【优化算法】树种优化算法（TSA）【含Matlab源码 1429期】

原创

Matlab科研 2021-11-08 11:05:01 ©著作权

文章标签 matlab 算法开发语言优化算法搜索 文章分类 数据结构与算法人工智能

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二、树种优化算法简介

树种算法是一种通过模拟大树的繁殖方式来寻找最优解的元启发式优化算法。

在基本树种算法中,首先利用式(1)在搜索空间中生成一批树木:

Ti,j=Lj,min+ri,j(Hj,min-Lj,min) (1)

其中,Ti,j为树木的位置;Lj,min为搜索空间的下界;HLj,min为搜索空间的上界;ri,j是一个随机数,取值范围为[0,1]。

通过式(1)随机生成的树木中,并不是所有的树木产生种子的能力都一样强,针对最小化问题,需要利用式(2)找出位置最优的树。

【优化算法】树种优化算法（TSA）【含Matlab源码 1429期】_优化算法

接着,位置最优的树木会产生新的种子。在TSA中,为了平衡算法全局搜索和局部搜索的能力,提出两种机制来产生新的种子,如式(3)和式(4)所示。式(3)侧重于全局搜索,全局搜索可以避免算法在迭代过程中陷入局部最优。式(4)侧重于局部搜索,局部搜索有利于算法的收敛。

Si,j=Ti,j+αi,j(Ti,j-Tr,j) (3)

Si,j=Ti,j+αi,j(Bj-Tr,j) (4)

其中,Si,j为第i颗树上繁殖的第i颗种子的第j个元素,Ti,j是第i颗树上的第j个元素,是当前位置最优的树上的第j个元素,αi,j是步长因子,是一个属于[-1,1]的随机数。

位置最优树木在产生新种子的过程中,由搜索趋势常数ST来决定采用式(3)还是式(4),ST为一常数。

三、部分源代码


%%%  

clear all 
clc
SearchAgents=30; 
Fun_name='F1';  
Max_iterations=1000; 
[lowerbound,upperbound,dimension,fitness]=fun_info(Fun_name);
[Best_score,Best_pos,TSA_curve]=tsa(SearchAgents,Max_iterations,lowerbound,upperbound,dimension,fitness);


figure('Position',[400 400 560 190])

subplot(1,2,1);
func_plot(Fun_name);
title('Objective space')
xlabel('x_1');
ylabel('x_2');
zlabel([Fun_name,'( x_1 , x_2 )'])

subplot(1,2,2);
plots=semilogx(TSA_curve,'Color','g');
set(plots,'linewidth',2)
hold on
title('Objective space')
xlabel('Iterations');
ylabel('Best score');

axis tight
grid on
box on
legend('TSA')

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

%%% Designed and Developed by Dr. Gaurav Dhiman (http://dhimangaurav.com/) %%%

function [lowerbound,upperbound,dimension,fitness] = fun_info(F)


switch F
    case 'F1'
        fitness = @F1;
        lowerbound=-100;
        upperbound=100;
        dimension=30;
        
    case 'F2'
        fitness = @F2;
        lowerbound=-10;
        upperbound=10;
        dimension=30;
        
    case 'F3'
        fitness = @F3;
        lowerbound=-100;
        upperbound=100;
        dimension=30;
        
    case 'F4'
        fitness = @F4;
        lowerbound=-100;
        upperbound=100;
        dimension=30;
        
    case 'F5'
        fitness = @F5;
        lowerbound=-30;
        upperbound=30;
        dimension=30;
        
    case 'F6'
        fitness = @F6;
        lowerbound=-100;
        upperbound=100;
        dimension=30;
        
    case 'F7'
        fitness = @F7;
        lowerbound=-1.28;
        upperbound=1.28;
        dimension=30;
        
    case 'F8'
        fitness = @F8;
        lowerbound=-500;
        upperbound=500;
        dimension=30;
        
    case 'F9'
        fitness = @F9;
        lowerbound=-5.12;
        upperbound=5.12;
        dimension=30;
        
    case 'F10'
        fitness = @F10;
        lowerbound=-32;
        upperbound=32;
        dimension=30;
        
    case 'F11'
        fitness = @F11;
        lowerbound=-600;
        upperbound=600;
        dimension=30;
        
    case 'F12'
        fitness = @F12;
        lowerbound=-50;
        upperbound=50;
        dimension=30;
        
    case 'F13'
        fitness = @F13;
        lowerbound=-50;
        upperbound=50;
        dimension=30;
        
