From d3147286673685fb5651696f7309e2db3356cf4f Mon Sep 17 00:00:00 2001 From: "A380-N-9025E0\\Tilk" <christian.tilk@univie.ac.at> Date: Fri, 4 Apr 2025 14:22:46 +0200 Subject: [PATCH] close to final --- Main.tex | 531 ++++++++++++++++++++++++++++------------ figure/GNN.jpg | Bin 0 -> 84858 bytes figure/ML_anw1.tex | 22 ++ figure/ML_anw2.tex | 27 ++ figure/ML_train.tex | 17 ++ figure/ML_train_new.tex | 44 ++++ figure/OR_algo.tex | 44 ++++ figure/ZIMPL0.PNG | Bin 0 -> 59494 bytes figure/ZIMPL1.PNG | Bin 0 -> 541096 bytes figure/ZIMPL2.PNG | Bin 0 -> 35805 bytes figure/ZIMPL3.PNG | Bin 0 -> 27111 bytes figure/ZIMPL4.PNG | Bin 0 -> 19448 bytes figure/ZIMPL5.PNG | Bin 0 -> 58319 bytes figure/ZIMPL8.PNG | Bin 0 -> 33321 bytes figure/ZIMPL9a.PNG | Bin 0 -> 10862 bytes figure/ZIMPL9b.PNG | Bin 0 -> 24022 bytes figure/catsdog.png | Bin 0 -> 270205 bytes figure/catsdog2.png | Bin 0 -> 746363 bytes figure/catsdog3.jpg | Bin 0 -> 57165 bytes 19 files changed, 528 insertions(+), 157 deletions(-) create mode 100644 figure/GNN.jpg create mode 100644 figure/ML_anw1.tex create mode 100644 figure/ML_anw2.tex create mode 100644 figure/ML_train.tex create mode 100644 figure/ML_train_new.tex create mode 100644 figure/OR_algo.tex create mode 100644 figure/ZIMPL0.PNG create mode 100644 figure/ZIMPL1.PNG create mode 100644 figure/ZIMPL2.PNG create mode 100644 figure/ZIMPL3.PNG create mode 100644 figure/ZIMPL4.PNG create mode 100644 figure/ZIMPL5.PNG create mode 100644 figure/ZIMPL8.PNG create mode 100644 figure/ZIMPL9a.PNG create mode 100644 figure/ZIMPL9b.PNG create mode 100644 figure/catsdog.png create mode 100644 figure/catsdog2.png create mode 100644 figure/catsdog3.jpg diff --git a/Main.tex b/Main.tex index 80b7cfc..129ed19 100644 --- a/Main.tex +++ b/Main.tex @@ -170,6 +170,16 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Titel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} +\tikzset{ + mynode/.style={ellipse, draw=black, align=center, fill=yellow!40,very thick, text centered, minimum width={40pt},minimum height={30pt}}, + mynode2/.style={rectangle, align=center,draw=black, fill=green!40,very thick, text centered, minimum width={75pt},minimum height={15pt}}, + mynode3/.style={rectangle,align=center, draw=black, fill=green!40,very thick, text centered, minimum width={180pt},minimum height={12pt}}, + mynodeB/.style={ellipse, draw=red, align=center, fill=yellow!40,very thick, text centered, minimum width={40pt},minimum height={30pt}}, + edge/.style = {->,> = latex',thick}, + mynode3B/.style={rectangle,align=center, draw=red, fill=green!40,very thick, text centered, minimum width={200pt},minimum height={15pt}}, +% myarrow/.style={->, >=latex', shorten >=1pt, thick}, +% mylabel/.style={text width=7em, text centered} +} % \setbeamercovered{invisible} %Standardkompiler txs:///pdflatex | txs:///bibtex | txs:///pdflatex | txs:///pdflatex @@ -189,20 +199,215 @@ %\date{\AdvanceDate[1]\today} \titlepage } - - - \frame{ + + + \frame{ \frametitle{Supervised Learning} -Learning: Pic from Proposal translated in englisch + \begin{columns}[T] + \begin{column}{0.68\textwidth} + \phantom{a}\\\medskip + \tikzstyle TestEdge=[-Triangle,line width=3pt,shorten >=3pt,green!40!black,dotted] +\tikzstyle TrainEdge=[-Triangle,thick,shorten >=3pt,line width=3pt] +\tikzset{ + Legend/.style={draw=white, top color=white, bottom color=white, inner sep=0.5em, minimum height=1cm,text width=10mm, align = left}} +\scalebox{0.7}{ +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small +\node[Legend] (Inst) {};%Trainingsdatenpunkte $i=1 \dots n$ +\node[mynode,below left=-1cm and 0.5cm of Inst] (Feat) {Input $X_1, \dots, X_n$};%Feature-Vektoren +\node[mynode,below right=-1cm and 0.5cm of Inst] (Out) {Output $Y_1, \dots, Y_n$}; +\node[mynode,below=1.5cm of Inst,align=center] (ML) {ML-Model }; +\node[mynode,below=4cm of Inst,align=center] (Pred) {Trained ML-Model}; + +\node[mynode,below left =2 cm and 0.5cm of Pred] (TestFeat) {Input $\hat{X}_1,, \dots, \hat{X}_m$}; +\node[mynode,below right=2 cm and 0.5cm of Pred] (OutTest) {Output $Y^*_1,\dots, Y^*_m$}; + +\only<2>{ +\node[mynodeB,below left=-1cm and 0.5cm of Inst] (Feat) {\textbf{Input $X_1, \dots, X_n$}};%Feature-Vektoren +\node[mynodeB,below right=-1cm and 0.5cm of Inst] (Out) {\textbf{Output $Y_1, \dots, Y_n$}}; +} +\only<3>{ +\node[mynodeB,below=1.5cm of Inst,align=center] (ML) {\textbf{ML-Model} }; +} +\only<4>{ +\node[mynodeB,below left =2 cm and 0.5cm of Pred] (TestFeat) {Input $\hat{X}_1,, \dots, \hat{X}_m$}; +} +\only<5>{ +\node[mynodeB,below right=2 cm and 0.5cm of Pred] (OutTest) {Output $Y^*_1,\dots, Y^*_m$}; +} +\path +%(TestInst) edge[TestEdge] (TestFeat) +(TestFeat) edge[TestEdge] (Pred) +(Pred) edge[TestEdge] (OutTest) +; + +\path +%(Inst) edge[TrainEdge] node {} (Out) +%(Inst) edge[TrainEdge] node {} (Feat) +(Feat) edge[TrainEdge] node {}(ML) +(Out) edge[TrainEdge] node {}(ML) +(ML) edge[TrainEdge] node {}(Pred) +; +\node[Legend, below left = 1.5cm and 1.5cm of Inst] (E1) {Training}; +\node[Legend, below left= 2.5cm and 1.5cm of Inst] (E2) {Test}; +\node[Legend, left = 1cm of E1] (S1) {}; +\node[Legend, left = 1cm of E2] (S2) {}; + +\path +(S1) edge[TrainEdge] (E1) +(S2) edge[TestEdge] (E2); +\end{tikzpicture} +} + \end{column} + \begin{column}{0.3\textwidth} + \begin{overprint} + \only<2>{ + \includegraphics[width=\textwidth]{figure/catsdog2}} + + \only<3>{ + \includegraphics[width=\textwidth]{figure/GNN} + } + \only<4->{ + \includegraphics[width=\textwidth]{figure/catsdog3} + \visible<5->{ + \begin{center} + \Large \textbf{It's a dog!} + \end{center} + } + } + \end{overprint} + \end{column} + \end{columns}\pause\bigskip +\large +\begin{center} +\visible<6->{ +\green{Works well for many classification and regression tasks!} +} +\end{center} + } + +\begin{frame} +\frametitle{Operations Research}\footnotesize + +\begin{columns}[T] +\begin{column}{.4\textwidth} +\adjustbox{max height=0.9 \textheight} +{ + \begin{tikzpicture} + +\scriptsize +\node[mynode] at (2,10.5) (1) {Problem}; +\node[mynode2] at (2,9) (2) {OR-expert}; + +\node[mynode] at (2,7.5) (3a) {Mathematical \\ model}; + +\node[mynode] at (2,6) (5a) {Algorithm}; + +\visible<4->{ +\node[mynodeB] at (0.5,4) (5b) {\textbf{\normalsize{Data set}}}; +\node[mynodeB] at (3.5,4) (6) {\textbf{\normalsize{Solution}}}; +} +\draw[edge] (1) -> (2); +\draw[edge] (2) -> (3a); +\draw[edge] (3a) -> (5a); +\visible<4->{ +\draw[edge] (5a) -> (6); +\draw[edge] (5b) -> (5a); +} + + +\onslide<1| trans:1>{ +\node[mynodeB] at (2,10.5) (a) {\normalsize{ \textbf{Problem}}}; +} +\visible<2| trans:2>{ +\node[mynodeB] at (2,7.5) (b) { \textbf{\normalsize{Mathematical}} \\ \textbf{\normalsize{model}}}; +} +\onslide<3| trans:3>{ +\node[mynodeB] at (2,6) (c) {\normalsize{\textbf{Algorithm}} }; +} +%\onslide<4| trans:4>{ +% \node[mynodeB] at (3.4,5.5) (d) {\normalsize{\textbf{Data set}} \\}; +%} +%\onslide<5| trans:5>{ +%\node[mynodeB] at (1.5,4.25) (e) {\normalsize{\textbf{Solution}}}; +%} + + +\end{tikzpicture} +} +\end{column} +\begin{column}{.6\textwidth} +\begin{overprint} +\onslide<1| trans:1> + \begin{bspBlock}{(Shortest path problem)} + Problem:\hfill\mbox{}\\[2ex] + \includegraphics[width=.99\textwidth]{figure/ZIMPL1} + \end{bspBlock} +% +\onslide<2| trans:2> + \begin{bspBlock}{(Shortest path problem)} + General mathematical model:\hfill\mbox{}\\[2ex] + \includegraphics[width=.99\textwidth]{figure/ZIMPL2} + \end{bspBlock} +% +\onslide<3| trans:3> + \begin{bspBlock}{(Dijkstra's Algorithm)} + \tiny + \begin{algorithm}[H] + \green{\tcp{Initialization}} + SET $d(s):= 0$, $pred(s):=undef$, $L:=\{s\}$\; + SET $d(j):=\infty$ for all $j\in V\setminus \{s\}$\; + \green{\tcp{Loop}} + \While{$L \ne \emptyset$} + { + SELECT $i\in L$ with $d(i)=\min_{k\in L} d(k)$\; + SET $L:=L\setminus\{i\}$~~\green{\tcp{$i$ is now ultimately marked}} + \For{$j: (i,j)\in\delta^+(i)$} + { + \If{$d(j)>d(i)+c_{ij}$} + { + \green{\tcp{Label}} + SET $d(j) := d(i)+c_{ij}$ and $pred(j):=i$\; + SET $L:=L \cup \{j\}$\; + } + } + } + \green{\tcp{Output: predecessors $pred(\cdot)$ and distances $d(\cdot)$}} +\end{algorithm} + \end{bspBlock} + % +%\onslide<4| trans:4> +% \begin{bspBlock}{(Shortest path problem)} +% \includegraphics[width=.99\textwidth]{figure/ZIMPL0}\\[3ex] +% Data set (in .zpl file):\hfill\mbox{}\\[2ex] +% \includegraphics[width=.99\textwidth]{figure/ZIMPL3} +% \end{bspBlock} +% +%% +% +%% +% +%% +\onslide<4| trans:4 > + \begin{bspBlock}{(Solution)} + \includegraphics[width=\textwidth]{figure/ZIMPL9b} + \end{bspBlock} + +\end{overprint} +\end{column} +\end{columns} +\end{frame} -works well for classification and regression tasks +\frame{ +\frametitle{Machine Learning and Operations Research} +\Large +\textbf{Key Question:}\\ +\begin{center} +\red{How can ML be used for solving optimisation problems?}\\[7ex]\pause -Die Kernfrage -ist, auf welche Weise ML in OR-Algorithmen eingesetzt werden -kann, denn kombinatorische Optimierungsprobleme unterscheiden -sich stark von den meisten Problemen, die aktuell durch ML gelst -werden\citep{BengioEtAl2021} +Combinatorial optimisation problems are quite different from most problems currently solved by ML \citep{BengioEtAl2021} +\end{center} } \section{Vehicle Routing Problems} @@ -383,13 +588,16 @@ Good/optimal solutions are often located in the border region. \frame{ \frametitle{Combine ML with OR Algorithms!} \small -\blue{Apply learning inside OR Algorithms} \citep{BengioEtAl2021}:\bigskip + Sometimes expert knowledge is not satisfactory and algorithmic decisions are taken greedily or according to ``best practice''.\\\bigskip\pause + {\large +\blue{$\Rightarrow:$ Apply learning inside OR Algorithms} \citep{BengioEtAl2021}:\medskip}\pause + \begin{itemize} %\item End to end learning (only for little constraint problems like TSP) -\item Learning to configure algorithms (expert knowledge is not satisfactory and the researcher wishes to find better ways of making decisions) -\item Machine learning alongside optimization algorithms (e.g., call ML Model for each recurring decision in an optimization algorithm) +\item Learning to configure algorithms (one-time decision) +\item Machine learning alongside optimization algorithms (recurring decisions) \end{itemize} -\bigskip +\bigskip\pause Most ML Applications in OR focus on heuristics! @@ -778,70 +986,32 @@ How can we find such a neighborhood?\\\smallskip\pause \blue{Dynamic Neighborhoo %------------------------------------------------ -\newcommand{\RF}{RF} -\newcommand{\modA}{DCH} -\newcommand{\modB}{Hom} -\newcommand{\modC}{Het} +\newcommand{\RF}{\texttt{RF}} +\newcommand{\modA}{\texttt{DCH}} +\newcommand{\modB}{\texttt{Hom}} +\newcommand{\modC}{\texttt{Het}} \begin{frame}{Learning Models} \small Models used to perform the classification task:\\\medskip \begin{itemize} - \item[\RF] Random Forest with engineered variables \item[\modA] Deep classification head of GNN encoded variables - \item[\modB] Homegeneous GNN to encode NG-Set - \item[\modC] Heterogeneous GNN to encode NG-Set + \item[\modB] Homogeneous GNN + \item[\modC] Heterogeneous GNN \pause + \item[\RF] Random Forest with engineered variables \end{itemize} + % Additional attention layers have been omitted due to computing capacity and simplified models' inability to learn connections. \end{frame} %------------------------------------------------ -\begin{frame}{Random Forest Classifier Model} -\small - - - \textbf{Random Forest Classifier:} - \begin{itemize} - \item Uses log loss (cross-entropy) as the splitting criterion. - \item Limits the depth of each tree to 100 levels to prevent overfitting. - \item Each split considers at most 4 features, controlling tree diversity. - \end{itemize} -\end{frame} %------------------------------------------------ -\begin{frame}{Encoding-Decoding GNN for Edge Prediction} - \textbf{Graph Encoder:} - \begin{itemize} - \item \textbf{Graph Type:} Homogeneous (single node and edge type) - \item \textbf{Convolution Layers:} - \begin{itemize} - \item \texttt{GCNConv1}: Projects input features to hidden space with ReLU activation. - \item \texttt{GCNConv4}: Produces output node embeddings. - \end{itemize} - \item \textbf{Output:} Node embeddings used for edge prediction or passed to a classification model. - \end{itemize} - - \textbf{Decoding Process:} - \begin{itemize} - \item Predicts edge scores using dot product of node embeddings. - \item Computes full graph adjacency matrix for all possible node pairs. - \end{itemize} +\begin{frame}{Deep classification head of GNN encoded variables (\modA)} +\textbf{Idea:} Encode nodes and classify with resulting node embeddings if ``$i$ is in neighborhood of $j$ or not''\\\pause\bigskip - \textbf{Goal:} Predict edges or provide embeddings for downstream tasks. -\end{frame} -\begin{frame}{Classification Head for Node/Graph-Level Tasks} - \textbf{Classification Model:} - \begin{itemize} - \item Fully connected feed-forward network for downstream tasks. - \item \textbf{Structure:} - \begin{itemize} - \item 3 hidden layers with ReLU activations. - \item \texttt{Input Size:} Embedding size from the encoder (e.g., 78). - \item \texttt{Output:} Binary classification via sigmoid activation. - \end{itemize} - \end{itemize} \textbf{Workflow:} \begin{enumerate} @@ -852,90 +1022,56 @@ How can we find such a neighborhood?\\\smallskip\pause \blue{Dynamic Neighborhoo \item Combining graph-based features with external data. \end{itemize} \end{enumerate} + \end{frame} + + +\begin{frame}{Homogeneous GNN (\modB)} +\textbf{Idea:} Learn the arcs in the $ng$-graph directly\\\bigskip\pause - \textbf{Goal:} Perform classification tasks using graph-based features. -\end{frame} - -%------------------------------------------------ - -\begin{frame}{Homogeneous GNN Model for Edge Prediction} - \textbf{Architecture:} + \textbf{Architecture:}\\\smallskip \begin{itemize} \item \textbf{Graph Type:} Homogeneous (single node and edge type) - \item \textbf{Convolution Layers:} - \begin{itemize} - \item 4 \texttt{GCNConv} layers for feature propagation and aggregation. - \end{itemize} - \item \textbf{Linear Layers:} - \begin{itemize} - \item Two optional linear transformations (\texttt{Linear1}, \texttt{Linear2}) for additional feature refinement. + \item 4 \blue{Convolution Layers} for feature propagation and aggregation (\texttt{GCNConv}) + \item Two linear transformations for additional feature refinement \end{itemize} - \end{itemize} -\end{frame} + \end{frame} +%------------------------------------------------ -\begin{frame}{Homogeneous GNN Model for Edge Prediction II} - \textbf{Encoding Process:} - \begin{enumerate} - \item Apply \texttt{GCNConv} layers sequentially: - \begin{itemize} - \item First 3 layers: Extract hierarchical features with ReLU activations. - \item Final layer: Produces the output embeddings. - \end{itemize} - \item Optional: Dropout for regularization and edge dropout to sparsify training graphs. - \end{enumerate} - - \textbf{Decoding Process:} - \begin{itemize} - \item Computes dot products between node embeddings to predict edge scores. - \end{itemize} - \textbf{Full Graph Prediction:} - \begin{itemize} - \item Computes pairwise similarities between all node embeddings for adjacency matrix reconstruction. - \end{itemize} - \textbf{Goal:} Predict edges in a homogeneous