代码
以下代码按照图中顺序依次：
1、
clc;
clear all;
close all
addpath addpath
%% 导入数据
% 训练集——190个样本
P_train = xlsread('data','training set','B2：G191')'; T_train= xlsread('data','training set','H2：H191')';
% 测试集——44个样本
P_test=xlsread('data','test set','B2:G45')';T_test=xlsread('data','test set','H2:H45')';
N = size(P_test, 2); % 测试集样本数
M = size(P_train, 2); % 训练集样本数
%% 数据归一化
[p_train, ps_input] = mapminmax(P_train, 0, 1);
p_test = mapminmax('apply', P_test, ps_input);
[t_train, ps_output] = mapminmax(T_train, 0, 1);
t_test = mapminmax('apply', T_test, ps_output);
%% 模型训练与预测
SearchAgents_no=20;
Max_iteration=20;
dim=2;
lb=[0.001,0.001];%参数下限
ub=[500,100];%参数上限
type = 'function estimation';
%% c和g寻优
[sig2,gamma]=sma_ls(SearchAgents_no,Max_iteration,dim,ub,lb,type,p_train',t_train',p_test',t_test'); %%蝴蝶优化算法
[alpha,b] = trainlssvm({
p_train',t_train',type,sig2,gamma,'RBF_kernel'}); %sig2,gamma,
t_sim1= simlssvm({
p_train',t_train',type,sig2,gamma,'RBF_kernel'},{
alpha,b},p_train');
t_sim2= simlssvm({
p_train',t_train',type,sig2,gamma,'RBF_kernel'},{
alpha,b},p_test');
t_sim1=t_sim1';t_sim2=t_sim2';
%% 数据反归一化
T_sim1 = mapminmax('reverse', t_sim1, ps_output);
T_sim2 = mapminmax('reverse', t_sim2, ps_output);
%% 均方根误差
error1 = sqrt(sum((T_sim1 - T_train).^2) ./ M);
error2 = sqrt(sum((T_sim2 - T_test ).^2) ./ N);
%% 绘图
figure
plot(1: M, T_train, 'r-*', 1: M, T_sim1, 'k-o', 'LineWidth', 1)
legend('真实值','预测值')
xlabel('预测样本')
ylabel('预测结果')
string = {
'训练集预测结果对比'; ['RMSE=' num2str(error1)]};
title(string)
xlim([1, M])
grid off
figure
plot(1: N, T_test, 'r-*', 1: N, T_sim2, 'k-o', 'LineWidth', 1)
legend('真实值','预测值')
xlabel('预测样本')
ylabel('预测结果')
string = {
'测试集预测结果对比';['RMSE=' num2str(error2)]};
title(string)
xlim([1, N])
grid off
%% 相关指标计算
disp(['训练集数据误差：'])
[mae_train,mse_train,rmse_train,mape_train,error_train,errorPercent_train,R_train]=calc_error(T_train,T_sim1); %
disp(['测试集数据误差：'])
[mae_test,mse_test,rmse_test,mape_test,error_test,errorPercent_test,R_test]=calc_error(T_test,T_sim2); %
2、
function [sig2,gamma]=sma_ls(N,Max_iter,dim,ub,lb,type,pn_train,tn_train,pn_test,tn_test);
% 种群初始化
fobj=@(x)fun(x,pn_train,tn_train,pn_test,tn_test,type);
bestPositions=zeros(1,dim);
Destination_fitness=inf;%设置初始全最优适应度
AllFitness = inf*ones(N,1);%初始所有种群的适应度
weight = ones(N,dim);%每一个黏菌的权重
%种群初始化
X=initialization(N,dim,ub,lb); %%佳点集种群初始化
it=1; %初始迭代次数
lb=ones(1,dim).*lb; % 下界
ub=ones(1,dim).*ub; % 上界
z=0.02; % 初始参数z
% 主循环
while it <= Max_iter
it
for i=1:N
% 检查是否在范围内
Flag4ub=X(i,:)>ub;
Flag4lb=X(i,:)<lb;
X(i,:)=(X(i,:).*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
AllFitness(i) = fobj(X(i,:));
end
[SmellOrder,SmellIndex] = sort(AllFitness); %%筛选出最优和最差的种群
worstFitness = SmellOrder(N);
bestFitness = SmellOrder(1);
S=bestFitness-worstFitness+eps; %避免分母为0的操作
%计算每一个黏菌的权重
for i=1:N
for j=1:dim
if i<=(N/2) %参考源码，式2.5
weight(SmellIndex(i),j) = 1+rand()*log10((bestFitness-SmellOrder(i))/(S)+1);
else
weight(SmellIndex(i),j) = 1-rand()*log10((bestFitness-SmellOrder(i))/(S)+1);
end
end
end
%更新当前最优的种群和适应度
if bestFitness < Destination_fitness
bestPositions=X(SmellIndex(1),:);
Destination_fitness = bestFitness;
end
a = atanh(-(it/Max_iter)+1); %参考原式2.4
b = 1-it/Max_iter;
% 更新每一代种群的位置
for i=1:N
if rand<z %Eq.(2.7)
X(i,:) = (ub-lb)*rand+lb;
else
p =tanh(abs(AllFitness(i)-Destination_fitness)); %Eq.(2.2)
vb = unifrnd(-a,a,1,dim); %Eq.(2.3)
vc = unifrnd(-b,b,1,dim);
for j=1:dim
r = rand();
A = randi([1,N]); % two positions randomly selected from population
B = randi([1,N]);
if r<p %Eq.(2.1)
X(i,j) = bestPositions(j)+ vb(j)*(weight(i,j)*X(A,j)-X(B,j));
else
X(i,j) = vc(j)*X(i,j);
end
end
end
end
trace(it,1)=Destination_fitness;
trace(it,2)=mean( AllFitness);
it=it+1;
end
%% %%%%%%%%%%%%%用SMA算法优化LSSVM中的参数c和g结束%%%%%%%%%%%%%%%%%%%%
bestX=bestPositions;
sig2=bestX(1);
gamma=bestX(2);
%%
figure;
hold on;
trace = round(trace*10000)/10000;
plot(trace(1:Max_iter,1),'r*-','LineWidth',1.5);
plot(trace(1:Max_iter,2),'bo-','LineWidth',1.5);
legend('最佳适应度','平均适应度');
xlabel('进化代数','FontSize',12);
ylabel('适应度','FontSize',12);
axis([0 Max_iter-1 0 100]);
grid on;
axis auto;
line1 = '适应度曲线Accuracy[ISMAmethod]';
line2 = ['(终止代数=', ...
