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<html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd"> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"> <!--This HTML is auto-generated from an M-file.To make changes, update the M-file and republish this document. --> <title>Particle Swarm Optimization Simulation</title> <meta name="generator" content="MATLAB 7.2"> <meta name="date" content="2008-06-07"> <meta name="m-file" content="PSO"><style>body { background-color: white; margin:10px;}h1 { color: #990000; font-size: x-large;}h2 { color: #990000; font-size: medium;}/* Make the text shrink to fit narrow windows, but not stretch too far in wide windows. On Gecko-based browsers, the shrink-to-fit doesn't work. */ p,h1,h2,div.content div { /* for MATLAB's browser */ width: 600px; /* for Mozilla, but the "width" tag overrides it anyway */ max-width: 600px; /* for IE */ width:expression(document.body.clientWidth > 620 ? "600px": "auto" );}pre.codeinput { background: #EEEEEE; padding: 10px;}@media print { pre.codeinput {word-wrap:break-word; width:100%;}} span.keyword {color: #0000FF}span.comment {color: #228B22}span.string {color: #A020F0}span.untermstring {color: #B20000}span.syscmd {color: #B28C00}pre.codeoutput { color: #666666; padding: 10px;}pre.error { color: red;}p.footer { text-align: right; font-size: xx-small; font-weight: lighter; font-style: italic; color: gray;} </style></head> <body> <div class="content"> <h1>Particle Swarm Optimization Simulation</h1> <introduction> <p>Animiation of birds movement of a swarm to get the global minimum solution</p> <p>Author: Wael Mansour (<a href="mailto:wael192@yahoo.com">wael192@yahoo.com</a>) </p> <p>MSc Student, Electrical Enginering Dept, Faculty of Engineering Cairo University, Egypt</p> </introduction> <h2>Contents</h2> <div> <ul> <li><a href="#1">Initialization</a></li> <li><a href="#2">Main Loop</a></li> </ul> </div> <h2>Initialization<a name="1"></a></h2><pre class="codeinput">clearclcn = 50; <span class="comment">% Size of the swarm " no of birds "</span>bird_setp = 50; <span class="comment">% Maximum number of "birds steps"</span>dim = 2; <span class="comment">% Dimension of the problem</span>c2 =1.2; <span class="comment">% PSO parameter C1</span>c1 = 0.12; <span class="comment">% PSO parameter C2</span>w =0.9; <span class="comment">% pso momentum or inertia</span>fitness=0*ones(n,bird_setp); <span class="comment">%-----------------------------%</span> <span class="comment">% initialize the parameter %</span> <span class="comment">%-----------------------------%</span>R1 = rand(dim, n);R2 = rand(dim, n);current_fitness =0*ones(n,1); <span class="comment">%------------------------------------------------%</span> <span class="comment">% Initializing swarm and velocities and position %</span> <span class="comment">%------------------------------------------------%</span>current_position = 10*(rand(dim, n)-.5);velocity = .3*randn(dim, n) ;local_best_position = current_position ; <span class="comment">%-------------------------------------------%</span> <span class="comment">% Evaluate initial population %</span> <span class="comment">%-------------------------------------------%</span><span class="keyword">for</span> i = 1:n current_fitness(i) = Live_fn(current_position(:,i));<span class="keyword">end</span>local_best_fitness = current_fitness ;[global_best_fitness,g] = min(local_best_fitness) ;<span class="keyword">for</span> i=1:n globl_best_position(:,i) = local_best_position(:,g) ;<span class="keyword">end</span> <span class="comment">%-------------------%</span> <span class="comment">% VELOCITY UPDATE %</span> <span class="comment">%-------------------%</span>velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(globl_best_position-current_position)); <span class="comment">%------------------%</span> <span class="comment">% SWARMUPDATE %</span> <span class="comment">%------------------%</span>current_position = current_position + velocity ; <span class="comment">%------------------------%</span> <span class="comment">% evaluate anew swarm %</span> <span class="comment">%------------------------%</span></pre><h2>Main Loop<a name="2"></a></h2><pre class="codeinput">iter = 0 ; <span class="comment">% Iterations’counter</span><span class="keyword">while</span> ( iter < bird_setp )iter = iter + 1;<span class="keyword">for</span> i = 1:n,current_fitness(i) = Live_fn(current_position(:,i)) ;<span