graph. -\end{frame} %------------------------------------------------ -\begin{frame}{Heterogeneous GNN Model for Edge Prediction} - \textbf{Architecture:} +\begin{frame}[noframenumbering]{Heterogeneous GNN (\modC)} + +\textbf{Idea:} Learn the arcs in the $ng$-gaph directly using different types of nodes and arcs\\\bigskip \pause + \textbf{Architecture:}\smallskip \begin{itemize} - \item \textbf{Node Types:} \texttt{stops}, \texttt{depot} - \item \textbf{Edge Types:} + \item \textbf{Node Types:} \texttt{customer}, \texttt{depot} + \item \textbf{Arc Types:} \begin{itemize} - \item \texttt{route} (\texttt{stops} $\to$ \texttt{stops}) - \item \texttt{remember} (\texttt{stops} $\to$ \texttt{stops}) - \item \texttt{departs} (\texttt{depot} $\to$ \texttt{stops}) - \item \texttt{return} (\texttt{stops} $\to$ \texttt{depot}) + \item \texttt{route} (\textit{customer} $\to$ \textit{customer}) + \item \texttt{remember} (\textit{customer} $\to$ \textit{customer}) + \item \texttt{departs} (\textit{depot} $\to$ \textit{customer}) + \item \texttt{return} (\textit{customer} $\to$ \textit{depot}) \end{itemize} - \item \textbf{Convolution Layers:} Uses \texttt{GCNConv} and \texttt{SAGEConv} for message passing. + \item \textbf{Convolution Layers:} (\texttt{GCNConv} and \texttt{SAGEConv}) \end{itemize} \end{frame} -\begin{frame}{Heterogeneous GNN Model for Edge Prediction II} - \textbf{Encoding Process:} - \begin{enumerate} - \item Linear projections for \texttt{stops} and \texttt{depot} inputs. - \item \textbf{Two-stage Convolution:} - \begin{itemize} - \item \textbf{Stage 1:} Combines \texttt{route}, \texttt{remember}, and \texttt{depot} connections using GCN/SAGE layers. - \item \textbf{Stage 2:} Refines embeddings using updated node features. - \end{itemize} - \item Produces final embeddings for \texttt{stops} and \texttt{depot}. - \end{enumerate} - \textbf{Decoding Process:} + + +\begin{frame}{Random Forest (\RF)} +\small + \begin{itemize} - \item Predicts sparse, directed \texttt{remember} edges using dot product of \texttt{stops} embeddings. + \item Uses log loss (cross-entropy) as the splitting criterion. + \item Limits the depth of each tree to 100 levels to prevent overfitting. + \item Each split considers at most 4 features, controlling tree diversity. \end{itemize} - - \textbf{Goal:} Predict sparse directed edges between \texttt{stops}. \end{frame} - - %\begin{frame}{Random forest summary} %\red{??? How to interpret?} % \begin{columns}[c] @@ -956,7 +1092,7 @@ How can we find such a neighborhood?\\\smallskip\pause \blue{Dynamic Neighborhoo % \end{columns} %\end{frame} -\begin{frame}{Preliminary Results -- Summary} +\begin{frame}{Preliminary Results -- \modA} % \begin{table} % \begin{tabular}{l l l} % \toprule @@ -969,44 +1105,37 @@ How can we find such a neighborhood?\\\smallskip\pause \blue{Dynamic Neighborhoo % \end{tabular} % \caption{Table caption} % \end{table} - - \begin{columns}[c] - \column{.5\textwidth} - \begin{figure}[h] - \centering - \includegraphics[width=0.9\textwidth]{figure/rf_clf1_roc.png} - \caption{\RF, Acc=0.923} - \end{figure} - - \column{.5\textwidth} - \begin{figure}[h] - - \centering - \includegraphics[width=\textwidth]{figure/m1n.png} - \caption{\modA, Acc=0.895} - \end{figure} - - \end{columns} +\begin{figure}[h] + \includegraphics[width=0.9\textwidth]{figure/m1n.png} +\end{figure}\Large +Accuracy 0.895 \end{frame} -\begin{frame}{Preliminary Results -- Summary} +\begin{frame}{Preliminary Results -- \modB~and \modC} +\Large \begin{columns}[c] \column{.5\textwidth} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{figure/m2n.png} - \caption{\modB, Acc=0.876} + \caption{\modB, Accuracy 0.876} \end{figure} \column{.5\textwidth} \begin{figure}[h] \centering \includegraphics[width=\textwidth]{figure/m3n.png} - \caption{\modC, Acc=0.785} + \caption{\modC, Accuracy 