Fabian Becker
b1553f3088
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42 lines
1.6 KiB
HTML
42 lines
1.6 KiB
HTML
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<title>Generalized Rastrigin's function</title>
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</head>
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<body>
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<h1 align="center">Generalized Rastrigin's function</h1>
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<center>
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<img src="images/rastrigintex.jpg" width="500" height="101">
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</center>
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<p>
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Rastrigin's function is symmetric. It is based on the simple <i>parabola function</i> (called f1 in the EvA 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 optima.
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<p>
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Values used for the following illustrations: <i>A</i>=10, <i>ω</i>=2*π, <i>n</i>=2.
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<br>
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<img src="images/rastrigin20.jpg" border="2">
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<br>
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Rastrigin's function within the co-domain -20>=<i>x</i>>=20
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<p>
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<img src="images/rastrigin5.jpg" border="2">
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<br>
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Rastrigin's function within the co-domain -5>=<i>x</i>>=5
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<p>
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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.
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<p>
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<img src="images/rastrigin1.jpg" border="2"><br>
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Rastrigin's function close to its optimum.
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<hr>
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More information about Rastrigin's function can be found at:
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<p>
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Darrell Whitley, Soraya Rana, John Dzubera, Keith E. Mathias. <i>Evaluating Evolutionary Algorithms. Artificial Intelligence</i>, 85(1-2):245-276. 1996.
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<p>
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Eberhard Schoeneburg, Frank Heinzmann, Sven Feddersen. <i>Genetische Algorithmen und Evolutionstrategien - Eine Einfuehrung in Theorie und Praxis der simulierten Evolution.</i> Addison-Wesley, 1994.
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</body>
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</html> |