Fractal Evolutionary algorithm de

%  Differential Evolutionary algorithm program  function DE       t0 = cputime;   % Timing     %%  Population initialization     T = 1000;                %  Maximum number of iterations       F0 = 0.5;                %  Mutation Rate      N = 100;                 %  Population size      D =  10;                 %   number of chromosomes in each individual, that is, the dimensionality of the problem to be asked      CR = 0.3;                %  Crossover Rate       Tmin  = zeros (1,t);  &nThe optimal value       bestx = zeros (T,D) for the bsp;    %  of the adaptive function of each generation The optimal Solution       value = zeros (1,N) for each generation of;     % ;       %%  applicable degree function:rastrigr  function minimum value     function y  = f (x)          y = sum (x.^2 - 10.* cos (2.*pi.*x)  + 10);       end      %%   Generate initial population       %  set boundaries       xmin =  -5.12;      xmax = 5.12;      x0  =  (xmax-xmin) *rand (n,d)  + xMin;  % N-by-D       xg = x0;      xg_next_1= zeros (N,D);       % initialization, storage mutation operationIntermediate value N-by-d        xg_next_2 = zeros (N,D);      % Initialize, store cross-operation intermediate value n-by-d        for t=1:t         %%  mutation Operation         for i  = 1:N  %  represents the first individual              % produces j,k,p three different numbers             dx =  Randperm (N);               r1 = &NBSP;DX (1);               r2 = &NBSP;DX (2);               r3 = &NBSP;DX (3);              % to make sure it differs from I                if r1 == i         &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;R1&NBSP;&NBSP;=&NBSP;DX (4);                   else if r2  == i                &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;R2&NBSP;=&NBSP;DX (4);                       else if  r3 == i               &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;R3&NBSP;=&NBSP;DX (4);                        end                  end                end               %  self-applicable mutation operator                suanzi = exp (1-t/(t + 1-t));               F = F0*2.^suanzi;               %  mutated individuals from three random parents      &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;&NBSP;H&NBSP;=&NBSP;XG (R1,:)  + f* (XG (R2,:)  - &NBSP;XG (R3,:));             %  examines individual variants, Prevent variation beyond the boundary             for j = 1:  d    &nbSp;           if h (j)  >xMin   & h (j)  < xMax    %  within the boundaries                          xg _next_1 (I,j)  = h (j);                   else  % out of boundary range                      xg_next_1 (i,j)  =  (xMax -  xmin) *rand + xmin;                   end               end          end          %%  cross-operation         for i = 1: N               dx = randperm (D);     % [1,2,3,... D] Random sequence                   for j = 1: d              &NBSP;&NBSP;&NBSP;&NBSP;&NBSP;IF&NBSP;RAND&NBSP;&LT;&NBSP;CR&NBSP;&NBSP;%&NBSP;&AMP;&NBSP;DX (1)  ~= j  % CR = 0.9                          xg_next_2 (i,j)  = XG_next_1 (i , j);                else                   &nBsp;   xg_next_2 (i,j)  = xg (i,j);                                    end               end          end          %%  Select operations           for i = 1:n               If f (Xg_next_2 (i,:))  <= f (XG (i,:))                   xg (i,:)  = xg_next_2 (i,:);             end        end         %%  finding the best value per generation         for i = 1:N               value (i)  = f (XG (i,:));           end          [value_min,pos_min] = min (value);         % The minimum value of the objective function in generation           tmin (t)  = value_min;              % Save the best individuals            bestx (t,:)  = xg (pos_min,:);          trace (t,1)  = t;          trace (t,2)  = value_min;          t = t +  1;      end    %%  Global Optimal value: Output     [value_min,pos_min] = min ( Tmin);      best_value = value_min       Best_vector =  bestx (Pos_min,:)         fprintf (' The time spent by de is:%f \n ', cputime - t0);       % plot the relationship between algebra and optimal function values          plot (Trace (:, 1), Trace (:, 2));  end

Output Result:

Best_value =

0

Best_vector =

1.0E-08 *

-0.1568-0.1476-0.0155 0.0578-0.0721-0.1532 0.1067 0.0799-0.0818-0.0518

The de is time consuming: 2.640625

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Fractal Evolutionary algorithm de