source: trunk/documentation/Test Functions/TestFunctions.tex @ 7857

\documentclass[12pt, a4paper]{article}

%include packages
\usepackage{a4}
\usepackage[dvips]{graphicx}
\usepackage[ansinew]{inputenc}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{amssymb}

\pagestyle{plain}
\pagenumbering{arabic}

\title{Real Valued Test Functions}
\author{Heuristic and Evolutionary Algorithms Laboratory (HEAL)}
\date{\today}

\begin{document}
  \maketitle

  \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)}
    \end{equation*}

    \begin{tabbing}
      \hspace{5cm}\=\kill
      \textbf{Dimensions:}     \> $n$ \\
      \textbf{Domain:}         \> $-32.768 \leq x_i \leq 32.768$ \\
      \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\
      \textbf{Operator:}       \> AckleyEvaluator \\
      \textbf{Charts:}         \> \\
    \end{tabbing}

    \begin{center}
      \includegraphics[width=0.45\textwidth]{Images/Ackley_large}
      \hfill
      \includegraphics[width=0.45\textwidth]{Images/Ackley_small}
    \end{center}

  \newpage

  \section*{Griewangk Function}
    \begin{equation*}
      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:}     \> $n$ \\
      \textbf{Domain:}         \> $-600.0 \leq x_i \leq 600.0$ \\
      \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=0.45\textwidth]{Images/Griewangk_large}
      \hfill
      \includegraphics[width=0.45\textwidth]{Images/Griewangk_small}
    \end{center}

\end{document}