0.785} \end{figure} \end{columns} \end{frame} - +\begin{frame}{Preliminary Results -- \RF} + \begin{figure}[h] + \centering + \includegraphics[height=0.8\textheight]{figure/rf_clf1_roc.png} + \caption{\RF, Accuracy 0.923} + \end{figure} + \end{frame} \begin{frame}{DNE-neighborhood vs learned neighborhood} @@ -1035,14 +1164,16 @@ Picture neighborhood vs learned neighborhood - are the learned rather sparse or \begin{frame}{Conclusion} \begin{itemize}\setlength\itemsep{1em} - \item Result using the encoding head were rather disappointing - \item (node-) encoding a complete graph seems to have disadvantages and some heuristics must be performed (e.g.,kNN). + \item Performance of GNNs rather disappointing (compared to \RF) + %\item (node-) encoding a complete graph seems to have disadvantages and some heuristics must be performed (e.g.,kNN). \item Do we need more/other engineered variables? - \item Heterogeneity in the nature of the graph hasn't shown increase in performance. + \item What are good attention layers? + \item Using heterogeneity in the nature of the graph has shown decrease in performance. \end{itemize}\pause \end{frame} \begin{frame}{Outlook} \begin{itemize}\setlength\itemsep{1em} + \item Evaluate importance of input features \item Evaluate the learning success by using the learned neighborhood in a fully-fledged branch-price-and-cut algorithm. \item Extend the research on other VRP-variants \item Use Learning in other parts of the branch-price-and-cut algorithm @@ -1057,7 +1188,9 @@ Picture neighborhood vs learned neighborhood - are the learned rather sparse or Questions or remarks?! \end{center} } - + \scriptsize + \bibliographystyle{apalike} + \bibliography{References} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% References %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1101,10 +1234,94 @@ Picture neighborhood vs learned neighborhood - are the learned rather sparse or \end{tikzpicture} \footnotesize For clarity only, $N_1=N_4$, $N_2=N_3$ and $N_5=N_6$ have been chosen here. \end{frame} - \scriptsize - \bibliographystyle{apalike} - \bibliography{References} - - + + \begin{frame}[noframenumbering]{\modA} + \textbf{Graph Encoder:} + \begin{itemize} + \item \textbf{Graph Type:} Homogeneous (single node and edge type) + \item \textbf{Convolution Layers:} + \begin{itemize} + \item \texttt{GCNConv1}: Projects input features to hidden space with ReLU activation. + \item \texttt{GCNConv4}: Produces output node embeddings. + \end{itemize} + \item \textbf{Output:} Node embeddings + \end{itemize} + +% \textbf{Decoding Process:} +% \begin{itemize} +% \item Predicts edge scores using dot product of node embeddings. +% \item Computes full graph adjacency matrix for all possible node pairs. +% \end{itemize} + + \textbf{Goal:} Predict edges or provide embeddings for downstream tasks. +\end{frame} + +\begin{frame}[noframenumbering]{\modA} + \textbf{Classification Model:} + \begin{itemize} + \item Fully connected feed-forward network for downstream tasks. + \item \textbf{Structure:} + \begin{itemize} + \item 3 hidden layers with ReLU activations. + \item \texttt{Input Size:} Embedding size from the encoder (e.g., 78). + \item \texttt{Output:} Binary classification via sigmoid activation. + \end{itemize} + \end{itemize} + + \textbf{Workflow:} + \begin{enumerate} + \item Encode node embeddings using GNN layers. + \item Pass embeddings to classification head for: + \begin{itemize} + \item Node/graph classification tasks. + \item Combining graph-based features with external data. + \end{itemize} + \end{enumerate} + + \textbf{Goal:} Perform classification tasks using graph-based features. +\end{frame} + \begin{frame}[noframenumbering]{Homogeneous GNN Model} + \textbf{Encoding Process:} + \begin{enumerate} + \item Apply \texttt{GCNConv} layers