num2str(Max_iter),',种群数量pop=', ...
num2str(N),')'];
line3 = ['Best c=',num2str(sig2),' g=',num2str(gamma), ...
' RMSE=',num2str((Destination_fitness))];
title({
line1;line2;line3},'FontSize',12);
3、
%_________________________________________________________________________________
% Salp Swarm Algorithm (SSA) source codes version 1.0
%
% Developed in MATLAB R2016a
%
% Author and programmer: Seyedali Mirjalili
%
% e-Mail: ali.mirjalili@gmail.com
% seyedali.mirjalili@griffithuni.edu.au
%
% Homepage: http://www.alimirjalili.com
%
% Main paper:
% S. Mirjalili, A.H. Gandomi, S.Z. Mirjalili, S. Saremi, H. Faris, S.M. Mirjalili,
% Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems
% Advances in Engineering Software
% DOI: http://dx.doi.org/10.1016/j.advengsoft.2017.07.002
%____________________________________________________________________________________
% This function initialize the first population of search agents
function Positions=initialization(SearchAgents_no,dim,ub,lb)
Boundary_no= size(ub,1); % numnber of boundaries
% If the boundaries of all variables are equal and user enter a signle
% number for both ub and lb
if Boundary_no==1
Positions=rand(SearchAgents_no,dim).*(ub-lb)+lb;
end
% If each variable has a different lb and ub
if Boundary_no>1
for i=1:dim
ub_i=ub(i);
lb_i=lb(i);
Positions(:,i)=rand(SearchAgents_no,1).*(ub_i-lb_i)+lb_i;
end
end
4、
function fitness=fun(Position,pn_train,tn_train,pn_test,tn_test,type)
sig2=Position(2);
gamma=Position(1);
[alpha,b] = trainlssvm({
pn_train,tn_train,type,gamma,sig2,'RBF_kernel'});
predict_test = simlssvm({
pn_train,tn_train,type,gamma,sig2,'RBF_kernel'},{
alpha,b},pn_test);
fitness= sqrt(sum((tn_test-predict_test).^2)/size(tn_test,1));
end
5、
function [mae,mse,rmse,mape,error,errorPercent,R]=calc_error(x1,x2)
%此函数用于计算预测值和实际（期望）值的各项误差指标
% 参数说明
%----函数的输入值-------
% x1：真实值
% x2：预测值
%----函数的返回值-------
% mae：平均绝对误差（是绝对误差的平均值，反映预测值误差的实际情况.）
% mse：均方误差（是预测值与实际值偏差的平方和与样本总数的比值）
% rmse：均方误差根（是预测值与实际值偏差的平方和与样本总数的比值的平方根，也就是mse开根号，
% 用来衡量预测值同实际值之间的偏差）
% mape：平均绝对百分比误差（是预测值与实际值偏差绝对值与实际值的比值，取平均值的结果，可以消除量纲的影响，用于客观的评价偏差）
% error：误差
% errorPercent：相对误差
if nargin==2
if size(x1,2)==1
x1=x1'; %将列向量转换为行向量
end
if size(x2,2)==1
x2=x2'; %将列向量转换为行向量
end
num=size(x1,2);%统计样本总数
error=x2-x1; %计算误差
errorPercent=abs(error)./x1; %计算每个样本的绝对百分比误差
mae=sum(abs(error))/num; %计算平均绝对误差
mse=sum(error.*error)/num; %计算均方误差
rmse=sqrt(mse); %计算均方误差根
mape=mean(errorPercent); %计算平均绝对百分比误差
r=corrcoef(x1,x2);
R=r(1,2);
%结果输出
disp(['平均绝对误差mae为： ',num2str(mae)])
disp(['均方误差mse为： ',num2str(mse)])
disp(['均方误差根rmse为： ',num2str(rmse)])
disp(['平均绝对百分比误差mape为： ',num2str(mape*100),' %'])
disp(['拟合优度/关联系数R为： ',num2str(R)])
else
disp('函数调用方法有误，请检查输入参数的个数')
end
end
数据
结果
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