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source: trunk/documentation/Test Functions/TestFunctions.tex @ 307

Last change on this file since 307 was 307, checked in by swagner, 16 years ago

Updated description of test functions

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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}
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