免疫算法在物流中心选址问题中的matlab实现

文章主要参考了《matlab智能算法30例》，仅供学习交流使用。

%% 免疫优化算法在物流配送中心选址中的应用
%% 清空环境
clc
clear

%% 算法基本参数           
sizepop=50;           % 种群规模
overbest=10;          % 记忆库容量
MAXGEN=100;            % 迭代次数
pcross=0.5;           % 交叉概率
pmutation=0.4;        % 变异概率
ps=0.95;              % 多样性评价参数
length=6;             % 配送中心数
M=sizepop+overbest;

%% step1 识别抗原,将种群信息定义为一个结构体
individuals = struct('fitness',zeros(1,M), 'concentration',zeros(1,M),'excellence',zeros(1,M),'chrom',[]);
%% step2 产生初始抗体群
individuals.chrom = popinit(M,length);
trace=[]; %记录每代最个体优适应度和平均适应度

%% 迭代寻优
for iii=1:MAXGEN

     %% step3 抗体群多样性评价
     for i=1:M
         individuals.fitness(i) = fitness(individuals.chrom(i,:));      % 抗体与抗原亲和度(适应度值）计算
         individuals.concentration(i) = concentration(i,M,individuals); % 抗体浓度计算
     end
     % 综合亲和度和浓度评价抗体优秀程度，得出繁殖概率
     individuals.excellence = excellence(individuals,M,ps);
          
     % 记录当代最佳个体和种群平均适应度
     [best,index] = min(individuals.fitness);   % 找出最优适应度 
     bestchrom = individuals.chrom(index,:);    % 找出最优个体
     average = mean(individuals.fitness);       % 计算平均适应度
     trace = [trace;best,average];              % 记录
     
     %% step4 根据excellence，形成父代群，更新记忆库（加入精英保留策略，可由s控制）
     bestindividuals = bestselect(individuals,M,overbest);   % 更新记忆库
     individuals = bestselect(individuals,M,sizepop);        % 形成父代群

     %% step5 选择，交叉，变异操作，再加入记忆库中抗体，产生新种群
     individuals = select(individuals,sizepop);                                                             % 选择
     individuals.chrom = Cross(pcross,individuals.chrom,sizepop,length);                                    % 交叉
     individuals.chrom = mutation(pmutation,individuals.chrom,sizepop,length);   % 变异
     individuals = incorporate(individuals,sizepop,bestindividuals,overbest);                               % 加入记忆库中抗体      

end

%% 画出免疫算法收敛曲线
figure(1)
plot(trace(:,1));
hold on
plot(trace(:,2),'--');
legend('最优适应度值','平均适应度值')
title('免疫算法收敛曲线','fontsize',12)
xlabel('迭代次数','fontsize',12)
ylabel('适应度值','fontsize',12)

%% 画出配送中心选址图
%城市坐标
city_coordinate=[1304,2312;3639,1315;4177,2244;3712,1399;3488,1535;3326,1556;3238,1229;4196,1044;4312,790;4386,570;
                 3007,1970;2562,1756;2788,1491;2381,1676;1332,695;3715,1678;3918,2179;4061,2370;3780,2212;3676,2578;
                 4029,2838;4263,2931;3429,1908;3507,2376;3394,2643;3439,3201;2935,3240;3140,3550;2545,2357;2778,2826;2370,2975];
carge=[20,90,90,60,70,70,40,90,90,70,60,40,40,40,20,80,90,70,100,50,50,50,80,70,80,40,40,60,70,50,30];
%找出最近配送点
for i=1:31
    distance(i,:)=dist(city_coordinate(i,:),city_coordinate(bestchrom,:)');
end
[a,b]=min(distance');

index=cell(1,length);

for i=1:length
%计算各个派送点的地址
index{i}=find(b==i);
end
figure(2)
title('最优规划派送路线')
cargox=city_coordinate(bestchrom,1);
cargoy=city_coordinate(bestchrom,2);
plot(cargox,cargoy,'rs','LineWidth',2,...
    'MarkerEdgeColor','r',...
    'MarkerFaceColor','b',...
    'MarkerSize',20)
hold on

plot(city_coordinate(:,1),city_coordinate(:,2),'o','LineWidth',2,...
    'MarkerEdgeColor','k',...
    'MarkerFaceColor','g',...
    'MarkerSize',10)

for i=1:31
    x=[city_coordinate(i,1),city_coordinate(bestchrom(b(i)),1)];
    y=[city_coordinate(i,2),city_coordinate(bestchrom(b(i)),2)];
    plot(x,y,'c');hold on
end

