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%--------------------------------------------------------------------------------------------------------------------------- % RUNge Kutta optimizer (RUN) % RUN Beyond the Metaphor: An Efficient Optimization Algorithm Based on Runge Kutta Method % Codes of RUN:http://imanahmadianfar.com/codes/ % Website of RUN:http://www.aliasgharheidari.com/RUN.html % Iman Ahmadianfar, Ali asghar Heidari, Amir H. Gandomi , Xuefeng Chu, and Huiling Chen % Last update: 04-22-2021 % e-Mail: im.ahmadian@gmail.com,i.ahmadianfar@bkatu.ac.ir. % e-Mail: as_heidari@ut.ac.ir, aliasghar68@gmail.com, % e-Mail (Singapore): aliasgha@comp.nus.edu.sg, t0917038@u.nus.edu %--------------------------------------------------------------------------------------------------------------------------- % Co-author: Ali Asghar Heidari(as_heidari@ut.ac.ir),Amir H Gandomi,Xuefeng Chu, Huiling Chen(chenhuiling.jlu@gmail.com), %--------------------------------------------------------------------------------------------------------------------------- % After use, please refer to the main paper: % Iman Ahmadianfar, Ali Asghar Heidari,Amir H Gandomi,Xuefeng Chu,Huiling Chen, % RUN Beyond the Metaphor: An Efficient Optimization Algorithm Based on Runge Kutta Method % Expert Systems With Applications, 2021, 115079, https://doi.org/10.1016/j.eswa.2021.115079 (Q1, 5-Year Impact Factor: 5.448, H-INDEX: 184) %--------------------------------------------------------------------------------------------------------------------------- % You can also follow the paper for related updates in researchgate: https://www.researchgate.net/profile/Iman_Ahmadianfar % Researchgate: https://www.researchgate.net/profile/Ali_Asghar_Heidari. % Website of RUN:% http://www.aliasgharheidari.com/RUN.html % You can also use and compare with our other new optimization methods: %(GBO)-2020-http://www.imanahmadianfar.com/codes. %(HGS)-2021- http://www.aliasgharheidari.com/HGS.html %(SMA)-2020- http://www.aliasgharheidari.com/SMA.html %(HHO)-2019- http://www.aliasgharheidari.com/HHO.html %--------------------------------------------------------------------------------------------------------------------------- function [Best_Cost,Best_X,Convergence_curve]=RUN(nP,MaxIt,lb,ub,dim,fobj) Cost=zeros(nP,1); % Record the Fitness of all Solutions X=initialization(nP,dim,ub,lb); % Initialize the set of random solutions Xnew2=zeros(1,dim); Convergence_curve = zeros(1,MaxIt); for i=1:nP Cost(i) = fobj(X(i,:)); % Calculate the Value of Objective Function end [Best_Cost,ind] = min(Cost); % Determine the Best Solution Best_X = X(ind,:); Convergence_curve(1) = Best_Cost; %% Main Loop of RUN it=1;%Number of iterations while it<MaxIt it=it+1; f=20.*exp(-(12.*(it/MaxIt))); % (Eq.17.6) Xavg = mean(X); % Determine the Average of Solutions SF=2.