Last change
on this file since 5551 was
307,
checked in by swagner, 17 years ago
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Updated description of test functions
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File size:
1.8 KB
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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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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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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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32 | \textbf{Charts:} \> \\
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33 | \end{tabbing}
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34 |
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35 | \begin{center}
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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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39 | \end{center}
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40 |
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41 | \newpage
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42 |
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43 | \section*{Griewangk Function}
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44 | \begin{equation*}
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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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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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50 | \textbf{Dimensions:} \> $n$ \\
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51 | \textbf{Domain:} \> $-600.0 \leq x_i \leq 600.0$ \\
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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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55 | \end{tabbing}
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56 |
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57 | \begin{center}
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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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61 | \end{center}
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62 |
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63 | \end{document} |
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