function fit=fitness(individual)
%计算个体适应度
%individual input 个体
%fit output 适应度值
%城市坐标
city_coordinate=[1304,2312;3639,1315;4177,2244;3712,1399;3488,1535;3326,1556;
    3238,1229;4196,1044;4312,790;4386,570;3007,1970;2562,1756;
    2788,1491;2381,1676;1332,695;3715,1678;3918,2179;4061,2370;
    3780,2212;3676,2578;4029,2838;4263,2931;3429,1908;3507,2376;
   3394,2643;3439,3201;2935,3240;3140,3550;2545,2357;2778,2826;
   2370,2975];
%货物量
carge=[20,90,90,60,70,70,40,90,90,70,60,40,40,40,20,80,90,70,100,50,50,50,80,70,80,40,40,60,70,50,30];
%找出最近配送点
for i=1:31
    %dist函数就是欧式距离加权函数
    distance(i,:)=dist(city_coordinate(i,:),city_coordinate(individual,:)');
end
[a,b]=min(distance');
%计算费用
for i=1:31
    expense(i)=carge(i)*a(i);
end
fit=sum(expense)+4.0e+4*length(find(a>3000));

end

function resemble=similar(individual1,individual2)
%计算个体individual1与individual2的相似度
%individual1,individual2 input  两个个体
%resemble output  相似度
k=zeros(1,length(individual1));
for i=1:length(individual1)
    if find(individual1(i)==individual2)
        k(i)=1;
    end
end
resemble=sum(k)/length(individual1);
end

function concentration = concentration(i,M,individuals)
% 计算个体浓度值
% i              input      第i个抗体
% M              input      种群规模
% individuals    input     个体
% concentration  output     浓度值

concentration=0;
for j=1:M
    xsd=similar(individuals.chrom(i,:),individuals.chrom(j,:));  % 第i个体与种群个体间的相似度
    % 相似度大于阀值
    if xsd>0.7
        concentration=concentration+1;
    end
end

concentration=concentration/M;

end

function exc = excellence(individuals,M,ps)
%计算个体繁殖概率
%individuals  input  种群
%M            input  种群规模
%ps           input  多样性评价参数
%exc          output 繁殖概率
fit = 1./individuals.fitness;
sumfit = sum(fit);
con = individuals.concentration;
sumcon = sum(con);
for i=1:M
    exc(i)=fit(i)/sumfit*ps+con(i)/sumcon*(1-ps);
end



end

function ret=Select(individuals,sizepop)
% 轮盘赌选择
% individuals input  : 种群信息
% sizepop     input  : 种群规模
% ret         output : 选择后得到的种群

excellence=individuals.excellence;
pselect=excellence./sum(excellence);
% 事实上 pselect = excellence；

index=[]; 
for i=1:sizepop   % 转sizepop次轮盘
    pick=rand;
    while pick==0    
        pick=rand;        
    end
    for j=1:sizepop   
        pick=pick-pselect(j);        
        if pick<0        
            index=[index j];
            break;  % 寻找落入的区间，此次转轮盘选中了染色体j
        end
    end
end
% 注意：在转sizepop次轮盘的过程中，有可能会重复选择某些染色体

individuals.chrom=individuals.chrom(index,:);
individuals.fitness=individuals.fitness(index);
individuals.concentration=individuals.concentration(index);
individuals.excellence=individuals.excellence(index);
ret=individuals;

end

function ret=Mutation(pmutation,chrom,sizepop,length1)
% 变异操作
% pmutation        input  : 变异概率
% chrom            input  : 抗体群
% sizepop          input  : 种群规模
% iii              input  : 进化代数
% MAXGEN           input  : 最大进化代数
% length1          input  : 抗体长度
% ret              output : 变异得到的抗体群
% 每一轮for循环中，可能会进行一次变异操作，染色体是随机选择的，变异位置也是随机选择的
for i=1:sizepop   
    
    % 变异概率
    pick=rand;
    while pick==0
        pick=rand;
    end
    index=unidrnd(sizepop);

   % 判断是否变异
    if pick>pmutation
        continue;
    end
    
    pos=unidrnd(length1);
    while pos==1
        pos=unidrnd(length1);
    end
    
    nchrom=chrom(index,:);
    nchrom(pos)=unidrnd(31);
    while length(unique(nchrom))==(length1-1)
        nchrom(pos)=unidrnd(31);
    end
    
    flag=test(nchrom);
    if flag==1
        chrom(index,:)=nchrom;
    end
    
end

ret=chrom;
end

function newindividuals = incorporate(individuals,sizepop,bestindividuals,overbest)
% 将记忆库中抗体加入，形成新种群
% individuals         input          抗体群
% sizepop             input          抗体数
% bestindividuals     input          记忆库
% overbest            input          记忆库容量

m = sizepop+overbest;
newindividuals = struct('fitness',zeros(1,m), 'concentration',zeros(1,m),'excellence',zeros(1,m),'chrom',[]);