*(0.5-rand(1,nP)).*f; % Determine the Adaptive Factor (Eq.17.5) for i=1:nP [~,ind_l] = min(Cost); lBest = X(ind_l,:); [A,B,C]=RndX(nP,i); % Determine Three Random Indices of Solutions [~,ind1] = min(Cost([A B C])); % Determine Delta X (Eqs. 11.1 to 11.3) gama = rand.*(X(i,:)-rand(1,dim).*(ub-lb)).*exp(-4*it/MaxIt); Stp=rand(1,dim).*((Best_X-rand.*Xavg)+gama); DelX = 2*rand(1,dim).*(abs(Stp)); % Determine Xb and Xw for using in Runge Kutta method if Cost(i)<Cost(ind1) Xb = X(i,:); Xw = X(ind1,:); else Xb = X(ind1,:); Xw = X(i,:); end SM = RungeKutta(Xb,Xw,DelX); % Search Mechanism (SM) of RUN based on Runge Kutta Method L=rand(1,dim)<0.5; Xc = L.*X(i,:)+(1-L).*X(A,:); % (Eq. 17.3) Xm = L.*Best_X+(1-L).*lBest; % (Eq. 17.4) vec=[1,-1]; flag = floor(2*rand(1,dim)+1); r=vec(flag); % An Interger number g = 2*rand; mu = 0.5+.1*randn(1,dim); % Determine New Solution Based on Runge Kutta Method (Eq.18) if rand<0.5 Xnew = (Xc+r.*SF(i).*g.*Xc) + SF(i).*(SM) + mu.*(Xm-Xc); else Xnew = (Xm+r.*SF(i).*g.*Xm) + SF(i).*(SM)+ mu.*(X(A,:)-X(B,:)); end % Check if solutions go outside the search space and bring them back FU=Xnew>ub;FL=Xnew<lb;Xnew=(Xnew.*(~(FU+FL)))+ub.*FU+lb.*FL; CostNew=fobj(Xnew); if CostNew<Cost(i) X(i,:)=Xnew; Cost(i)=CostNew; end %% Enhanced solution quality (ESQ) (Eq. 19) if rand<0.5 EXP=exp(-5*rand*it/MaxIt); r = floor(Unifrnd(-1,2,1,1)); u=2*rand(1,dim); w=Unifrnd(0,2,1,dim).*EXP; %(Eq.19-1) [A,B,C]=RndX(nP,i); Xavg=(X(A,:)+X(B,:)+X(C,:))/3; %(Eq.19-2) beta=rand(1,dim); Xnew1 = beta.*(Best_X)+(1-beta).*(Xavg); %(Eq.19-3) for j=1:dim if w(j)<1 Xnew2(j) = Xnew1(j)+r*w(j)*abs((Xnew1(j)-Xavg(j))+randn); else Xnew2(j) = (Xnew1(j)-Xavg(j))+r*w(j)*abs((u(j).*Xnew1(j)-Xavg(j))+randn); end end FU=Xnew2>ub;FL=Xnew2<lb;Xnew2=(Xnew2.*(~(FU+FL)))+ub.*FU+lb.*FL; CostNew=fobj(Xnew2); if CostNew<Cost(i) X(i,:)=Xnew2; Cost(i)=CostNew; else if rand<w(randi(dim)) SM = RungeKutta(X(i,:),Xnew2,DelX); Xnew = (Xnew2-rand.*Xnew2)+ SF(i)*(SM+(2*rand(1,dim).*Best_X-Xnew2)); % (Eq. 20) FU=Xnew>ub;FL=Xnew<lb;Xnew=(Xnew.*(~(FU+FL)))+ub.*FU+lb.*FL; CostNew=fobj(Xnew); if CostNew<Cost(i) X(i,:)=Xnew; Cost(i)=CostNew; end end end end % End of ESQ %% Determine the Best Solution if Cost(i)<Best_Cost Best_X=X(i,:); Best_Cost=Cost(i); end end % Save Best Solution at each iteration Convergence_curve(it) = Best_Cost; disp(['it : ' num2str(it) ', Best Cost = ' num2str(Convergence_curve(it) )]); end end % A funtion to determine a random number %with uniform distribution (unifrnd function in Matlab) function z=Unifrnd(a,b,c,dim) a2 = a/2; b2 = b/2; mu = a2+b2; sig = b2-a2; z = mu + sig .* (2*rand(c,dim)-1); end % A function to determine thress random indices of solutions function [A,B,C]=RndX(nP,i) Qi=randperm(nP);Qi(Qi==i)=[]; A=Qi(1);B=Qi(2);C=Qi(3); end