%---------------------------------------------------------------------------------------------------------------------------
% Author, inventor and programmer: Iman Ahmadianfar,
% Assistant Professor, Department of Civil Engineering, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran
% Researchgate: https://www.researchgate.net/profile/Iman_Ahmadianfar
% e-Mail: im.ahmadian@gmail.com, i.ahmadianfar@bkatu.ac.ir,
%---------------------------------------------------------------------------------------------------------------------------
% Co-author:
% Omid Bozorg-Haddad(OBHaddad@ut.ac.ir)
% Xuefeng Chu(xuefeng.chu@ndsu.edu)
%---------------------------------------------------------------------------------------------------------------------------
% Please refer to the main paper:
% Gradient-Based Optimizer: A New Metaheuristic Optimization Algorithm
% SIman Ahmadianfar, Omid Bozorg-Haddad, Xuefeng Chu
% Information Sciences,2020
% DOI: https://doi.org/10.1016/j.ins.2020.06.037
% https://www.sciencedirect.com/science/article/pii/S0020025520306241
% ------------------------------------------------------------------------------------------------------------
% Website of GBO: http://imanahmadianfar.com/
% You can find and run the GBO code online at http://imanahmadianfar.com/
% You can find the GBO paper at https://doi.org/10.1016/j.ins.2020.06.037
% Please follow the paper for related updates in researchgate: https://www.researchgate.net/profile/Iman_Ahmadianfar
%---------------------------------------------------------------------------------------------------------------------------
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [Best_Cost,Best_X,Convergence_curve]=GBO(nP,MaxIt,lb,ub,dim,fobj)
%% Initialization
nV = dim; % Number f Variables
pr = 0.5; % Probability Parameter
lb = ones(1,dim).*lb; % lower boundary
ub = ones(1,dim).*ub; % upper boundary
Cost = zeros(nP,1);
X = initialization(nP,nV,ub,lb); %Initialize the set of random solutions
Convergence_curve = zeros(1,MaxIt);
for i=1:nP
Cost(i) = fobj(X(i,:)); % Calculate the Value of Objective Function
end
[~,Ind] = sort(Cost);
Best_Cost = Cost(Ind(1)); % Determine the vale of Best Fitness
Best_X = X(Ind(1),:);
Worst_Cost=Cost(Ind(end)); % Determine the vale of Worst Fitness
Worst_X=X(Ind(end),:);
%% Main Loop
for it=1:MaxIt
beta = 0.2+(1.2-0.2)*(1-(it/MaxIt)^3)^2; % Eq.(14.2)
alpha = abs(beta.*sin((3*pi/2+sin(3*pi/2*beta)))); % Eq.(14.1)
for i=1:nP
A1 = fix(rand(1,nP)*nP)+1; % Four positions randomly selected from population
r1 = A1(1);r2 = A1(2);
r3 = A1(3);r4 = A1(4);
Xm = (X(r1,:)+X(r2,:)+X(r3,:)+X(r4,:))/4; % Average of Four positions randomly selected from population
ro = alpha.*(2*rand-1);ro1 = alpha.*(2*rand-1);
eps = 5e-3*rand; % Randomization Epsilon
DM = rand.*ro.*(Best_X-X(r1,:));Flag = 1; % Direction of Movement Eq.(18)
GSR=GradientSearchRule(ro1,Best_X,Worst_X,X(i,:),X(r1,:),DM,eps,Xm,Flag);
DM = rand.*ro.*(Best_X-X(r1,:));
X1 = X(i,:) - GSR + DM; % Eq.(25)
DM = rand.*ro.*(X(r1,:)-X(r2,:));Flag = 2;
GSR=GradientSearchRule(ro1,Best_X,Worst_X,X(i,:),X(r1,:),DM,eps,Xm,Flag);
DM = rand.*ro.*(X(r1,:)-X(r2,:));
X2 = Best_X - GSR + DM; % Eq.(26)
Xnew=zeros(1,nV);
for j=1:nV
ro=alpha.*(2*rand-1);
X3=X(i,j)-ro.*(X2(j)-X1(j));
ra=rand;rb=rand;
Xnew(j) = ra.*(rb.*X1(j)+(1-rb).*X2(j))+(1-ra).*X3; % Eq.(27)
end
% Local escaping operator(LEO) % Eq.(28)
if rand<pr
k = fix(rand*nP)+1;
f1 = -1+(1-(-1)).*rand();f2 = -1+(1-(-1)).*rand();
ro = alpha.*(2*rand-1);
Xk = unifrnd(lb,ub,1,nV);%lb+(ub-lb).*rand(1,nV); % Eq.(28.8)
L1=rand<0.5;u1 = L1.*2*rand+(1-L1).*1;u2 = L1.*rand+(1-L1).*1;
u3 = L1.*rand+(1-L1).*1;
L2=rand<0.5;
Xp = (1-L2).*X(k,:)+(L2).*Xk; % Eq.(28.7)
if u1<0.5
Xnew = Xnew + f1.*(u1.*Best_X-u2.*Xp)+f2.*ro.*(u3.*(X2-X1)+u2.*(X(r1,:)-X(r2,:)))/2;
else
Xnew = Best_X + f1.*(u1.*Best_X-u2.*Xp)+f2.*ro.*(u3.*(X2-X1)+u2.*(X(r1,:)-X(r2,:)))/2;
end
end
% Check if solutions go outside the search space and bring them back
Flag4ub=Xnew>ub;
Flag4lb=Xnew<lb;
Xnew=(Xnew.*(~(Flag4ub+Flag4lb)))+ub.*Flag4ub+lb.*Flag4lb;
Xnew_Cost = fobj(Xnew);
% Update the Best Position
if Xnew_Cost<Cost(i)
X(i,:)=Xnew;
Cost(i)=Xnew_Cost;
if Cost(i)<Best_Cost
Best_X=X(i,:);
Best_Cost=Cost(i);
end
end
% Update the Worst Position
if Cost(i)>Worst_Cost
Worst_X= X(i,:);
Worst_Cost= Cost(i);
end
end
Convergence_curve(it) = Best_Cost;
% Show Iteration Information
disp(['Iteration ' num2str(it) ': Best Fitness = ' num2str(Convergence_curve(it))]);
end
end
% _________________________________________________
% Gradient Search Rule
function GSR=GradientSearchRule(ro1,Best_X,Worst_X,X,Xr1,DM,eps,Xm,Flag)
nV = size(X,2);
Delta = 2.*rand.*abs(Xm-X); % Eq.(16.2)
Step = ((Best_X-Xr1)+Delta)/2; % Eq.(16.1)
DelX = rand(1,nV).*(abs(Step)); % Eq.(16)
GSR = randn.*ro1.*(2*DelX.*X)./(Best_X-Worst_X+eps); % Gradient search rule Eq.(15)
if Flag == 1
Xs = X - GSR + DM; % Eq.(21)
else
Xs = Best_X - GSR + DM;
end
yp = rand.*(0.5*(Xs+X)+rand.*DelX); % Eq.(22.6)
yq = rand.*(0.5*(Xs+X)-rand.*DelX); % Eq.(22.7)
GSR = randn.*ro1.*(2*DelX.*X)./(yp-yq+eps); % Eq.(23)
end
