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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>evaluate_objective</title> <meta name="generator" content="MATLAB 7.0"> <meta name="date" content="2006-03-16"> <meta name="m-file" content="evaluate_objective"><style>body { background-color: white; margin:10px;}h1 { color: #990000; font-size: x-large;}h2 { color: #990000; font-size: medium;}p.footer { text-align: right; font-size: xx-small; font-weight: lighter; font-style: italic; color: gray;}pre.codeinput { margin-left: 30px;}span.keyword {color: #0000FF}span.comment {color: #228B22}span.string {color: #A020F0}span.untermstring {color: #B20000}span.syscmd {color: #B28C00}pre.showbuttons { margin-left: 30px; border: solid black 2px; padding: 4px; background: #EBEFF3;}pre.codeoutput { color: gray; font-style: italic;}pre.error { color: red;}/* 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 { /* 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" );} </style></head> <body> <h2>Contents</h2> <div> <ul> <li><a href="#1">function f = evaluate_objective(x, M, V)</a></li> <li><a href="#2">Kursawe proposed by Frank Kursawe.</a></li> <li><a href="#3">Check for error</a></li> </ul> </div> <h2>function f = evaluate_objective(x, M, V)<a name="1"></a></h2> <p>Function to evaluate the objective functions for the given input vector x. x is an array of decision variables and f(1), f(2), etc are the objective functions. The algorithm always minimizes the objective function hence if you would like to maximize the function then multiply the function by negative one. M is the numebr of objective functions and V is the number of decision variables. </p> <p>This functions is basically written by the user who defines his/her own objective function. Make sure that the M and V matches your initial user input. Make sure that the </p> <p>An example objective function is given below. It has two six decision variables are two objective functions.</p><pre class="codeinput"><span class="comment">% f = [];</span><span class="comment">% %% Objective function one</span><span class="comment">% % Decision variables are used to form the objective function.</span><span class="comment">% f(1) = 1 - exp(-4*x(1))*(sin(6*pi*x(1)))^6;</span><span class="comment">% sum = 0;</span><span class="comment">% for i = 2 : 6</span><span class="comment">% sum = sum + x(i)/4;</span><span class="comment">% end</span><span class="comment">% %% Intermediate function</span><span class="comment">% g_x = 1 + 9*(sum)^(0.25);</span><span class="comment">%</span><span class="comment">% %% Objective function two</span><span class="comment">% f(2) = g_x*(1 - ((f(1))/(g_x))^2);</span></pre><h2>Kursawe proposed by Frank Kursawe.<a name="2"></a></h2> <p>Take a look at the following reference A variant of evolution strategies for vector optimization. In H. P. Schwefel and R. Männer, editors, Parallel Problem Solving from Nature. 1st Workshop, PPSN I, volume 496 of Lecture Notes in Computer Science, pages 193-197, Berlin, Germany, oct 1991. Springer-Verlag. </p> <p>Number of objective is two, while it can have arbirtarly many decision variables within the range -5 and 5. Common number of variables is 3. </p><pre class="codeinput">f = [];<span class="comment">% Objective function one</span>sum = 0;<span class="keyword">for</span> i = 1 : V - 1 sum = sum - 10*exp(-0.2*sqrt((x(i))^2 + (x(i + 1))^2));<span class="keyword">end</span><span class="comment">% Decision variables are used to form the objective function.</span>f(1) = sum;<span class="comment">% Objective function two</span>sum = 0;<span class="keyword">for</span> i = 1 : V sum = sum + (abs(x(i))^0.8 + 5*(sin(x(i)))^3);<span class="keyword">end</span><span class="comment">% Decision variables are used to form the objective function.</span>f(2) = sum;</pre><h2>Check for error<a name="3"></a></h2><pre class="codeinput"><span class="keyword">if</span> length(f) ~= M error(<span class="string">'The number of decision variables does not match you previous input. Kindly check your objective function'</span>);<span class="keyword">end</span></pre><p class="footer"><br> Published with MATLAB® 7.0<br></p> <!--##### SOURCE BEGIN #####
%% function f = evaluate_objective(x, M, V)
% Function to evaluate the objective functions for the given input vector
% x. x is an array of decision variables and f(1), f(2), etc are the
% objective functions. The algorithm always minimizes the objective
% function hence if you would like to maximize the function then multiply
% the function by negative one. M is the numebr of objective functions and
% V is the number of decision variables.
%
% This functions is basically written by the user who defines his/her own
% objective function. Make sure that the M and V matches your initial user
% input. Make sure that the
%
% An example objective function is given below. It has two six decision
% variables are two objective functions.
% f = [];
% %% Objective function one
% % Decision variables are used to form the objective function.
% f(1) = 1 - exp(-4*x(1))*(sin(6*pi*x(1)))^6;
% sum = 0;
% for i = 2 : 6
% sum = sum + x(i)/4;
% end
% %% Intermediate function
% g_x = 1 + 9*(sum)^(0.25);
%
% %% Objective function two
% f(2) = g_x*(1 - ((f(1))/(g_x))^2);
%% Kursawe proposed by Frank Kursawe.
% Take a look at the following reference
% A variant of evolution strategies for vector optimization.
% In H. P. Schwefel and R. M盲nner, editors, Parallel Problem Solving from
% Nature. 1st Workshop, PPSN I, volume 496 of Lecture Notes in Computer
% Science, pages 193-197, Berlin, Germany, oct 1991. Springer-Verlag.
%
% Number of objective is two, while it can have arbirtarly many decision
% variables within the range -5 and 5. Common number of variables is 3.
f = [];
% Objective function one
sum = 0;
for i = 1 : V - 1
sum = sum - 10*exp(-0.2*sqrt((x(i))^2 + (x(i + 1))^2));
end
% Decision variables are used to form the objective function.
f(1) = sum;
% Objective function two
sum = 0;
for i = 1 : V
sum = sum + (abs(x(i))^0.8 + 5*(sin(x(i)))^3);
end
% Decision variables are used to form the objective function.
f(2) = sum;
%% Check for error
if length(f) ~= M
error('The number of decision variables does not match you previous input. Kindly check your objective function');
end##### SOURCE END #####--> </body></html>?? 快捷鍵說明
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