added most content for ep

diff --git a/Latex/presentation/presentation20200716.tex b/Latex/presentation/presentation20200716.tex
index a6a1f00..31f560c 100644 (file)
--- a/Latex/presentation/presentation20200716.tex
+++ b/Latex/presentation/presentation20200716.tex
@@ -346,7 +346,7 @@ each insertion /* not the BS from the paper */
     \draw[blue,fill=blue!20,opacity=0.8] (O) -- (K) -- (M) -- (I) -- cycle;
     \draw[blue,fill=blue!20,opacity=0.8] (K) -- (M) -- (N) -- (L) -- cycle;
     \draw[blue,fill=blue!20,opacity=0.8] (I) -- (M) -- (N) -- (J) -- cycle;
-    
+    \draw[->,thick,red] (O) -- (N);
     %% Following is for debugging purposes so you can see where the points are
     %% These are last so that they show up on top
     %\foreach \xy in {O, A, B, C, D, E, F, G, H, I, J, K, L, M, N}{
@@ -372,12 +372,66 @@ each insertion /* not the BS from the paper */
 %------------------------------------------------
 
 \begin{frame}
-\frametitle{EP Heuristic, Restrictions and Variants}
-TODO Bells and whistles - all options. The description of each option goes to 
-the appendix on slide \ref{appendix}.
+\frametitle{EP Heuristic, Restrictions}
+Input: an order containing \textbf{N} items. Output: a list of \textbf{M} boxes 
+packed with the input items.
+\begin{columns}[T]
+    \begin{column}{0.5\textwidth}
+        Precondition: all items are sorted in decreasing order. 
+        Criteria:
+        \begin{itemize}
+            \item area
+            \item height
+            \item first height, then volume
+            \item first volume, then height
+            \item first area, then height
+            \item first height, then area
+        \end{itemize}
+        
+    \end{column}
+    \begin{column}{0.5\textwidth} 
+        Postconditions:
+        \begin{itemize}
+            \item successor items are of sizes less or equal to predecessor ones
+            \item all items keep their orientation after insertion into a box 
+        \end{itemize}
+    \end{column}
+\end{columns}
+
 
 \end{frame}
 
+%------------------------------------------------
+
+\begin{frame}
+\frametitle{EP Heuristic, Variants}
+Input: an order containing \textbf{N} items. Output: a list of \textbf{M} boxes 
+packed with the input items.
+\begin{columns}[T]
+    \begin{column}{0.5\textwidth}
+        EP-FFD: first fit.
+        \begin{itemize}
+            \item Put an item into a box
+            \item If the current box is too full for the item, pick a new box
+            \item Time complexity: $\Omega(3\cdot M \cdot N) \subseteq O(N^2)$
+        \end{itemize}
+        
+    \end{column}
+    \begin{column}{0.5\textwidth} 
+        EP-BFD: best fit. Before inserting the current item,
+        \begin{itemize}
+            \item if no previously packed box has enough room, place the item 
+            in a new box
+            \item otherwise, pick one which maximizes $f_m$
+            \item Time complexity: depends on $f_m$
+        \end{itemize}
+    \end{column}
+\end{columns}
+The merit function $f_m$ is one of: maximize free volume after item insertion, 
+minimize packing size, minimize packing size leveled, maximize residual spaces 
+- details on slide \ref{appendix}. 
+
+\end{frame}
 
 %------------------------------------------------
 
@@ -387,7 +441,7 @@ the appendix on slide \ref{appendix}.
 \begin{itemize}
     \item Implemented using Python3, standard libraries for (algebraic) 
     computation, data structures, sorting
-    \item Disadvantage: runtime overhead, no third-party optimizer support
+    \item Disadvantages: runtime overhead, no third-party optimizer support
     \item Advantages: portable, 100\% 
     \href{https://opensource.com/article/17/8/enterprise-open-source-advantages}{
      FOSS} \footnote{\url{https://opensource.org/faq}}
@@ -490,17 +544,43 @@ Balance act? Pick \dots
 
 \section{Appendix}
 
+\begin{frame}[allowframebreaks]
+\frametitle{EP heuristic, merit functions}
+\label{appendix}
+Convention: the parts after $max$ are introduced by the complexity of each 
+merit function. 
+\begin{enumerate}[1.]
+    \item Maximize free volume: pick the box which would be left with the most 
+    free volume after accommodating the item. Time complexity: $O(N^2 + 
+    max\{N, 
+    N\})$ = $O(N^2)$
+    \item Minimize the maximum packing size: choose the box where either the 
+    item is placed on top or, if not possible, the box with the most free 
+    surface. Time complexity: as above
+    \item Level the EPs: choose the box whose EPs will have the least increase 
+    in height. Time complexity: as above
+    \item Maximize the utilization of the EPs’ Residual Space (RS). RS is 
+    roughly the same concept as EMSs in the Genetic Algorithm, namely the cubes 
+    defined by projecting the EPs to the walls of a box. Pick the box with the 
+    smallest RS still fitting the item. \\ Time complexity:  $O(N^2 + max\{N, 
+    N^2\})$ = $O(N^2)$
+    
+\end{enumerate}
+
+\end{frame}
+
+
+%------------------------------------------------
+
 \begin{frame}
 \frametitle{Details}
-\label{appendix}
+\label{appendix1}
 TODO Here come corner cases and issues. Use if questions arise 
 Example: why does EP heuristic mandate a decreasing order of items? Why does GA 
 use exactly N chromosomes and M mutations \dots
 
 \end{frame}
 
-
-
 %
 %%------------------------------------------------
 %