% Weighted Superposition Attraction (WSA): A swarm intelligence algorithm for optimization problems

% by Adil Baykasoglu and Sener Akpinar

% Matlab code of WSA for Schaffer1 (SF1) function

clc;

clear all;

close all;

%-------PARAMETERS-------

indiv=100;

Maxiter=150;

step=0.035;

Fi=0.0001;

lamda=-0.8;

%------FUNCTION DATA-----

dim=2;

UL=100;

LL=-100;

%------OTHER VARIABLES----

iteration=1;

TT=3;

BF=zeros(1,Maxiter);

I=zeros(1,Maxiter);

best_solution=zeros(1,dim);

best_fitness=100000000;

file=fopen('individuals.dat','w');

file1=fopen('best_individual.dat','w');

%**********************3-D PLOT AND CONTOUR PLOT OF SF1********************

[x,y] = meshgrid(-100:200/100:100,-100:200/100:100);

a=sin(sqrt(x.^2+y.^2)).^2-0.5;

b=(1+0.001*(x.^2+y.^2)).^2;

sum = a./b;

sum = sum +0.5;

z=sum;

figure(1)

surf(x,y,z);

xlabel('x1','fontSize',14);

ylabel('x2','fontSize',14);

zlabel('f(x1,x2)','fontSize',14)

title('Schaffer 1','fontSize',14);

shading interp;

figure(2)

contour(x,y,z);

xlabel('x1','fontSize',14);

ylabel('x2','fontSize',14);

title('Initial Individuals','fontSize',14);

%**************************************************************************

tic %STARTS EXECUTION TIME

initial=LL+rand(indiv,dim)*(UL-LL);%GENERATES INITIAL SOLUTIONS

%**********************FITNESS EVALUATION**********************************

fitness=zeros(1,indiv);

for i=1:indiv

fact1 = (sin(sqrt(initial(i,1)^2-initial(i,2))^2))^2 - 0.5;

fact2 = (1 + 0.001*(initial(i,1)^2+initial(i,2)^2))^2;

fitness(1,i) = 0.5 + fact1/fact2;

if (best_fitness>fitness(1,i))

best_fitness=fitness(1,i);

best_solution(1,:)=initial(i,:);

end

%**************************************************************************

%*****************SCATTERING INITIAL INDIVIDUALS ON CONTOUR PLOT***********

for i=1:indiv

text(initial(i,1),initial(i,2),fitness(1,i),'*','FontSize',20, 'Color', [0 0 0]);

end

%**************************************************************************

%*********RANKING OF INITIAL SOLUTIONS WITH REGARD TO FITNESS VALUES*******

for k=1:indiv

ek = fitness(1,k);

i = k;

for j=k+1:indiv

if (fitness(1,j)<ek)

ek = fitness(1,j);

i = j;

end

temp=zeros(1,dim);

for j=1:dim

temp(1,j)=initial(k,j);

initial(k,j)=initial(i,j);

initial(i,j)=temp(1,j);

end

fitness(1,i)=fitness(1,k);

fitness(1,k)=ek;

end

%**************************************************************************

%****************WRITING INITIAL INDIVIDUALS TO A FILE*********************

fprintf(file,'Initial Individuals\n');

fprintf(file,'------------------\n');

for i=1:indiv

for j=1:dim

fprintf(file,'%g\t',initial(i,j));

end

fprintf(file,'\tFitness=%g\n',fitness(1,i));

end

%**************************************************************************

while iteration<=Maxiter

%********************DETERMINATION OF AGGREGATE VECTOR*********************

weight=zeros(1,indiv);

aggre=zeros(1,dim);

for i=1:indiv

weight(1,i)=i^(lamda);

for j=1:dim

aggre(1,j)=(aggre(1,j)+initial(i,j))*weight(1,i);

end

%**************************************************************************

%***************FITNESS EVALUATION OF AGGREGATE VECTOR*********************

fact1 = (sin(sqrt(aggre(1,1)^2-aggre(1,2)^2)))^2 - 0.5;

fact2 = (1 + 0.001*(aggre(1,1)^2+aggre(1,2)^2))^2;

f_aggre = 0.5 + fact1/fact2;

