算術優化算法（Matlab代碼實作）

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⛳️座右銘：行百裡者，半于九十。

目錄

​​💥1 概述​​

​​📚2 運作結果​​

​​🎉3 參考文獻​​

​​🌈4 Matlab代碼實作​​

💥1 概述

  算術優化算法 （AOA），利用數學中主要算術運算符的分布行為，包括（乘法 （M）、除法 （D）、減法 （S） 和加法 （A））。AOA經過數學模組化和實施，以優化各種問題。

📚2 運作結果

🎉3 參考文獻

function [Best_FF,Best_P,Conv_curve]=AOA(N,M_Iter,LB,UB,Dim,F_obj)
 display('AOA Working');
 %Two variables to keep the positions and the fitness value of the best-obtained solutionBest_P=zeros(1,Dim);
 Best_FF=inf;
 Conv_curve=zeros(1,M_Iter);%Initialize the positions of solution
 X=initialization(N,Dim,UB,LB);
 Xnew=X;
 Ffun=zeros(1,size(X,1));% (fitness values)
 Ffun_new=zeros(1,size(Xnew,1));% (fitness values)MOP_Max=1;
 MOP_Min=0.2;
 C_Iter=1;
 Alpha=5;
 Mu=0.499; for i=1:size(X,1)
     Ffun(1,i)=F_obj(X(i,:));  %Calculate the fitness values of solutions
     if Ffun(1,i)<Best_FF
         Best_FF=Ffun(1,i);
         Best_P=X(i,:);
     end
 end
     
     while C_Iter<M_Iter+1  %Main loop
     MOP=1-((C_Iter)^(1/Alpha)/(M_Iter)^(1/Alpha));   % Probability Ratio 
     MOA=MOP_Min+C_Iter*((MOP_Max-MOP_Min)/M_Iter); %Accelerated function
    
     %Update the Position of solutions
     for i=1:size(X,1)   % if each of the UB and LB has a just value 
         for j=1:size(X,2)
            r1=rand();
             if (size(LB,2)==1)
                 if r1<MOA
                     r2=rand();
                     if r2>0.5
                         Xnew(i,j)=Best_P(1,j)/(MOP+eps)*((UB-LB)*Mu+LB);
                     else
                         Xnew(i,j)=Best_P(1,j)*MOP*((UB-LB)*Mu+LB);
                     end
                 else
                     r3=rand();
                     if r3>0.5
                         Xnew(i,j)=Best_P(1,j)-MOP*((UB-LB)*Mu+LB);
                     else
                         Xnew(i,j)=Best_P(1,j)+MOP*((UB-LB)*Mu+LB);
                     end
                 end               
             end
             
            
             if (size(LB,2)~=1)   % if each of the UB and LB has more than one value 
                 r1=rand();
                 if r1<MOA
                     r2=rand();
                     if r2>0.5
                         Xnew(i,j)=Best_P(1,j)/(MOP+eps)*((UB(j)-LB(j))*Mu+LB(j));
                     else
                         Xnew(i,j)=Best_P(1,j)*MOP*((UB(j)-LB(j))*Mu+LB(j));
                     end
                 else
                     r3=rand();
                     if r3>0.5
                         Xnew(i,j)=Best_P(1,j)-MOP*((UB(j)-LB(j))*Mu+LB(j));
                     else
                         Xnew(i,j)=Best_P(1,j)+MOP*((UB(j)-LB(j))*Mu+LB(j));
                     end
                 end               
             end
             
         end
         
         Flag_UB=Xnew(i,:)>UB; % check if they exceed (up) the boundaries
         Flag_LB=Xnew(i,:)<LB; % check if they exceed (down) the boundaries
         Xnew(i,:)=(Xnew(i,:).*(~(Flag_UB+Flag_LB)))+UB.*Flag_UB+LB.*Flag_LB;
  
         Ffun_new(1,i)=F_obj(Xnew(i,:));  % calculate Fitness function 
         if Ffun_new(1,i)<Ffun(1,i)
             X(i,:)=Xnew(i,:);
             Ffun(1,i)=Ffun_new(1,i);
         end
         if Ffun(1,i)<Best_FF
         Best_FF=Ffun(1,i);
         Best_P=X(i,:);
         end
        
     end
         %Update the convergence curve
     Conv_curve(C_Iter)=Best_FF;
     
     %Print the best solution details after every 50 iterations
     if mod(C_Iter,50)==0
         display(['At iteration ', num2str(C_Iter), ' the best solution fitness is ', num2str(Best_FF)]);
     end
      
     C_Iter=C_Iter+1;  % incremental iteration
    
 end      

​​🌈​​4 Matlab代碼實作