42 lines
1.6 KiB
HTML
42 lines
1.6 KiB
HTML
<html>
|
||
<head>
|
||
<title>Generalized Rastrigin's function</title>
|
||
</head>
|
||
<body>
|
||
<h1 align="center">Generalized Rastrigin's function</h1>
|
||
<center>
|
||
<img src="images/rastrigintex.jpg" width="500" height="101">
|
||
</center>
|
||
<p>
|
||
Rastrigin's function is symmetric. It is based on the simple <i>sphere function</i> (called f_1 in the JavaEva© context), but it is multimodal because a modulation term on the basis of the cosine function is added. This evokes hills and valleys which are misleading local optimums.
|
||
<p>
|
||
Values are used for the following illustrations: <i>A</i>=10, <i>ω</i>=2*π, <i>n</i>=2.
|
||
|
||
<br>
|
||
<img src="images/rastrigin20.jpg" border="2">
|
||
|
||
<br>
|
||
|
||
Rastrigin's function within the co-domain -20>=<i>x</i>>=20
|
||
|
||
<p>
|
||
<img src="images/rastrigin5.jpg" border="2">
|
||
<br>
|
||
|
||
Rastrigin's function within the co-domain -5>=<i>x</i>>=5
|
||
|
||
<p>
|
||
|
||
Like Ackley's function a simple evolutionary algorithm would get stuck in a local optimum, while a broader searching algorithm would get out of the local optimum closer to the global optimum, which in this case is: f(<i>x</i>) = f(0, 0, ... , 0) = 0.
|
||
<p>
|
||
<img src="images/rastrigin1.jpg" border="2"><br>
|
||
Rastrigin's function close to its optimum.
|
||
|
||
<hr>
|
||
More information about Rastrigin's function can be found at:
|
||
<p>
|
||
Darrell Whitley, Soraya Rana, John Dzubera, Keith E. Mathias. <i>Evaluating Evolutionary Algorithms. Artificial Intelligence</i>, 85(1-2):245-276. 1996.
|
||
<p>
|
||
Eberhard Schoeneburg, Frank Heinzmann, Sven Feddersen. <i>Genetische Algorithmen und Evolutionstrategien - Eine Einfuehrung in Theorie und Praxis der simulierten Evolution.</i> Addison-Wesley, 1994.
|
||
</body>
|
||
</html> |