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Importing release version 322 from old repos

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Marcel Kronfeld
2007-12-11 16:38:11 +00:00
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<html>
<head>
<title>Generalized Rastrigin's function</title>
</head>
<body><EFBFBD>
<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<76> 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>&#969;</i>=2*&#960;, <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>