documentation/Test Functions/TestFunctions.tex

   1 \documentclass[12pt, a4paper]{article}
   2
   3 %include packages
   4 \usepackage{a4}
   5 \usepackage[dvips]{graphicx}
   6 \usepackage[ansinew]{inputenc}
   7 \usepackage{epsfig}
   8 \usepackage{amsmath}
   9 \usepackage{amssymb}
  10
  11 \pagestyle{plain}
  12 \pagenumbering{arabic}
  13
  14 \title{Real Valued Test Functions}
  15 \author{Heuristic and Evolutionary Algorithms Laboratory (HEAL)}
  16 \date{\today}
  17
  18 \begin{document}
  19         \maketitle
  20
  21         \section*{Ackley Function}
  22                 \begin{equation*}
  23                         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)}
  24                 \end{equation*}
  25
  26                 \begin{tabbing}
  27                         \hspace{5cm}\=\kill
  28                         \textbf{Dimensions:}     \> $n$ \\
  29                         \textbf{Domain:}         \> $-32.768 \leq x_i \leq 32.768$ \\
  30                         \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\
  31                         \textbf{Operator:}       \> AckleyEvaluator \\
  32                         \textbf{Charts:}         \> \\
  33                 \end{tabbing}
  34
  35                 \begin{center}
  36                         \includegraphics[width=0.45\textwidth]{Images/Ackley_large}
  37                         \hfill
  38                         \includegraphics[width=0.45\textwidth]{Images/Ackley_small}
  39                 \end{center}
  40
  41         \newpage
  42
  43         \section*{Griewangk Function}
  44                 \begin{equation*}
  45                         f(x) = 1 + \sum_{i=1}^n \frac{x_i^2}{4000} - \prod_{i=1}^n cos(\frac{x_i}{\sqrt i})
  46                 \end{equation*}
  47
  48                 \begin{tabbing}
  49                         \hspace{5cm}\=\kill
  50                         \textbf{Dimensions:}     \> $n$ \\
  51                         \textbf{Domain:}         \> $-600.0 \leq x_i \leq 600.0$ \\
  52                         \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\
  53                         \textbf{Operator:}       \> GriewangkEvaluator \\
  54                         \textbf{Charts:}         \> \\
  55                 \end{tabbing}
  56
  57                 \begin{center}
  58                         \includegraphics[width=0.45\textwidth]{Images/Griewangk_large}
  59                         \hfill
  60                         \includegraphics[width=0.45\textwidth]{Images/Griewangk_small}
  61                 \end{center}
  62
  63 \end{document}