Having investigated the performance characteristics
of extreme sampling in \tion{settings} - \tion{variance},
this section compares the performance of extreme
sampling with the previous discretization method.
As mentioned in \tion{itlMetaheur}, the original
discretization method used with ITL \cite{fea02a,me02c,me03j}
was a diagonal striping discretization.
We will compare this older method with our best-performing
extreme sampling method, \ie the \bore selector with
$M/N$ set to 500/75.
\fig{bothDis} compares diagonal discretization with
the \bore method as a reminder from \tion{itlMetaheur}.

\begin{figure}[h]
\centering
\begin{tabular}{cc}
\includegraphics[height=2.0in]{Figures/borediag.pdf} &
~~~~~~~~~\includegraphics[height=2.0in]{Figures/borestrat.pdf} \\
\end{tabular}
\caption{Diagonal striping and \bore}\label{fig:bothDis}
\end{figure}



\fig{boreId} shows the search trajectories for
diagonal striping and \bore discretization in
the \aero and \holo models.
%At this time we only have data for the \aero and \holo.
For the \bore trajectory this figure uses the best of the 
ten trials from each of the models, based on benefit/cost ratio.
For the diagonal trajectory this figure uses the best of the 
30 trials from each of the models, based on benefit/cost ratio.
In addition, the original diagonal experiments required batch
sizes (\ie the value of $M$) of 2000.
Even with this larger batch size and more trials to choose from,
\fig{boreId} makes it clear that \bore outperforms
diagonal striping significantly in both models shown.

\begin{figure}
\centering
\begin{tabular}{cc}
\includegraphics[height=2.20in]{Figures/aeroDiagComparsion} &
\includegraphics[height=2.20in]{Figures/holoDiagComparsion} \\
\end{tabular}
\caption{Comparison of \bore to diagonal striping}\label{fig:boreId}
\end{figure}

For the \aero model, \bore found a solution with a much higher 
expected benefit and a slightly lower cost.
In the \holo model,
\bore found a solution with a much lower cost and only
a slightly lower expected benefit.
\ble{endPoints} gives the exact values of the endpoints
for the cost, benefit, and normalized benefit/cost ratio.

\begin{table} 
\centering
\begin{tabular}{rccccccc|}
\vline & \multicolumn{3}{c}{\bore}  & \vline & \multicolumn{3}{c}{diagonal} \vline \\
model \vline & cost & benefit & normalized ratio & \vline & cost & benefit & normalized ratio\\
\hline
\aero \vline & .366 & .569  & 1.55 & \vline & .392 & .392  & 1.00  \\
\holo \vline & .198 & .0869 & .439 & \vline & .343 & .0898 & .262  \\
\end{tabular}
\caption{Normalized benefit/cost ratios in \bore and diagonal striping}\label{table:endPoints}
\end{table} 


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