% --------------------------------------------------------------------% % Flower pollenation algorithm (FPA), or flower algorithm % % Programmed by Xin-She Yang @ May 2012 % % --------------------------------------------------------------------% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %% % Notes: This demo program contains the very basic components of % % the flower pollination algorithm (FPA), or flower algorithm (FA), % % for single objective optimization. It usually works well for % % unconstrained functions only. For functions/problems with % % limits/bounds and constraints, constraint-handling techniques % % should be implemented to deal with constrained problems properly. % % % % Citation details: % % 1 )Xin-She Yang, Flower pollination algorithm for global optimization,% % Unconventional Computation and Natural Computation, % % Lecture Notes in Computer Science, Vol. 7445 , pp. 240 - 249 ( 2012 ). % % 2 )X. S. Yang, M. Karamanoglu, X. S. He, Multi-objective flower % % algorithm for optimization, Procedia in Computer Science, % % vol. 18 , pp. 861 - 868 ( 2013 ). % %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %%% %% clc clear all close all n=30; % Population size, typically 10 to 25 p= 0 . 8 ; % probabibility switch % Iteration parameters N_iter= 3000 ; % Total number of iterations fitnessMSE = ones( 1 ,N_iter); % % Dimension of the search variables Example 1 d= 2 ; Lb = - 1 *ones( 1 ,d); Ub = 1 *ones( 1 ,d); % % Dimension of the search variables Example 2 % d= 3 ; % Lb = [- 2 - 1 - 1 ]; % Ub = [ 2 1 1 ]; % % % Dimension of the search variables Example 3 % d= 3 ; % Lb = [- 1 - 1 - 1 ]; % Ub = [ 1 1 1 ]; % % % % % Dimension of the search variables Example 4 % d= 9 ; % Lb = - 1.5 *ones( 1 ,d); % Ub = 1.5 *ones( 1 ,d); % Initialize the population/solutions for i= 1 :n , Sol(i, : )=Lb+(Ub-Lb).*rand( 1 ,d); % To simulate the filters use fitnessX() functions in the next line Fitness(i)=fitness(Sol(i, : )); end % Find the current best [fmin,I]=min(Fitness); best=Sol(I, : ); S=Sol; % Start the iterations -- Flower Algorithm for t= 1 :N_iter , % Loop over all bats/solutions for i= 1 :n , % Pollens are carried by insects and thus can move in % large scale, large distance. % This L should replace by Levy flights % Formula: x_i^{t+ 1 }=x_i^t+ L (x_i^t-gbest) if rand>p, %% L=rand; L=Levy(d); dS=L.*(Sol(i,:)-best); S(i,:)=Sol(i,:)+dS; % Check if the simple limits/bounds are OK S(i, : )=simplebounds(S(i, : ),Lb,Ub); % If not , then local pollenation of neighbor flowers else epsilon=rand; % Find random flowers in the neighbourhood JK=randperm(n); % As they are random, the first two entries also random % If the flower are the same or similar species, then % they can be pollenated, otherwise, no action. % Formula: x_i^{t+ 1 }+epsilon*(x_j^t-x_k^t) S(i, : )=S(i, : )+epsilon*(Sol(JK( 1 ), : )-Sol(JK( 2 ), : )); % Check if the simple limits/bounds are OK S(i, : )=simplebounds(S(i, : ),Lb,Ub); end % Evaluate new solutions % To simulate the filters use fitnessX() functions in the next % line Fnew=fitness(S(i, : )); % If fitness improves (better solutions found), update then if (Fnew<=Fitness(i)), Sol(i, : )=S(i, : ); Fitness(i)=Fnew; end % Update the current global best if Fnew<=fmin, best=S(i, : ) ; fmin=Fnew ; end end % Display results every 100 iterations if round(t/ 100 )==t/ 100 , best fmin end fitnessMSE(t) = fmin; end %figure, plot( 1 :N_iter ,fitnessMSE); % Output/display disp([ ’Total number of evaluations: ’ ,num2str(N_iter*n)]); disp([ ’Best solution=’ ,num2str(best), ’ fmin=’ ,num2str(fmin)]); figure( 1 ) plot( fitnessMSE) xlabel( ’Iteration’ ); ylabel( ’Best score obtained so far’ );