%%%%%%%%%%%%%%%%%%种群刷新%%%%%%%%%%%%%%%%%%%%%%% bf=rand(D,NP/2)*(Xs-Xx)+Xx; for np=1:NP/2 bMSLL(np)=func2(bf(:,np)); end %%%%%%%%%%%%%%%%%%%新生成种群激励度%%%%%%%%%%%%%%%%%%%% for np=1:NP/2 for j=1:NP/2 ndc(j)=sum(sqrt((bf(:,np)-bf(:,j)).^2)); if ndc(j)<detas ndc(j)=1; else ndc(j)=0; end end bND(np)=sum(ndc)/NP/2; end bMSLL = alfa*bMSLL- belta*bND; %%%%%%%%%%%%%%免疫种群与新生种群合并%%%%%%%%%%%%%%%%%%% f1=[af,bf]; MSLL1=[aMSLL,bMSLL]; [SortMSLL,Index]=sort(MSLL1); Sortf=f1(:,Index); gen=gen+1; trace(gen)=func2(Sortf(:,1)); end %%%%%%%%%%%%%%%%%%%%%%%输出优化结果%%%%%%%%%%%%%%%%%%%%%%%% Bestf=Sortf(:,1); %最优变量 trace(end); %最优值 figure,plot(trace) xlabel('迭代次数') ylabel('目标函数值') title('亲和度进化曲线')