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\chapter{Search strategy}\label{sec:search}
Monte-Carlo search for first candidates, followed by parallel hill
climbing search, extended by long jumps.

In the following graphic we see 100.000 design evaluations (that take
less than 7 seconds on my computer), consisting out of 20 hill
climbing search \emph{runs} from 20 different designs as starting
point which were selected by a Monte-Carlo search. We can see that 10
out of the 20 search runs were not able to achieve the efficieny the
other 10 achieved. We can see, that there were most likely at least
four local maxima the hill climbing search found and got stuck:

\begin{knitrout}\scriptsize
\definecolor{shadecolor}{rgb}{0.969, 0.969, 0.969}\color{fgcolor}\begin{kframe}
\begin{alltt}
\hlkwd{set.seed}\hlstd{(}\hlnum{42}\hlstd{)}
\hlstd{x} \hlkwb{<-} \hlkwd{searchCrossOverDesign}\hlstd{(}\hlkwc{s}\hlstd{=}\hlnum{9}\hlstd{,} \hlkwc{p}\hlstd{=}\hlnum{5}\hlstd{,} \hlkwc{v}\hlstd{=}\hlnum{4}\hlstd{,} \hlkwc{model}\hlstd{=}\hlnum{4}\hlstd{)}
\hlkwd{plot}\hlstd{(x)}
\end{alltt}
\end{kframe}
\includegraphics[width=\maxwidth]{figure/SearchStrategy-1} 
\begin{kframe}\begin{alltt}
\hlkwd{plot}\hlstd{(x,} \hlkwc{type}\hlstd{=}\hlnum{2}\hlstd{)}
\end{alltt}
\end{kframe}
\includegraphics[width=\maxwidth]{figure/SearchStrategy-2} 

\end{knitrout}

%For a given cross-over design we create a row-column design, calculate the information matrix $A_r$ for this design from
%\[A_r=r^\delta-\tfrac{1}{s}N_pN_p'-\tfrac{1}{p}N_sN_s'+\tfrac{1}{ps}rr'.\]
%For details see \cite{j1995cyclic} and \cite{john2004crossover}.












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