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main.tex

@@ -305,10 +305,67 @@ rates for fully random search with 400 iterations.
 \caption{Dependence on iterations number: D=3}
 \end{figure}
 
+As prev we investigated the stability
+of the algorithm with regards to the number of iterations. We present here
+the result in dimension 3 in the graph~\ref{iter_sa}. Once again we
+restricted the window between 80 and 180 points were curves are split.
+An interesting phenomena can be observed: the error rates are somehow 
+invariant w.r.t.\ the number of iteration and once again the 1000 iterations
+threshold seems to appear --- point 145 is a light split between iteration 
+1600 and the others, but excepted for that point, getting more than 1000
+iterations tends be be a waste of time. The error rate is for 80 points the
+biggest and is about $15\%$ of the value, which is similar to the error
+rates for fully random search with 400 iterations.
+
+
 \section{Results}
+Eventually we made extensive experiments to compare the three previously
+presented heuristics. The parameters chosen for the heuristics have been 
+chosen using the experiments conducted in the previous sections
+Results are compiled in the last 
+figures~\ref{wrap2},~\ref{wrap2z},~\ref{wrap3z},~\ref{wrap4z}. The 
+recognizable curve of decrease
+of the discrepancy is still clearly recognizable in the graph~\ref{wrap2}, 
+made for points ranged between 10 and 600. We then present the result 
+in the --- now classic --- window 80 points - 180 points ---. 
+For all dimensions, the superiority of non-trivial algorithms --- simulated
+annealing and genetic search --- is clear over fully random search. 
+Both curves for these heuristics are way below the error band of random 
+search. As a result \emph{worse average results of non trivial heuristics are
+better than best average results when sampling points at random}.
+In dimension 2~\ref{wrap2z}, the best results are given by the gentic search,
+wheras in dimension 3 and 4~\ref{wrap3z},~\ref{wrap4z}, best results are
+given by simmulated annealing. It is also noticable that in that range
+of points the error rates are roughly the same for all heuristics: 
+\emph{for 1000 iteration, the stability of the results is globally the
+same for each heuristic}.
 
+\begin{figure}
+\includegraphics[scale=0.3]{Results/wrap_2.png}
+\caption{Comparison of all heuristics: D=2}
+\label{wrap2}
+\end{figure}
+
+\begin{figure}
+\includegraphics[scale=0.3]{Results/wrap_2_zoom.png}
+\caption{Comparison of all heuristics (zoom): D=2}
+  \label{wrap2z}
+\end{figure}
+
+\begin{figure}
+\includegraphics[scale=0.3]{Results/wrap_3.png}
+\caption{Comparison of all heuristics: D=3}
+  \label{wrap3z}
+\end{figure}
+
+\begin{figure}
+\includegraphics[scale=0.3]{Results/wrap_4.png}
+\caption{Comparison of all heuristics: D=4}
+  \label{wrap4z}
+\end{figure}
 
 \section{Conclusion}
-\bibliographystyle{alpha}
-\bibliography{bi}
+
+  \bibliographystyle{alpha}
+  \bibliography{bi}
 \end{document}