sequentially: + \begin{itemize} + \item First 3 layers: Extract hierarchical features with ReLU activations. + \item Final layer: Produces the output embeddings. + \end{itemize} + \item Optional: Dropout for regularization and edge dropout to sparsify training graphs. + \end{enumerate} + + \textbf{Decoding Process:} + \begin{itemize} + \item Computes dot products between node embeddings to predict edge scores. + \end{itemize} + + \textbf{Full Graph Prediction:} + \begin{itemize} + \item Computes pairwise similarities between all node embeddings for adjacency matrix reconstruction. + \end{itemize} + + \textbf{Goal:} Predict edges in a homogeneous graph. +\end{frame} + +\begin{frame}[noframenumbering]{Heterogeneous GNN Model} + \textbf{Encoding Process:} + \begin{enumerate} + \item Linear projections for \texttt{customer} and \texttt{depot} inputs. + \item \textbf{Two-stage Convolution:} + \begin{itemize} + \item \textbf{Stage 1:} Combines \texttt{customer}, \texttt{ng}, and \texttt{depot} connections using GCN/SAGE layers. + \item \textbf{Stage 2:} Refines embeddings using updated node features. + \end{itemize} + \item Produces final embeddings for \texttt{customer} and \texttt{depot}. + \end{enumerate} + + \textbf{Decoding Process:} + \begin{itemize} + \item Predicts sparse, directed \texttt{ng} edges using dot product of \texttt{customer} embeddings. + \end{itemize} + + \textbf{Goal:} Predict sparse directed edges between \texttt{customer}. +\end{frame} \end{document} diff --git a/figure/GNN.jpg b/figure/GNN.jpg new file mode 100644 index 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HcmV?d00001 diff --git a/figure/ML_anw1.tex b/figure/ML_anw1.tex new file mode 100644 index 0000000..641bbdb --- /dev/null +++ b/figure/ML_anw1.tex @@ -0,0 +1,22 @@ + +\begin{center} + + +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small +\node[mynode] (Inst) {Testdatenpunkt}; +\node[mynode,below=0.5 cm of Inst] (Feat) {Feature-Vector}; +\node[mynode,below=0.5 cm of Feat] (ML) {Trainiertes ML-Verfahren}; +\node[mynode,below=0.5 cm of ML] (Out) {Vorhergesagter Output}; +\path +(Inst) edge[-Triangle,thick,shorten >=3pt] (Feat) +(Feat) edge[-Triangle,thick,shorten >=3pt] (ML) +(ML) edge[-Triangle,thick,shorten >=3pt] (Out) +; +\end{tikzpicture} + + + + + +\end{center} \ No newline at end of file diff --git a/figure/ML_anw2.tex b/figure/ML_anw2.tex new file mode 100644 index 0000000..7cf86b3 --- /dev/null +++ b/figure/ML_anw2.tex @@ -0,0 +1,27 @@ + +\begin{center} + + + + +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small +\node[large, below=1cm of Inst,text depth = 7 cm] (OR) {}; +\node[mynode, above = 1cm of OR] (Inst) {Testinstanz}; +\node[mynode,below right=-4.5cm and -9cm of OR] (Feat) {Feature-Vector}; +\node[mynode,below right=-4.5cm and -4cm of OR] (Out) {Output}; +\node[mynode,below =-7cm of OR] (Ver) {OR-Verfahren}; +\node[mynode,below =-2cm of OR] (ML) {Trainiertes ML-Verfahren}; +\node[mynode2,right =2cm of OR] (Los) {Lösung}; + +\path +(Inst) edge[thick] (OR) +(Ver) edge[thick] (Feat) +(Feat) edge[thick] (ML) +(ML) edge[thick] (Out) +(Out) edge[thick] (Ver) +(OR) edge[thick] (Los) +; +\end{tikzpicture} + +\end{center} \ No newline at end of file diff --git a/figure/ML_train.tex b/figure/ML_train.tex new file mode 100644 index 0000000..4dadbe7 --- /dev/null +++ b/figure/ML_train.tex @@ -0,0 +1,17 @@ + +\begin{center} +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small + +\node[mynode] (Inst) {Trainingsdatenpunkt}; +\node[mynode,below left=1cm and -0.5cm of Inst] (Feat) {Feature-Vector}; +\node[mynode,below right=1cm and -0.5cm of Inst] (Out) {Berechneter Output}; +\node[mynode,below=3cm of Inst,align=center] (ML) {ML-Verfahren }; +\path +(Inst) edge[-Triangle,thick,shorten >=3pt] node {} (Out) +(Inst) edge[-Triangle,thick,shorten >=3pt] node {} (Feat) +(Feat) edge[-Triangle,thick,shorten >=3pt] node {}(ML) +(Out) edge[-Triangle,thick,shorten >=3pt] node {}(ML) +; +\end{tikzpicture} +\end{center} \ No newline at end of file diff --git a/figure/ML_train_new.tex b/figure/ML_train_new.tex new file mode 100644 index 0000000..1c1366f --- /dev/null +++ b/figure/ML_train_new.tex @@ -0,0 +1,44 @@ +\tikzstyle TestEdge=[-Triangle,line width=3pt,shorten >=3pt,green!40!black,dotted] +\tikzstyle TrainEdge=[-Triangle,thick,shorten >=3pt,line width=3pt] +\tikzset{ + Legend/.style={draw=white, top color=white, bottom color=white, inner sep=0.5em, minimum height=1cm,text width=10mm, align = left}} + +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small + +\node[Legend] (Inst) {};%Trainingsdatenpunkte $i=1 \dots n$ +\node[mynode,below left=-1cm and -0.5cm of Inst] (Feat) {Input $X_1, \dots, X_n$};%Feature-Vektoren +\node[mynode,below right=-1cm and -0.5cm of Inst] (Out) {Output $Y_1, \dots, Y_n$}; +\node[mynode,below=1.5cm of Inst,align=center] (ML) {ML-Model }; +\node[mynode,below=4cm of Inst,align=center] (Pred) {Prediction}; + + +\node[Legend, above left = 1cm and 2.5cm of Pred] (TestInst) {}; %Testdatenpunkt $j$ +\node[mynode,below=1 cm of TestInst] (TestFeat) {Input $\hat{X}_1,, \dots, \hat{X}_m$}; + +\node[mynode,right=1.5 cm of Pred] (OutTest) {Output $Y^*_1,\dots, Y^*_m$}; +\path +%(TestInst) edge[TestEdge] (TestFeat) +(TestFeat) edge[TestEdge] (Pred) +(Pred) edge[TestEdge] (OutTest) +; + +\path +%(Inst) edge[TrainEdge] node {} (Out) +%(Inst) edge[TrainEdge] node {} (Feat) +(Feat) edge[TrainEdge] node {}(ML) +(Out) edge[TrainEdge] node {}(ML) +(ML) edge[TrainEdge] node {}(Pred) +; + + + +\node[Legend, below right = 1cm and 5cm of Inst] (E1) {Training}; +\node[Legend, below = -0.25cm of E1] (E2) {Test}; +\node[Legend, left = 1cm of E1] (S1) {}; +\node[Legend, left = 1cm of E2] (S2) {}; + +\path +(S1) edge[TrainEdge] (E1) +(S2) edge[TestEdge] (E2); +\end{tikzpicture} diff --git a/figure/OR_algo.tex b/figure/OR_algo.tex new file mode 100644 index 0000000..1c1366f --- /dev/null +++ b/figure/OR_algo.tex @@ -0,0 +1,44 @@ +\tikzstyle TestEdge=[-Triangle,line width=3pt,shorten >=3pt,green!40!black,dotted] +\tikzstyle TrainEdge=[-Triangle,thick,shorten >=3pt,line width=3pt] +\tikzset{ + Legend/.style={draw=white, top color=white, bottom color=white, inner sep=0.5em, minimum height=1cm,text width=10mm, align = left}} + +\begin{tikzpicture}[->, node distance=0.8cm, auto] +\small + +\node[Legend] (Inst) {};%Trainingsdatenpunkte $i=1 \dots n$ +\node[mynode,below left=-1cm and -0.5cm of Inst] (Feat) {Input $X_1, \dots, X_n$};%Feature-Vektoren +\node[mynode,below right=-1cm and -0.5cm of Inst] (Out) {Output $Y_1, \dots, Y_n$}; +\node[mynode,below=1.5cm of Inst,align=center] (ML) {ML-Model }; +\node[mynode,below=4cm of Inst,align=center] (Pred) {Prediction}; + + +\node[Legend, above left = 1cm and 2.5cm of Pred] (TestInst) {}; %Testdatenpunkt $j$ +\node[mynode,below=1 cm of TestInst] (TestFeat) {Input $\hat{X}_1,, \dots, \hat{X}_m$}; + +\node[mynode,right=1.5 cm of Pred] (OutTest) {Output $Y^*_1,\dots, Y^*_m$}; +\path +%(TestInst) edge[TestEdge] (TestFeat) +(TestFeat) edge[TestEdge] (Pred) +(Pred) edge[TestEdge] (OutTest) +; + +\path +%(Inst) edge[TrainEdge] node {} (Out) +%(Inst) edge[TrainEdge] node {} (Feat) +(Feat) edge[TrainEdge] node {}(ML) +(Out) edge[TrainEdge] node {}(ML) +(ML) edge[TrainEdge] node {}(Pred) +; + + + +\node[Legend, below right = 1cm and 5cm of Inst] (E1) {Training}; +\node[Legend, below = -0.25cm of E1] (E2) {Test}; +\node[Legend, left = 1cm of E1] (S1) {}; +\node[Legend, left = 1cm of E2] (S2) {}; + +\path +(S1) edge[TrainEdge] (E1) +(S2) edge[TestEdge] (E2); +\end{tikzpicture} diff --git a/figure/ZIMPL0.PNG b/figure/ZIMPL0.PNG new 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