【优化算法】正弦余弦算法（SCA）【含Matlab源码 1308期】-一一网

一、正弦余弦算法简介

正弦余弦算法(Sine Cosine Algorithm, SCA)是一种新的群体智能优化算法，具有参数少、结构简单以及易实现等特点，因此，利用正弦和余弦函数的波动性和周期性进行迭代寻优。假设种群规模为M,即包含M个个体，每个个体的维度为D,那么，个体i在第j维的空间位置表示为Xij,i∈{1,2,…,M},j∈{1,2,…,D}。首先，在解空间内随机产生M个个体的初始位置，对应种群规模的大小。然后，计算每个个体的适应度值，并记录当前最优个体位置。最后，循环至满足终止条件，输出最优解。在每次迭代中，个体位置的更新表达式为
在这里插入图片描述
其中：Xij(t)为个体i在第t次迭代时的位置在第j维的分量；Pj(t)为第t次迭代种群当前最优个体在第j维的分量；r2∈[0,2π]、r3∈[0,2]和r4∈[0,1]为3个随机参数；r1为控制参数，随着迭代次数的增加从a递减到0,可表示为
在这里插入图片描述
其中：a为常数；t为当前的迭代次数；T为最大迭代次数。

二、部分源代码


clear all 
clc

SearchAgents_no=30; % Number of search agents

Function_name='F1'; % Name of the test function that can be from F1 to F23 (Table 1,2,3 in the paper)

Max_iteration=1000; % Maximum numbef of iterations

% Load details of the selected benchmark function
[lb,ub,dim,fobj]=Get_Functions_details(Function_name);

[Best_score,Best_pos,cg_curve]=SCA(SearchAgents_no,Max_iteration,lb,ub,dim,fobj);

figure('Position',[284   214   660   290])
%Draw search space
subplot(1,2,1);
func_plot(Function_name);
title('Test function')
xlabel('x_1');
ylabel('x_2');
zlabel([Function_name,'( x_1 , x_2 )'])
grid off

%Draw objective space
subplot(1,2,2);
semilogy(cg_curve,'Color','b')
title('Convergence curve')
xlabel('Iteration');
ylabel('Best flame (score) obtained so far');

axis tight
grid off
box on
legend('SCA')

display(['The best solution obtained by SCA is : ', num2str(Best_pos)]);
display(['The best optimal value of the objective funciton found by SCA is : ', num2str(Best_score)]);

 

function [Destination_fitness,Destination_position,Convergence_curve]=SCA(N,Max_iteration,lb,ub,dim,fobj)

display('SCA is optimizing your problem');

%Initialize the set of random solutions
X=initialization(N,dim,ub,lb);

Destination_position=zeros(1,dim);
Destination_fitness=inf;

Convergence_curve=zeros(1,Max_iteration);
Objective_values = zeros(1,size(X,1));

% Calculate the fitness of the first set and find the best one
for i=1:size(X,1)
    Objective_values(1,i)=fobj(X(i,:));
    if i==1
        Destination_position=X(i,:);
        Destination_fitness=Objective_values(1,i);
    elseif Objective_values(1,i)<Destination_fitness
        Destination_position=X(i,:);
        Destination_fitness=Objective_values(1,i);
    end
    
    All_objective_values(1,i)=Objective_values(1,i);
end

%Main loop
t=2; % start from the second iteration since the first iteration was dedicated to calculating the fitness
while t<=Max_iteration
    
    % Eq. (3.4)
    a = 2;
    Max_iteration = Max_iteration;
    r1=a-t*((a)/Max_iteration); % r1 decreases linearly from a to 0
    
    % Update the position of solutions with respect to destination
    for i=1:size(X,1) % in i-th solution
        for j=1:size(X,2) % in j-th dimension
            
            % Update r2, r3, and r4 for Eq. (3.3)
            r2=(2*pi)*rand();
            r3=2*rand;
            r4=rand();
            
            % Eq. (3.3)
            if r4<0.5
                % Eq. (3.1)
                X(i,j)= X(i,j)+(r1*sin(r2)*abs(r3*Destination_position(j)-X(i,j)));
            else
                % Eq. (3.2)
                X(i,j)= X(i,j)+(r1*cos(r2)*abs(r3*Destination_position(j)-X(i,j)));
            end
            
        end
    end
           

function func_plot(func_name)

[lb,ub,dim,fobj]=Get_Functions_details(func_name);

switch func_name 
    case 'F1' 
        x=-100:2:100; y=x; %[-100,100]
        
    case 'F2' 
        x=-100:2:100; y=x; %[-10,10]
        
    case 'F3' 
        x=-100:2:100; y=x; %[-100,100]
        
    case 'F4' 
        x=-100:2:100; y=x; %[-100,100]
    case 'F5' 
        x=-200:2:200; y=x; %[-5,5]
    case 'F6' 
        x=-100:2:100; y=x; %[-100,100]
    case 'F7' 
        x=-1:0.03:1;  y=x;  %[-1,1]
    case 'F8' 
        x=-500:10:500;y=x; %[-500,500]
    case 'F9' 
        x=-5:0.1:5;   y=x; %[-5,5]    
    case 'F10' 
        x=-20:0.5:20; y=x;%[-500,500]
    case 'F11' 
        x=-500:10:500; y=x;%[-0.5,0.5]
    case 'F12' 
        x=-10:0.1:10; y=x;%[-pi,pi]
    case 'F13' 
        x=-5:0.08:5; y=x;%[-3,1]
    case 'F14' 
        x=-100:2:100; y=x;%[-100,100]
    case 'F15' 
        x=-5:0.1:5; y=x;%[-5,5]
    case 'F16' 
        x=-1:0.01:1; y=x;%[-5,5]
    case 'F17' 
        x=-5:0.1:5; y=x;%[-5,5]
    case 'F18' 
        x=-5:0.06:5; y=x;%[-5,5]
    case 'F19' 
        x=-5:0.1:5; y=x;%[-5,5]
    case 'F20' 
        x=-5:0.1:5; y=x;%[-5,5]        
    case 'F21' 
        x=-5:0.1:5; y=x;%[-5,5]
    case 'F22' 
        x=-5:0.1:5; y=x;%[-5,5]     
    case 'F23' 
        x=-5:0.1:5; y=x;%[-5,5]  
end    

    

L=length(x);
f=[];

for i=1:L
    for j=1:L
        if strcmp(func_name,'F15')==0 && strcmp(func_name,'F19')==0 && strcmp(func_name,'F20')==0 && strcmp(func_name,'F21')==0 && strcmp(func_name,'F22')==0 && strcmp(func_name,'F23')==0
            f(i,j)=fobj([x(i),y(j)]);
        end
        if strcmp(func_name,'F15')==1
            f(i,j)=fobj([x(i),y(j),0,0]);
        end
        if strcmp(func_name,'F19')==1
            f(i,j)=fobj([x(i),y(j),0]);
        end
        if strcmp(func_name,'F20')==1
            f(i,j)=fobj([x(i),y(j),0,0,0,0]);
        end       
        if strcmp(func_name,'F21')==1 || strcmp(func_name,'F22')==1 ||strcmp(func_name,'F23')==1
            f(i,j)=fobj([x(i),y(j),0,0]);
        end          
    end
end



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