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# Changeset 305 for trunk/documentation/Test Functions/TestFunctions.tex

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Timestamp:
06/06/08 12:51:19 (16 years ago)
Message:

Updated template document for description of real valued test functions

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1 edited

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 r303 \section*{Ackley Function} \begin{equation*} f(x) = 20 + e - 20 \cdot e^{\frac{1}{5} \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2}} - e^{\frac{1}{n} \sum_{i=1}^n \cos(2 \pi x_i)} f(x) = 20 + e - 20 \cdot e^{-\frac{1}{5} \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2}} - e^{\frac{1}{n} \sum_{i=1}^n \cos(2 \pi x_i)} \end{equation*} \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\ \textbf{Operator:}       \> AckleyEvaluator \\ \textbf{Chart:}          \> \\ \textbf{Charts:}         \> \\ \end{tabbing} \begin{center} \includegraphics[width=0.6\textwidth]{Images/Ackley} \includegraphics[width=0.45\textwidth]{Images/Ackley_large} \hfill \includegraphics[width=0.45\textwidth]{Images/Ackley_small} \end{center} \section*{Beale Function} \section*{Griewangk Function} \begin{equation*} f(x) = (1.5 - x_1 (1 - x_2))^2 + (2.25 - x_1 (1 - x_2^2))^2 + (2.625 - x_1 (1 - x_2^3))^2 f(x) = 1 + \sum_{i=1}^n \frac{x_i^2}{4000} - \prod_{i=1}^n cos(\frac{x_i}{\sqrt i}) \end{equation*} \begin{tabbing} \hspace{5cm}\=\kill \textbf{Dimensions:}     \> $2$ \\ \textbf{Domain:}         \> $-4.5 \leq x_i \leq 4.5$ \\ \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (3.0, 0.5)$ \\ \textbf{Operator:}       \> BealeEvaluator \\ \textbf{Chart:}          \> \\ \textbf{Dimensions:}     \> $n$ \\ \textbf{Domain:}         \> $-600.0 \leq x_i \leq 600$ \\ \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\ \textbf{Operator:}       \> GriewangkEvaluator \\ \textbf{Charts:}         \> \\ \end{tabbing} \begin{center} \includegraphics[width=0.6\textwidth]{Images/Ackley} \includegraphics[width=0.45\textwidth]{Images/Griewangk_large} \hfill \includegraphics[width=0.45\textwidth]{Images/Griewangk_small} \end{center} \end{document}