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# source:trunk/documentation/Test Functions/TestFunctions.tex@303

Last change on this file since 303 was 303, checked in by swagner, 16 years ago

Added template document for describing real valued test functions

File size: 1.6 KB
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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{Chart:}          \> \\
33    \end{tabbing}
34
35    \begin{center}
36      \includegraphics[width=0.6\textwidth]{Images/Ackley}
37    \end{center}
38
39  \section*{Beale Function}
40    \begin{equation*}
41      f(x) = (1.5 - x_1 (1 - x_2))^2 + (2.25 - x_1 (1 - x_2^2))^2 + (2.625 - x_1 (1 - x_2^3))^2
42    \end{equation*}
43
44    \begin{tabbing}
45      \hspace{5cm}\=\kill
46      \textbf{Dimensions:}     \> $2$ \\
47      \textbf{Domain:}         \> $-4.5 \leq x_i \leq 4.5$ \\
48      \textbf{Global Optimum:} \> $f(x) = 0.0$ at $x = (3.0, 0.5)$ \\
49      \textbf{Operator:}       \> BealeEvaluator \\
50      \textbf{Chart:}          \> \\
51    \end{tabbing}
52
53    \begin{center}
54      \includegraphics[width=0.6\textwidth]{Images/Ackley}
55    \end{center}
56
57
58
59\end{document}
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