% 遗传操作得到的抗体
for i=1:sizepop
    newindividuals.fitness(i) = individuals.fitness(i);   
    newindividuals.concentration(i) = individuals.concentration(i);   
    newindividuals.excellence(i) = individuals.excellence(i);   
    newindividuals.chrom(i,:) = individuals.chrom(i,:);   
end
% 记忆库中抗体
for i=sizepop+1:m
    newindividuals.fitness(i) = bestindividuals.fitness(i-sizepop);   
    newindividuals.concentration(i) = bestindividuals.concentration(i-sizepop);   
    newindividuals.excellence(i) = bestindividuals.excellence(i-sizepop);   
    newindividuals.chrom(i,:) = bestindividuals.chrom(i-sizepop,:);   
end

end

function psd=popinit(M,length) 
ss=[];
for i=1:M
    a=randperm(31,length);
    ss(i,:)=a;
end
psd=ss;

end

function rets=bestselect(individuals,m,n)
% 初始化记忆库,依据excellence，将群体中高适应度低相似度的overbest个个体存入记忆库
% m                  input          抗体数
% n                  input          记忆库个体数\父代群规模
% individuals        input          抗体群
% bestindividuals    output         记忆库\父代群

% 精英保留策略，将fitness最好的s个个体先存起来，避免因其浓度高而被淘汰
s=3;
rets=struct('fitness',zeros(1,n), 'concentration',zeros(1,n),'excellence',zeros(1,n),'chrom',[]);
[fitness,index] = sort(individuals.fitness);
for i=1:s
    rets.fitness(i) = individuals.fitness(index(i));   
    rets.concentration(i) = individuals.concentration(index(i));
    rets.excellence(i) = individuals.excellence(index(i));
    rets.chrom(i,:) = individuals.chrom(index(i),:);
end

% 剩余m-s个个体
leftindividuals=struct('fitness',zeros(1,m-s), 'concentration',zeros(1,m-s),'excellence',zeros(1,m-s),'chrom',[]);
for k=1:m-s
    leftindividuals.fitness(k) = individuals.fitness(index(k+s));   
    leftindividuals.concentration(k) = individuals.concentration(index(k+s));
    leftindividuals.excellence(k) = individuals.excellence(index(k+s));
    leftindividuals.chrom(k,:) = individuals.chrom(index(k+s),:);
end

% 将剩余抗体按excellence值排序
[excellence,index]=sort(1./leftindividuals.excellence);

% 在剩余抗体群中按excellence再选n-s个最好的个体
for i=s+1:n
    rets.fitness(i) = leftindividuals.fitness(index(i-s));
    rets.concentration(i) = leftindividuals.concentration(index(i-s));
    rets.excellence(i) = leftindividuals.excellence(index(i-s));
    rets.chrom(i,:) = leftindividuals.chrom(index(i-s),:);
end

end

function ret=Cross(pcross,chrom,sizepop,length)
% 交叉操作
% pcorss                input  : 交叉概率
% chrom                 input  : 抗体群
% sizepop               input  : 种群规模
% length                input  : 抗体长度
% ret                   output : 交叉得到的抗体群

% 每一轮for循环中，可能会进行一次交叉操作，随机选择染色体是和交叉位置，是否进行交叉操作则由交叉概率（continue）控制
for i=1:sizepop  
    
    % 随机选择两个染色体进行交叉
    pick=rand;
    while prod(pick)==0
        pick=rand(1);
    end
    
    if pick>pcross
        continue;
    end
    
    % 找出交叉个体
    index(1)=unidrnd(sizepop);
    index(2)=unidrnd(sizepop);
    while index(2)==index(1)
        index(2)=unidrnd(sizepop);
    end
    
    % 选择交叉位置
    pos=ceil(length*rand);
    while pos==1
        pos=ceil(length*rand);
    end

    % 个体交叉
    chrom1=chrom(index(1),:);
    chrom2=chrom(index(2),:);
    
    k=chrom1(pos:length);
    chrom1(pos:length)=chrom2(pos:length);
    chrom2(pos:length)=k; 
    
    % 满足约束条件赋予新种群
    flag1=test(chrom(index(1),:));
    flag2=test(chrom(index(2),:));
    
    if flag1*flag2==1
        chrom(index(1),:)=chrom1;
        chrom(index(2),:)=chrom2;
    end
    
end

ret=chrom;
end

function flag=test(code)
% 检查个体是否满足距离约束
% code    input     个体
% flag    output    是否满足要求标志

city_coordinate=[1304,2312;3639,1315;4177,2244;3712,1399;3488,1535;3326,1556;3238,1229;4196,1044;4312,790;4386,570;
                 3007,1970;2562,1756;2788,1491;2381,1676;1332,695;3715,1678;3918,2179;4061,2370;3780,2212;3676,2578;
                 4029,2838;4263,2931;3429,1908;3507,2376;3394,2643;3439,3201;2935,3240;3140,3550;2545,2357;2778,2826;2370,2975];

flag=1;
if max( max(dist( city_coordinate(code,:)') ) )>3000
    flag=0;
end

end

结果展示如下：