Last change
on this file since 4950 was
307,
checked in by swagner, 16 years ago
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Updated description of test functions
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File size:
1.8 KB
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[303] | 1 | \documentclass[12pt, a4paper]{article}
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| 2 |
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| 3 | %include packages
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| 4 | \usepackage{a4}
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| 5 | \usepackage[dvips]{graphicx}
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| 6 | \usepackage[ansinew]{inputenc}
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| 7 | \usepackage{epsfig}
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| 8 | \usepackage{amsmath}
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| 9 | \usepackage{amssymb}
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| 10 |
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| 11 | \pagestyle{plain}
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| 12 | \pagenumbering{arabic}
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| 13 |
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| 14 | \title{Real Valued Test Functions}
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| 15 | \author{Heuristic and Evolutionary Algorithms Laboratory (HEAL)}
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| 16 | \date{\today}
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| 17 |
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| 18 | \begin{document}
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| 19 | \maketitle
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| 20 |
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| 21 | \section*{Ackley Function}
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| 22 | \begin{equation*}
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[305] | 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)}
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[303] | 24 | \end{equation*}
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| 25 |
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| 26 | \begin{tabbing}
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| 27 | \hspace{5cm}\=\kill
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| 28 | \textbf{Dimensions:} \> $n$ \\
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| 29 | \textbf{Domain:} \> $-32.768 \leq x_i \leq 32.768$ \\
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| 30 | \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\
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| 31 | \textbf{Operator:} \> AckleyEvaluator \\
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[305] | 32 | \textbf{Charts:} \> \\
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[303] | 33 | \end{tabbing}
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| 34 |
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| 35 | \begin{center}
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[305] | 36 | \includegraphics[width=0.45\textwidth]{Images/Ackley_large}
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| 37 | \hfill
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| 38 | \includegraphics[width=0.45\textwidth]{Images/Ackley_small}
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[303] | 39 | \end{center}
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| 40 |
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[306] | 41 | \newpage
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| 42 |
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[305] | 43 | \section*{Griewangk Function}
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[303] | 44 | \begin{equation*}
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[305] | 45 | f(x) = 1 + \sum_{i=1}^n \frac{x_i^2}{4000} - \prod_{i=1}^n cos(\frac{x_i}{\sqrt i})
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[303] | 46 | \end{equation*}
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| 47 |
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| 48 | \begin{tabbing}
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| 49 | \hspace{5cm}\=\kill
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[305] | 50 | \textbf{Dimensions:} \> $n$ \\
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[307] | 51 | \textbf{Domain:} \> $-600.0 \leq x_i \leq 600.0$ \\
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[305] | 52 | \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (0.0, 0.0, \dots, 0.0)$ \\
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| 53 | \textbf{Operator:} \> GriewangkEvaluator \\
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| 54 | \textbf{Charts:} \> \\
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[303] | 55 | \end{tabbing}
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| 56 |
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| 57 | \begin{center}
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[305] | 58 | \includegraphics[width=0.45\textwidth]{Images/Griewangk_large}
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| 59 | \hfill
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| 60 | \includegraphics[width=0.45\textwidth]{Images/Griewangk_small}
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[303] | 61 | \end{center}
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| 62 |
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| 63 | \end{document} |
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