    case 'F14'
        fitness = @F14;
        lowerbound=-65.536;
        upperbound=65.536;
        dimension=2;
        
    case 'F15'
        fitness = @F15;
        lowerbound=-5;
        upperbound=5;
        dimension=4;
        
    case 'F16'
        fitness = @F16;
        lowerbound=-5;
        upperbound=5;
        dimension=2;
        
    case 'F17'
        fitness = @F17;
        lowerbound=[-5,0];
        upperbound=[10,15];
        dimension=2;
        
    case 'F18'
        fitness = @F18;
        lowerbound=-2;
        upperbound=2;
        dimension=2;
        
    case 'F19'
        fitness = @F19;
        lowerbound=0;
        upperbound=1;
        dimension=3;
        
    case 'F20'
        fitness = @F20;
        lowerbound=0;
        upperbound=1;
        dimension=6;     
        
    case 'F21'
        fitness = @F21;
        lowerbound=0;
        upperbound=10;
        dimension=4;    
        
    case 'F22'
        fitness = @F22;
        lowerbound=0;
        upperbound=10;
        dimension=4;    
        
    case 'F23'
        fitness = @F23;
        lowerbound=0;
        upperbound=10;
        dimension=4;            
end

end

% F1

function R = F1(x)
R=sum(x.^2);
end

% F2

function R = F2(x)
R=sum(abs(x))+prod(abs(x));
end

% F3

function R = F3(x)
dimension=size(x,2);
R=0;
for i=1:dimension
    R=R+sum(x(1:i))^2;
end
end

% F4

function R = F4(x)
R=max(abs(x));
end

% F5

function R = F5(x)
dimension=size(x,2);
R=sum(100*(x(2:dimension)-(x(1:dimension-1).^2)).^2+(x(1:dimension-1)-1).^2);
end

% F6

function R = F6(x)
R=sum(abs((x+.5)).^2);
end

% F7

function R = F7(x)
dimension=size(x,2);
R=sum([1:dimension].*(x.^4))+rand;
end

% F8

function R = F8(x)
R=sum(-x.*sin(sqrt(abs(x))));
end

% F9

function R = F9(x)
dimension=size(x,2);
R=sum(x.^2-10*cos(2*pi.*x))+10*dimension;
end

% F10

function R = F10(x)
dimension=size(x,2);
R=-20*exp(-.2*sqrt(sum(x.^2)/dimension))-exp(sum(cos(2*pi.*x))/dimension)+20+exp(1);
end

% F11

function R = F11(x)
dimension=size(x,2);
R=sum(x.^2)/4000-prod(cos(x./sqrt([1:dimension])))+1;
end

% F12

function R = F12(x)
dimension=size(x,2);
R=(pi/dimension)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)+sum((((x(1:dimension-1)+1)./4).^2).*...
(1+10.*((sin(pi.*(1+(x(2:dimension)+1)./4)))).^2))+((x(dimension)+1)/4)^2)+sum(Ufun(x,10,100,4));
end

% F13

function R = F13(x)
dimension=size(x,2);
R=.1*((sin(3*pi*x(1)))^2+sum((x(1:dimension-1)-1).^2.*(1+(sin(3.*pi.*x(2:dimension))).^2))+...
((x(dimension)-1)^2)*(1+(sin(2*pi*x(dimension)))^2))+sum(Ufun(x,5,100,4));
end

% F14

function R = F14(x)
aS=[-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32;,...
-32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 0 16 16 16 16 16 32 32 32 32 32];

for j=1:25
    bS(j)=sum((x'-aS(:,j)).^6);
end
R=(1/500+sum(1./([1:25]+bS))).^(-1);
end

% F15

function R = F15(x)
aK=[.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246];
bK=[.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK;
R=sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);
end

% F16

function R = F16(x)
R=4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+4*(x(2)^4);
end

% F17

function R = F17(x)
R=(x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*cos(x(1))+10;
end

% F18

function R = F18(x)
R=(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+3*x(2)^2))*...
    (30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*x(2)-36*x(1)*x(2)+27*(x(2)^2)));
end

% F19

function R = F19(x)
aH=[3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];
pH=[.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 .5743 .8828];
R=0;
for i=1:4
    R=R-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end

% F20

function R = F20(x)
aH=[10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 .05 10 .1 14];
cH=[1 1.2 3 3.2];
pH=[.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 .1004 .9991;...
.2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 .8732 .5743 .1091 .0381];
R=0;
for i=1:4
    R=R-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));
end
end