class="keyword">end</span><span class="keyword">for</span> i = 1 : n <span class="keyword">if</span> current_fitness(i) < local_best_fitness(i) local_best_fitness(i) = current_fitness(i); local_best_position(:,i) = current_position(:,i) ; <span class="keyword">end</span> <span class="keyword">end</span> [current_global_best_fitness,g] = min(local_best_fitness);<span class="keyword">if</span> current_global_best_fitness < global_best_fitness global_best_fitness = current_global_best_fitness; <span class="keyword">for</span> i=1:n globl_best_position(:,i) = local_best_position(:,g); <span class="keyword">end</span><span class="keyword">end</span> velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(globl_best_position-current_position)); current_position = current_position + velocity;x=current_position(1,:);y=current_position(2,:);clf plot(x, y , <span class="string">'h'</span>) axis([-5 5 -5 5]);pause(.2)<span class="keyword">end</span> <span class="comment">% end of while loop its mean the end of all step that the birds move it</span> [Jbest_min,I] = min(current_fitness) <span class="comment">% minimum fitness</span> current_position(:,I) <span class="comment">% best solution</span><span class="comment">%</span></pre><pre class="codeoutput">Jbest_min = -186.2872I = 9ans = -1.5108 -0.9673</pre><img vspace="5" hspace="5" src="PSO_01.png"> <p class="footer"><br> Published with MATLAB® 7.2<br></p> </div> <!--##### SOURCE BEGIN #####%% Particle Swarm Optimization Simulation
% Animiation of birds movement of a swarm to get the global minimum solution
%
% Author: Wael Mansour (wael192@yahoo.com)
%
% MSc Student, Electrical Enginering Dept,
% Faculty of Engineering Cairo University, Egypt
%% Initialization
clear
clc
n = 50; % Size of the swarm " no of birds "
bird_setp = 50; % Maximum number of "birds steps"
dim = 2; % Dimension of the problem
c2 =1.2; % PSO parameter C1
c1 = 0.12; % PSO parameter C2
w =0.9; % pso momentum or inertia
fitness=0*ones(n,bird_setp);
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
% initialize the parameter %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
R1 = rand(dim, n);
R2 = rand(dim, n);
current_fitness =0*ones(n,1);
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
% Initializing swarm and velocities and position %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
current_position = 10*(rand(dim, n)-.5);
velocity = .3*randn(dim, n) ;
local_best_position = current_position ;
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
% Evaluate initial population %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
for i = 1:n
current_fitness(i) = Live_fn(current_position(:,i));
end
local_best_fitness = current_fitness ;
[global_best_fitness,g] = min(local_best_fitness) ;
for i=1:n
globl_best_position(:,i) = local_best_position(:,g) ;
end
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
% VELOCITY UPDATE %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH-%
velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(globl_best_position-current_position));
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
% SWARMUPDATE %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
current_position = current_position + velocity ;
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
% evaluate anew swarm %
%REPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASHREPLACE_WITH_DASH_DASH%
%% Main Loop
iter = 0 ; % Iterations鈥檆ounter
while ( iter < bird_setp )
iter = iter + 1;
for i = 1:n,
current_fitness(i) = Live_fn(current_position(:,i)) ;
end
for i = 1 : n
if current_fitness(i) < local_best_fitness(i)
local_best_fitness(i) = current_fitness(i);
local_best_position(:,i) = current_position(:,i) ;
end
end
[current_global_best_fitness,g] = min(local_best_fitness);
if current_global_best_fitness < global_best_fitness
global_best_fitness = current_global_best_fitness;
for i=1:n
globl_best_position(:,i) = local_best_position(:,g);
end
end
velocity = w *velocity + c1*(R1.*(local_best_position-current_position)) + c2*(R2.*(globl_best_position-current_position));
current_position = current_position + velocity;
x=current_position(1,:);
y=current_position(2,:);
clf
plot(x, y , 'h')
axis([-5 5 -5 5]);
pause(.2)
end % end of while loop its mean the end of all step that the birds move it
[Jbest_min,I] = min(current_fitness) % minimum fitness
current_position(:,I) % best solution
%
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