灰 狼 优 化 算 法 ( G W O ) 原 理 ( 2 0 2 0 )

GWO（灰狼优化）算法MATLAB源码逐行中文注解以优化SVM算法的参数c和g为例，对GWO算法MATLAB源码进行了逐行中文注解。

tic % 计时器%% 清空环境变量close allformat compact%% 数据提取% 载入测试数据wine,其中包含的数据为classnumber = 3,wine:178*13的矩阵,wine_labes:178*1的列向量load wine.mat% 选定训练集和测试集% 将第一类的1-30,第二类的60-95,第三类的131-153做为训练集train_wine = [wine(1:30,:);wine(60:95,:);wine(131:153,:)];% 相应的训练集的标签也要分离出来train_wine_labels = [wine_labels(1:30);wine_labels(60:95);wine_labels(131:153)] ;% 将第一类的31-59,第二类的96-130,第三类的154-178做为测试集test_wine = [wine(31:59,:);wine(96:130,:);wine(154:178,:)];% 相应的测试集的标签也要分离出来test_wine_labels = [wine_labels(31:59);wine_labels(96:130);wine_labels(154:178 )];%% 数据预处理% 数据预处理,将训练集和测试集归一化到[0,1]区间[mtrain,ntrain] = size(train_wine);[mtest,ntest] = size(test_wine);dataset = [train_wine;test_wine];% mapminmax为MATLAB自带的归一化函数[dataset_scale,ps] = mapminmax(dataset',0,1);dataset_scale = dataset_scale';train_wine = dataset_scale(1:mtrain,:);test_wine = dataset_scale( (mtrain+1):(mtrain+mtest),: );%% 利用灰狼算法选择最佳的SVM参数c和gSearchAgents_no=10; % 狼群数量，Number of search agents Max_iteration=10; % 最大迭代次数，Maximum numbef of iterationsdim=2; % 此例需要优化两个参数c和g，number of yourvariableslb=[0.01,0.01]; % 参数取值下界ub=[100,100]; % 参数取值上界% v = 5; % SVM Cross Validation参数,默认为5% initialize alpha, beta, and delta_posAlpha_pos=zeros(1,dim); % 初始化Alpha狼的位置Alpha_score=inf; % 初始化Alpha狼的目标函数值，change this to -inf for maximization problemsBeta_pos=zeros(1,dim); % 初始化Beta狼的位置Beta_score=inf; % 初始化Beta狼的目标函数值，change this to -inf for maximization problemsDelta_pos=zeros(1,dim); % 初始化Delta狼的位置Delta_score=inf; % 初始化Delta狼的目标函数值，change this to -inf for maximization problems%Initialize the positions of search agentsPositions=initialization(SearchAgents_no,dim,ub,lb);Convergence_curve=zeros(1,Max_iteration);l=0; % Loop counter循环计数器% Main loop主循环while lMax_iteration % 对迭代次数循环for i=1:size(Positions,1) % 遍历每个狼% Return back the search agents that go beyond theboundaries of the search space% 若搜索位置超过了搜索空间，需要重新回到搜索空间Flag4ub=Positions(i,:)ub;Flag4lb=Positions(i,:)lb;% 若狼的位置在最大值和最小值之间，则位置不需要调整，若超出最大值，最回到最大值边界；% 若超出最小值，最回答最小值边界Positions(i,:)=(Positions(i,:).*(~(Flag4ub+Flag4lb)))+ub.*F lag4ub+lb.*Flag4lb; % ~表示取反% 计算适应度函数值cmd = [' -c ',num2str(Positions(i,1)),' -g ',num2str(Positions(i,2))];model=svmtrain(train_wine_labels,train_wine,cmd); % SVM 模型训练[~,fitness]=svmpredict(test_wine_labels,test_wine,model); % SVM模型预测及其精度fitness=100-fitness(1); % 以错误率最小化为目标% Update Alpha, Beta, and Deltaif fitnessAlpha_score % 如果目标函数值小于Alpha狼的目标函数值Alpha_score=fitness; % 则将Alpha狼的目标函数值更新为最优目标函数值，Update alphaAlpha_pos=Positions(i,:); % 同时将Alpha狼的位置更新为最优位置if fitnessAlpha_score fitnessBeta_score % 如果目标函数值介于于Alpha狼和Beta狼的目标函数值之间Beta_score=fitness; % 