Abschnitt~\ref{sect:tranformation} beschrieben, ein Algorithmus, der Mutation
einsetzt, wird in Abschnitt~\ref{sect:sn-evolution-cut} vorgestellt.
+
+\begin{figure}
+ \begin{center}
+ \input{images/16-hillis.tex}
+ \end{center}
+ \caption{Das 16-Sortiernetzwerk, das \textit{Hillis} in~\cite{H1992} angibt.
+ Es besteht aus 61~Komparatoren in 11~Schichten.}
+ \label{fig:16-hillis}
+\end{figure}
+Evolutionäre Algorithmen wurden bereits mehrfach eingesetzt, um
+Sortiernetzwerke zu untersuchen. \textit{W.~Daniel Hillis} verwendete
+\emph{Co-Evolution} um neben Komparatornetzwerken auch „schwierige Eingaben“
+zu optimieren~\cite{H1992}. Diese \emph{Parasiten} genannten Eingaben wurden
+daran gemessen, bei wievielen Komparatornetzwerken sie beweisen konnten, dass
+sie keine Sortiernetzwerke sind. So mussten bei neuen Individuen~/
+Komparatornetzwerken nicht alle 0-1-Folgen, sondern nur erfolgreiche
+Parasiten~/ schwierige Eingaben überprüft werden. Auf diese Art und Weise
+gelang es \textit{Hillis} ein 16-Sortiernetzwerk mit 61~Komparatoren
+anzugeben, das in Abbildung~\ref{fig:16-hillis} zu sehen ist.
+
+\begin{figure}
+ \centering
+ \subfigure{\input{images/13-juille-0.tex}}
+ \subfigure{\input{images/13-juille-1.tex}}
+ \caption{13-Sortiernetzwerke, die von \textit{Hugues Juillé} mithilfe des
+ END-Algorithmus gefunden wurden. Sie bestehen jeweils aus 45~Komparatoren in
+ 10~Schichten.}
+ \label{fig:13-juille}
+\end{figure}
+\textit{Hugues Juillé} entwickelte ein Verfahren, das er \emph{Evolving
+Non-Determinism} (END) nannte. Dabei handelt es sich nicht um einen
+\emph{Evolutionären Algorithmus}, wie sie hier vorgestellt wurden, sondern um
+eine verteilte, probabilistische Breitensuche, die an die \emph{Strahlsuche}
+(englisch: \textit{beam search}), ein Verfahren der Künstlichen Intelligenz,
+angelehnt ist. Die aufwendigste Operation bei diesem Ansatz ist die
+Bewertungsfunktion, die abschätzt, wieviele Komparatoren zu einem
+Komparatornetzwerk hinzugefügt werden müssen, um ein Sortiernetzwerk zu
+erhalten. Mit diesem Ansatz gelang es \textit{Juillé} zwei 13-Sortiernetzwerke
+anzugeben, die mit 45~Komparatoren effizienter sind als alle bis dahin
+Bekannten (Abbildung~\ref{fig:13-juille}).
+
\newpage
\section{Bekannte konstruktive Sortiernetzwerke}
\label{sect:konstruktive_netzwerke}
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Year = 2009,
Month = {März}
}
+
+@inproceedings{J1995,
+ Author = {Hugues Juillé},
+ Title = {Evolution of Non-Deterministic Incremental Algorithms as a New Approach for Search in State Spaces},
+ Booktitle = {Lecture Notes in Computer Science},
+ Year = 1995,
+ Pages = {246--260}
+}
+
+@inbook{H1992,
+ Author = {W.~Daniel Hillis},
+ Title = {Artificial Life II},
+ Chapter = {Co-evolving parasites improve simulated evolution as an optimization procedure},
+ Publisher = {Addison-Wesley},
+ Year = 1992
+}
projects / diplomarbeit.git / commitdiff