FOA Source Codes of MATLAB

From now on, I am going to share the FOA source codes of MATLAB to all of you.

There are two topics:

One is optimization with/without constraints and the other one is (stochastic) optimal control with/without constraints.


1. Optimization without constraints.
2. Optimization with constraints.
3. Deterministic optimal control with/without constraints.
4. Stochastic optimal control with/without constraints.


1.    Optimization without constraints: QP

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Pan's Original 2D-FOA
%% EMA Economic Department, Soochow University, Taipei,Taiwan
%
% Copyright by W-T Pan (2011)
% Revised by W-Y Lin (2011)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Topic: How to find  the max value of a quadratic function

% Clear the operating environment.
tic
clc
clear

% Randomize the initial Drosophila population positions.
X_axis=10*rand();
Y_axis=10*rand();

% Set parameters
maxgen=100;  % No.of iterations
sizepop=20;  % Population size

% Start the FOA: Flies use the sense of smell to find food

for i=1:sizepop

% The Drosophila uses its olfactory to search the food
% by random direction and distance

X(i)=X_axis+2*rand()-1;
Y(i)=Y_axis+2*rand()-1;

% Due to the fly cannot find the exact location of the prey, so we first estimate the distance from the origin (Dist).
% And then calculate the flavor concentration determination value (S), it is the inverse of the distance.

D(i)=(X(i)^2+Y(i)^2)^0.5;
S(i)=1/D(i);

% Concentration determination value (S) is substituted into the fitness function, i.e. the concentration of the flavor (Smelli) of the flies.

Smell(i)=7-S(i)^2;

end

% Identify the highest concentration values of this fruit fly Drosophila groups (find the maximum value).

[bestSmell bestindex]=max(Smell);

% Retain the best  Concentration values and best x, y coordinates of the flies

X_axis=X(bestindex);
Y_axis=Y(bestindex);
Smellbest=bestSmell;

% Start the Drosophila iterative optimization

for g=1:maxgen   

 for i=1:sizepop

X(i)=X_axis+2*rand()-1;
Y(i)=Y_axis+2*rand()-1;
D(i)=(X(i)^2+Y(i)^2)^0.5;
S(i)=1/D(i);
Smell(i)=7-S(i)^2;

end

[bestSmell bestindex]=max(Smell);

% Determine whether the  concentration value is greater than the previous one.
% If so, the best value and its location of the fly is retained.
% Then all flies utilize their visual to find this best position.

if bestSmell>Smellbest
X_axis=X(bestindex);
Y_axis=Y(bestindex);
Smellbest=bestSmell;

end

% Record  the optimal Smell value of each generation to yy array.
% Record the coordinates of the optimal iterations

yy(g)=Smellbest;
Xbest(g)=X_axis;
Ybest(g)=Y_axis;

% *** Draw the optimal concentration values and flight path for every iteration

figure(1)
plot(yy)
grid  on;
title('Optimization process 7-X^2','fontsize',14)
xlabel('Iteration Number','fontsize',12);ylabel('Smell','fontsize',14);

figure(2)
plot(Xbest,Ybest,'b.');
grid on;
title('Fruit fly flying route 7-X^2','fontsize',14)
xlabel('X-axis','fontsize',12);ylabel('Y-axis','fontsize',12);
pause(0.5)
end
toc

Simulated results:

Here X＞＝0 (constraint), Optimal value (Smell) = 7.

Reference:

1. Pan, W.-T. (2011). Fruit Fly Optimization Algorithm. Taiwan: Tsang Hai Book  Publishing Co., ISBN 978-986-6184-70-3. (in chinese).

2. Nien Benjamin (2011) Application of Data Mining and Fruit Fly Optimization Algorithm to Construct  Financial Crisis Early Warning Model – A Case Study of Listed Companies in Taiwan, Master Thesis, Department of Economics, Soochow University, Taiwan (in chinese), Adviser: Wei-Yuan Lin.

Jing Si Aphorism:

Be honest and truthful in everything you do.

Be gentle and forgiving in your relationships with others

 

 

 Soochow University EMA