则将Beta狼的目标函数值更新为最优目标函数值，Update betaBeta_pos=Positions(i,:); % 同时更新Beta狼的位置if fitnessAlpha_score fitnessBeta_score fitnessDelta_score % 如果目标函数值介于于Beta狼和Delta狼的目标函数值之间Delta_score=fitness; % 则将Delta狼的目标函数值更新为最优目标函数值，Update deltaDelta_pos=Positions(i,:); % 同时更新Delta狼的位置a=2-l*((2)-Max_iteration); % 对每一次迭代，计算相应的a 值，a decreases linearly fron 2 to 0% Update the Position of search agents including omegas for i=1:size(Positions,1) % 遍历每个狼for j=1:size(Positions,2) % 遍历每个维度% 包围猎物，位置更新r1=rand(); % r1 is a random number in [0,1]r2=rand(); % r2 is a random number in [0,1]A1=2*a*r1-a; % 计算系数A，Equation (3.3)C1=2*r2; % 计算系数C，Equation (3.4)% Alpha狼位置更新D_alpha=abs(C1*Alpha_pos(j)-Positions(i,j)); % Equation (3.5)-part 1X1=Alpha_pos(j)-A1*D_alpha; % Equation (3.6)-part 1r1=rand();r2=rand();A2=2*a*r1-a; % 计算系数A，Equation (3.3)C2=2*r2; % 计算系数C，Equation (3.4)% Beta狼位置更新D_beta=abs(C2*Beta_pos(j)-Positions(i,j)); % Equation (3.5)-part 2X2=Beta_pos(j)-A2*D_beta; % Equation (3.6)-part 2r1=rand();r2=rand();A3=2*a*r1-a; % 计算系数A，Equation (3.3)C3=2*r2; % 计算系数C，Equation (3.4)% Delta狼位置更新D_delta=abs(C3*Delta_pos(j)-Positions(i,j)); % Equation (3.5)-part 3X3=Delta_pos(j)-A3*D_delta; % Equation (3.5)-part 3% 位置更新Positions(i,j)=(X1+X2+X3)-3;% Equation (3.7)Convergence_curve(l)=Alpha_score;bestc=Alpha_pos(1,1);bestg=Alpha_pos(1,2);bestGWOaccuarcy=Alpha_score;%% 打印参数选择结果disp('打印选择结果');str=sprintf('Best Cross Validation Accuracy = %g%%，Best c = %g，Best g = %g',bestGWOaccuarcy*100,bestc,bestg);disp(str)%% 利用最佳的参数进行SVM网络训练cmd_gwosvm = ['-c ',num2str(bestc),' -g ',num2str(bestg)];model_gwosvm = svmtrain(train_wine_labels,train_wine,cmd_gwosvm);%% SVM网络预测[predict_label,accuracy] = svmpredict(test_wine_labels,test_wine,model_gwosvm);% 打印测试集分类准确率total = length(test_wine_labels);right = sum(predict_label == test_wine_labels);disp('打印测试集分类准确率');str = sprintf( 'Accuracy = %g%% (%d-%d)',accuracy(1),right,total);disp(str);%% 结果分析% 测试集的实际分类和预测分类图plot(test_wine_labels,'o');plot(predict_label,'r*');xlabel('测试集样本','FontSize',12);ylabel('类别标签','FontSize',12);legend('实际测试集分类','预测测试集分类');title('测试集的实际分类和预测分类图','FontSize',12);%% 显示程序运行时间% This function initialize the first population of search agentsfunctionPositions=initialization(SearchAgents_no,dim,ub,lb) Boundary_no= size(ub,2); % numnber of boundaries% If the boundaries of all variables are equal and user enter a signle% number for both ub and lbif Boundary_no==1Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;% If each variable has a different lb and ubif Boundary_no1for i=1:dimub_i=ub(i);lb_i=lb(i);Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i;群体智能优化算法是一类基于概率的随机搜索进化算法，各个算法之间存在结构、研究内容、计算方法等具有较大的相似性。