Hi am MIZANUR RAHMAN i would like to get details on matlab code for firefly algorithm on RELIABILITY BASED RECONFIGURATION OF DISTRIBUTION SYSTEM

Firefly Algorithm (FA) is a metaheuristic algorithm for global optimization, which is inspired by flashing behavior of firefly insects. This algorithm is proposed by Xin-She Yang in 2008. Fireflies use the flashing behavior to attract other fireflies, usually for sending signals to opposite sex. However, in the mathematical model, used inside Firefly Algorithm, simply the fireflies are unisex, and any firefly can attract other fireflies.
Attractiveness of a firefly is proportional to its brightness and for any couple of fireflies, the brighter one will attract the other; so the less bright one is moved towards the brighter one. This is performed for any binary combination of fireflies in the population, on every iteration of algorithm. For more information, you can refer to the related article on Wikipedia, here.
In this post, we are going to share with you, the open-source MATLAB implementation of Firefly Algorithm (FA), which is easy to use within your research and projects, if you are familiar with MATLAB programming language.


% ======================================================== %
% Files of the Matlab programs included in the book: %
% Xin-She Yang, Nature-Inspired Metaheuristic Algorithms, %
% Second Edition, Luniver Press, (2010). 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_mincon
% parameters [n N_iteration alpha betamin gamma]
para=[40 500 0.5 0.2 1];
format long;

help fa_mincon.m
% This demo uses the Firefly Algorithm to solve the
% [Spring Design Problem as described by Cagnina et al.,
% Informatica, vol. 32, 319-326 (2008). ]

% Simple bounds/limits
disp('Solve the simple spring design problem ...');
Lb=[0.05 0.25 2.0];
Ub=[2.0 1.3 15.0];

% Initial random guess
u0=Lb+(Ub-Lb).*rand(size(Lb));

[u,fval,NumEval]=ffa_mincon(@cost,@constraint,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)
z=(2+x(3))*x(1)^2*x(2);

% Constrained optimization using penalty methods
% by changing f to F=f+ \sum lam_j*g^2_j*H_j(g_j)
% where H(g)=0 if g<=0 (true), =1 if g is false

%%% Put your own constraints here --------------------%%%
function [g,geq]=constraint(x)
% All nonlinear inequality constraints should be here
% If no inequality constraint at all, simple use g=[];
g(1)=1-x(2)^3*x(3)/(71785*x(1)^4);
% There was a typo in Cagnina et al.'s paper,
% the factor should 71785 insteady of 7178 !
tmpf=(4*x(2)^2-x(1)*x(2))/(12566*(x(2)*x(1)^3-x(1)^4));
g(2)=tmpf+1/(5108*x(1)^2)-1;
g(3)=1-140.45*x(1)/(x(2)^2*x(3));
g(4)=x(1)+x(2)-1.5;

% all nonlinear equality constraints should be here
% If no equality constraint at all, put geq=[] as follows
geq=[];

%%% 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 ======
% Inputs: fhandle => @cost (your own cost function,
% can be an external file )
% nonhandle => @constraint, all nonlinear constraints
% can be an external file or a function
% 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,nonhandle,u0, Lb, Ub, para)
% Check input parameters (otherwise set as default values)
if nargin<6, para=[20 50 0.25 0.20 1]; end
if nargin<5, Ub=[]; end
if nargin<4, Lb=[]; end
if nargin<3,
disp('Usuage: FA_mincon(@cost, @constraint,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)=Fun(fhandle,nonhandle,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

% -----------------------------------------
% d-dimensional objective function
function z=Fun(fhandle,nonhandle,u)
% Objective
z=fhandle(u);

% Apply nonlinear constraints by the penalty method
% Z=f+sum_k=1^N lam_k g_k^2 *H(g_k) where lam_k >> 1
z=z+getnonlinear(nonhandle,u);

function Z=getnonlinear(nonhandle,u)
Z=0;
% Penalty constant >> 1
lam=10^15; lameq=10^15;
% Get nonlinear constraints
[g,geq]=nonhandle(u);

% Apply inequality constraints as a penalty function
for k=1:length(g),
Z=Z+ lam*g(k)^2*getH(g(k));
end
% Apply equality constraints (when geq=[], length->0)
for k=1:length(geq),
Z=Z+lameq*geq(k)^2*geteqH(geq(k));
end

% Test if inequalities hold
% H(g) which is something like an index function
function H=getH(g)
if g<=0,
H=0;
else
H=1;
end

% Test if equalities hold
function H=geteqH(g)
if g==0,
H=0;
else
H=1;
end
%% ==== End of Firefly Algorithm implementation ======