%**************************************************************************

%*********************DIRECTION DETERMINATION******************************

product_1=zeros(indiv,dim);

direction=zeros(indiv,dim);

for i=1:indiv

if fitness(i)>=f_aggre

for j=1:dim

product_1(i,j)=aggre(1,j)-initial(i,j);

end

for d=1:dim

direction(i,d)=sign(product_1(i,d));

end

elseif fitness(i)<f_aggre

if rand()<exp(fitness(i)-f_aggre)

for j=1:dim

product_1(i,j)=aggre(1,j)-initial(i,j);

end

for d=1:dim

direction(i,d)=sign(product_1(i,d));

end

else

for d=1:dim

direction(i,d)= sign(-1 + (1+1)*rand());

end

%**************************************************************************

%***********************MOVEMENT OF INDIVIDUALS****************************

A=iteration/(iteration+1);

B=exp(-A);

r=rand();

if r<=0.95

step=step-B*Fi*step;

else

step=step+B*Fi*step;

end

for i=1:indiv

for d=1:dim

initial(i,d)=initial(i,d)+step*direction(i,d)*abs(initial(i,d));

if initial (i,d)<LL

initial(i,d)=LL;

elseif initial(i,d)>UL

initial(i,d)=UL;

end

%**************************************************************************

%**********************FITNESS EVALUATION**********************************

fitness=zeros(1,indiv);

for i=1:indiv

fact1 = (sin(sqrt(initial(i,1)^2-initial(i,2))^2))^2 - 0.5;

fact2 = (1 + 0.001*(initial(i,1)^2+initial(i,2)^2))^2;

fitness(1,i) = 0.5 + fact1/fact2;

if (best_fitness>fitness(1,i))

best_fitness=fitness(1,i);

best_solution(1,:)=initial(i,:);

end

%**************************************************************************

%**************RANKING SOLUTIONS WITH REGARD TO FITNESS VALUES*************

for k=1:indiv

ek = fitness(1,k);

i = k;

for j=k+1:indiv

if (fitness(1,j)<ek)

ek = fitness(1,j);

i = j;

end

temp=zeros(1,dim);

for j=1:dim

temp(1,j)=initial(k,j);

initial(k,j)=initial(i,j);

initial(i,j)=temp(1,j);

end

fitness(1,i)=fitness(1,k);

fitness(1,k)=ek;

end

%**************************************************************************

%WRITING INDIVIDUALS OF A DESIRED ITERATION TO A FILE AND DRAW CONTOUR PLOT

if(mod(iteration,15)==0)

fprintf(file,'\nIndividuals of %d.Iteration\n', iteration);

fprintf(file,'------------------\n');

for i=1:indiv

for j=1:dim

fprintf(file,'%e\t',initial(i,j));

end

fprintf(file,'\tFitness=%g\n',fitness(1,i));

end

TT=TT+1;

figure(TT)

contour(x,y,z);

xlabel('x1','fontSize',14);

ylabel('x2','fontSize',14);

tit=strcat({'Individuals of '},{num2str(iteration)},{'.Iteration'});

title(tit,'FontSize',14)

for i=1:indiv

text(initial(i,1),initial(i,2),fitness(1,i),'*','FontSize',20, 'Color', [0 0 0]);

end

%**************************************************************************

%************WRITING BEST FITNESS AND BEST INDIVIDUAL TO A FILE************

fprintf(file1,'%d. ITERATION\n\nBEST FITNESS=%e\n\n',iteration, best_fitness);

fprintf(file1,'BEST SOLUTION:\n\n');

for j=1:dim

fprintf(file1,'%g\t',best_solution(1,j));

end

fprintf(file1,'\n\n-----------------------------\n\n');

%**************************************************************************

BF(1,iteration)=best_fitness;

I(1,iteration)=iteration;

iteration=iteration+1;

end

fclose(file);

fclose(file1);

toc%END OF EXECUTION TIME

%******************PLOTTING BEST FITNESS VERSUS ITERATION******************

figure (3)

plot(I,BF);

xlabel('Iteration Number','fontSize',14);

ylabel('Fitness Value','fontSize',14);

%**************************************************************************