![% --------------------------------------------------------------------%
% 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). %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [best,fmin,N_iter]=fpa_demo(para)
% Default parameters
if nargin<1,
para=[20 0.8];
end
n=para(1); % Population size, typically 10 to 25
p=para(2); % probabibility switch
% Iteration parameters
N_iter=2000; % Total number of iterations
% Dimension of the search variables
d=3;
Lb=-2*ones(1,d);
Ub=2*ones(1,d);
% Initialize the population/solutions
for i=1:n,
Sol(i,:)=Lb+(Ub-Lb).*rand(1,d);
Fitness(i)=Fun(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;](https://image.slidesharecdn.com/fpademo-160331211830/85/Flower-Pollination-Algorithm-matlab-code-1-320.jpg)
![% 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
Fnew=Fun(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
end
% Output/display
disp(['Total number of evaluations: ',num2str(N_iter*n)]);
disp(['Best solution=',num2str(best),' fmin=',num2str(fmin)]);
% Application of simple constraints
function s=simplebounds(s,Lb,Ub)
% Apply the lower bound
ns_tmp=s;
I=ns_tmp<Lb;
ns_tmp(I)=Lb(I);
% Apply the upper bounds
J=ns_tmp>Ub;
ns_tmp(J)=Ub(J);
% Update this new move
s=ns_tmp;
% Draw n Levy flight sample
function L=Levy(d)
% Levy exponent and coefficient
% For details, see Chapter 11 of the following book:
% Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014).
beta=3/2;](https://image.slidesharecdn.com/fpademo-160331211830/85/Flower-Pollination-Algorithm-matlab-code-2-320.jpg)
Flower Pollination Algorithm (matlab code)
- 1. % --------------------------------------------------------------------% % 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). % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [best,fmin,N_iter]=fpa_demo(para) % Default parameters if nargin<1, para=[20 0.8]; end n=para(1); % Population size, typically 10 to 25 p=para(2); % probabibility switch % Iteration parameters N_iter=2000; % Total number of iterations % Dimension of the search variables d=3; Lb=-2*ones(1,d); Ub=2*ones(1,d); % Initialize the population/solutions for i=1:n, Sol(i,:)=Lb+(Ub-Lb).*rand(1,d); Fitness(i)=Fun(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;
- 2. % 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 Fnew=Fun(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 end % Output/display disp(['Total number of evaluations: ',num2str(N_iter*n)]); disp(['Best solution=',num2str(best),' fmin=',num2str(fmin)]); % Application of simple constraints function s=simplebounds(s,Lb,Ub) % Apply the lower bound ns_tmp=s; I=ns_tmp<Lb; ns_tmp(I)=Lb(I); % Apply the upper bounds J=ns_tmp>Ub; ns_tmp(J)=Ub(J); % Update this new move s=ns_tmp; % Draw n Levy flight sample function L=Levy(d) % Levy exponent and coefficient % For details, see Chapter 11 of the following book: % Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, (2014). beta=3/2;
- 3. sigma=(gamma(1+beta)*sin(pi*beta/2)/(gamma((1+beta)/2)*beta*2^((beta- 1)/2)))^(1/beta); u=randn(1,d)*sigma; v=randn(1,d); step=u./abs(v).^(1/beta); L=0.01*step; % Objective function and here we used Rosenbrock's 3D function function z=Fun(u) z=(1-u(1))^2+100*(u(2)-u(1)^2)^2+100*(u(3)-u(2)^2)^2;