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% ======================================================== %
% Files of the Matlab programs included in the book: %
% Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, %
% Second Edition, Luniver Press, (2010). www.luniver.com %
% ======================================================== %
% -------------------------------------------------------- %
% Firefly Algorithm for constrained optimization using %
% for the design of a spring (benchmark) %
% by Xin-She Yang (Cambridge University) Copyright @2009 %
% -------------------------------------------------------- %
function fa_ndim
% parameters [n N_iteration alpha betamin gamma]
para=[20 500 0.5 0.2 1];
help fa_ndim.m
% Simple bounds/limits for d-dimensional problems
d=15;
Lb=zeros(1,d);
Ub=2*ones(1,d);
% Initial random guess
u0=Lb+(Ub-Lb).*rand(1,d);
[u,fval,NumEval]=ffa_mincon(@cost,u0,Lb,Ub,para);
% Display results
bestsolution=u
bestojb=fval
total_number_of_function_evaluations=NumEval
%%% Put your own cost/objective function here --------%%%
%% Cost or Objective function
function z=cost(x)
% Exact solutions should be (1,1,...,1)
z=sum((x-1).^2);
%%% End of the part to be modified -------------------%%%
%%% --------------------------------------------------%%%
%%% Do not modify the following codes unless you want %%%
%%% to improve its performance etc %%%
% -------------------------------------------------------
% ===Start of the Firefly Algorithm Implementation ======
% Lb = lower bounds/limits
% Ub = upper bounds/limits
% para == optional (to control the Firefly algorithm)
% Outputs: nbest = the best solution found so far
% fbest = the best objective value
% NumEval = number of evaluations: n*MaxGeneration
% Optional:
% The alpha can be reduced (as to reduce the randomness)
% ---------------------------------------------------------
% Start FA
function [nbest,fbest,NumEval]...
=ffa_mincon(fhandle,u0, Lb, Ub, para)
% Check input parameters (otherwise set as default values)
if nargin<5, para=[20 500 0.25 0.20 1]; end
if nargin<4, Ub=[]; end
if nargin<3, Lb=[]; end
if nargin<2,

disp('Usuage: FA_mincon(@cost,u0,Lb,Ub,para)');
end
% n=number of fireflies
% MaxGeneration=number of pseudo time steps
% ------------------------------------------------
% alpha=0.25; % Randomness 0--1 (highly random)
% betamn=0.20; % minimum value of beta
% gamma=1; % Absorption coefficient
% ------------------------------------------------
n=para(1); MaxGeneration=para(2);
alpha=para(3); betamin=para(4); gamma=para(5);
% Total number of function evaluations
NumEval=n*MaxGeneration;
% Check if the upper bound & lower bound are the same size
if length(Lb) ~=length(Ub),
disp('Simple bounds/limits are improper!');
return
end
% Calcualte dimension
d=length(u0);
% Initial values of an array
zn=ones(n,1)*10^100;
% ------------------------------------------------
% generating the initial locations of n fireflies
[ns,Lightn]=init_ffa(n,d,Lb,Ub,u0);
% Iterations or pseudo time marching
for k=1:MaxGeneration, %%%%% start iterations
% This line of reducing alpha is optional
alpha=alpha_new(alpha,MaxGeneration);
% Evaluate new solutions (for all n fireflies)
for i=1:n,
zn(i)=fhandle(ns(i,:));
Lightn(i)=zn(i);
end
% Ranking fireflies by their light intensity/objectives
[Lightn,Index]=sort(zn);
ns_tmp=ns;
for i=1:n,
ns(i,:)=ns_tmp(Index(i),:);
end
%% Find the current best
nso=ns; Lighto=Lightn;
nbest=ns(1,:); Lightbest=Lightn(1);
% For output only
fbest=Lightbest;
% Move all fireflies to the better locations
[ns]=ffa_move(n,d,ns,Lightn,nso,Lighto,nbest,...
Lightbest,alpha,betamin,gamma,Lb,Ub);
end %%%%% end of iterations
% -------------------------------------------------------

% ----- All the subfunctions are listed here ------------
% The initial locations of n fireflies
function [ns,Lightn]=init_ffa(n,d,Lb,Ub,u0)
% if there are bounds/limits,
if length(Lb)>0,
for i=1:n,
ns(i,:)=Lb+(Ub-Lb).*rand(1,d);
end
else
% generate solutions around the random guess
for i=1:n,
ns(i,:)=u0+randn(1,d);
end
end
% initial value before function evaluations
Lightn=ones(n,1)*10^100;
% Move all fireflies toward brighter ones
function [ns]=ffa_move(n,d,ns,Lightn,nso,Lighto,...
nbest,Lightbest,alpha,betamin,gamma,Lb,Ub)
% Scaling of the system
scale=abs(Ub-Lb);
% Updating fireflies
for i=1:n,
% The attractiveness parameter beta=exp(-gamma*r)
for j=1:n,
r=sqrt(sum((ns(i,:)-ns(j,:)).^2));
% Update moves
if Lightn(i)>Lighto(j), % Brighter and more attractive
beta0=1; beta=(beta0-betamin)*exp(-gamma*r.^2)+betamin;
tmpf=alpha.*(rand(1,d)-0.5).*scale;
ns(i,:)=ns(i,:).*(1-beta)+nso(j,:).*beta+tmpf;
end
end % end for j
end % end for i
% Check if the updated solutions/locations are within limits
[ns]=findlimits(n,ns,Lb,Ub);
% This function is optional, as it is not in the original FA
% The idea to reduce randomness is to increase the convergence,
% however, if you reduce randomness too quickly, then premature
% convergence can occur. So use with care.
function alpha=alpha_new(alpha,NGen)
% alpha_n=alpha_0(1-delta)^NGen=10^(-4);
% alpha_0=0.9
delta=1-(10^(-4)/0.9)^(1/NGen);
alpha=(1-delta)*alpha;
% Make sure the fireflies are within the bounds/limits
function [ns]=findlimits(n,ns,Lb,Ub)
for i=1:n,
% Apply the lower bound
ns_tmp=ns(i,:);
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

ns(i,:)=ns_tmp;
end
%% ==== End of Firefly Algorithm implementation ======

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