% appendix
\chapter{Algorithm}
\label{ch:appendix_Algorithm}

%\section{Work flow process}
%\label{sec:WorkFlow}

\begin{figure}
    \centering
 	\includegraphics[width=0.9\textwidth]{images/WallaceiX/Matching.pdf}
	\caption[Chord Graphic of matching tournament]{12 selected hexagons, which represent genotypes, involve in a tournament. The 10 dots around each hexagon represent 10 rounds of the competition. Each round, 4 genotypes are engaged, resulting into 2 winners and 2 losers. Each chord represent a individual gaming, the red end is connecting to the winner, while the grey end to the loser. Some of the pairs might be chosen for more than once. So one chord might contain the result of multiple gaming from different rounds. All the hexagons are placed clockwise according to their rankings, for the one at 12 o'clock overwhelms the other, while the one at 1 o'clock is the lowest ranked. So the chords' red end are always towards the larger figure, clockwise.}
	\label{fig:Matching}
    \hfill
\end{figure}

\begin{figure}
 	\includegraphics[width=0.95\textwidth]{images/WallaceiX/ProcessFlow.png}
	\caption{The whole process flow of NSGA2}
	\label{fig:ProcessFlow}
    \hfill
\end{figure}

In \cref{fig:Matching,fig:ProcessFlow} I introduce the logic of the algorithm. And in \cref{fig:GH canvas part 1/2,fig:GH canvas part 2/2} it's the general canvas. We can use it to navigate to the subsidiary sections which we can find in \cref{ch:Workflow}. Here present a clearer connections among the sections.

~\\
This \cref{fig:ProcessFlow} shows how the data are operated during the process, and which datum out of the data is selected out and being modified. When the iteration meets its limit, in this case is when "n" reaches 99 gen., the process terminates. So in the record, we can collect the genotypes and phenotypes of all gen.s.



%\section{Grasshopper canvas}
%\label{sec:appendix_Grasshopper canvas}


%\newpage
\centering
\begin{sidewaysfigure}
	\centering
	\includegraphics[width=0.95\textwidth]{images/tables/WorkflownTools.png}
	\caption{General workflow and tools used}
	\label{fig:General workflow}
	\hfill
\end{sidewaysfigure}
\begin{sidewaysfigure}
	\centering
	\includegraphics[width=0.95\textwidth]{images/GH/Master-CITE_B.png}
	\caption{General GH canvas, part 2/2}
	\label{fig:GH canvas part 2/2}
	\hfill
\end{sidewaysfigure}

\begin{sidewaysfigure}
    \centering
	\includegraphics[width=\textwidth]{images/GH/Master-CITE_A.png}
	\caption{General GH canvas, part 1/2}
	\label{fig:GH canvas part 1/2}
    \hfill
\end{sidewaysfigure}

\begin{figure}
	\includegraphics[width=0.95\textwidth]{images/WallaceiX/Dendrogram.png}
	\caption{Heritage relation dendrogram}
	\label{fig:Dendrogram}
	\hfill
\end{figure}

\chapter{Result matrix}
\label{ch:appendix_ResultMatrix}

\raggedright

We've choose some of our result matrix here. For a quick scan of the outcome from the algorithm. They're also reference of the conclusion in \cref{ch:Application,ch:Conclusion}.


~\\
For more information, you're welcome to visit:

~\\
\href{https://github.com/ArchVittorio/GeneticfAlgorithm_HB_cities}{https://github.com/ArchVittorio/GeneticfAlgorithm\_HB\_cities}


~\\
All the result matrix are stored in this repository. It will be helpful for the researchers who want to see all the details.



\centering


\newpage
\section{Torino}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Torino/S2_Torino_GEN.050.png}
	\caption{Torino.\glsxtrshort{Gen}50}
	\label{fig:Torino.Gen.50}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Torino/S2_Torino_GEN.096.png}
	\caption{Torino.\glsxtrshort{Gen}96}
	\label{fig:Torino.Gen.96}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Torino/S2_Torino_GEN.097.png}
	\caption{Torino.\glsxtrshort{Gen}97}
	\label{fig:Torino.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Torino/S2_Torino_GEN.098.png}
	\caption{Torino.\glsxtrshort{Gen}98}
	\label{fig:Torino.Gen.98}
    \hfill
\end{table}
~\\

\newpage
\section{Geneva}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Geneva/S2_Geneva_GEN.050.png}
	\caption{Geneva.\glsxtrshort{Gen}50}
	\label{fig:Geneva.Gen.50}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Geneva/S2_Geneva_GEN.096.png}
	\caption{Geneva.\glsxtrshort{Gen}96}
	\label{fig:Geneva.Gen.96}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Geneva/S2_Geneva_GEN.097.png}
	\caption{Geneva.\glsxtrshort{Gen}97}
	\label{fig:Geneva.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Geneva/S2_Geneva_GEN.098.png}
	\caption{Geneva.\glsxtrshort{Gen}98}
	\label{fig:Geneva.Gen.98}
    \hfill
\end{table}
~\\

\newpage
\section{Oslo}



\begin{table}[h]
    \centering
	\includegraphics[width=.88\linewidth]{images/cities/Oslo/Oslo_GEN.097.png}
	\caption{Oslo.\glsxtrshort{Gen}97}
	\label{fig:Oslo.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.88\linewidth]{images/cities/Oslo/Oslo_GEN.098.png}
	\caption{Oslo.\glsxtrshort{Gen}98}
	\label{fig:Oslo.Gen.98}
    \hfill
\end{table}

\newpage
\section{Kiev}

\begin{table}[h]
    \centering
	\includegraphics[width=.88\linewidth]{images/cities/Kiev/Kiev_GEN.097.png}
	\caption{Kiev.\glsxtrshort{Gen}97}
	\label{fig:Kiev.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.88\linewidth]{images/cities/Kiev/Kiev_GEN.098.png}
	\caption{Kiev.\glsxtrshort{Gen}98}
	\label{fig:Kiev.Gen.98}
    \hfill
\end{table}

\newpage
\section{Roma}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Roma/S2_Roma_GEN.050.png}
	\caption{Roma.\glsxtrshort{Gen}50}
	\label{fig:Roma.Gen.50}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Roma/S2_Roma_GEN.096.png}
	\caption{Roma.\glsxtrshort{Gen}96}
	\label{fig:Roma.Gen.96}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Roma/S2_Roma_GEN.097.png}
	\caption{Roma.\glsxtrshort{Gen}97}
	\label{fig:Roma.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Roma/S2_Roma_GEN.098.png}
	\caption{Roma.\glsxtrshort{Gen}98}
	\label{fig:Roma.Gen.98}
    \hfill
\end{table}
~\\

\newpage
\section{Palermo}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Palermo/S1_palermo_GEN.050.png}
	\caption{Palermo.\glsxtrshort{Gen}50}
	\label{fig:Palermo.Gen.50}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Palermo/S1_palermo_GEN.096.png}
	\caption{Palermo.\glsxtrshort{Gen}96}
	\label{fig:Palermo.Gen.96}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Palermo/S1_palermo_GEN.097.png}
	\caption{Palermo.\glsxtrshort{Gen}97}
	\label{fig:Palermo.Gen.97}
    \hfill
\end{table}

\begin{table}[h]
    \centering
	\includegraphics[width=.90\linewidth]{images/cities/Palermo/S1_palermo_GEN.098.png}
	\caption{Palermo.\glsxtrshort{Gen}98}
	\label{fig:Palermo.Gen.98}
    \hfill
\end{table}
