diff --git a/.DS_Store b/.DS_Store index 48a09dbcb61241b0841ae783fa838baeac547c0e..8240b679aef72fa65953700605112293a5a6236c 100644 GIT binary patch delta 94 zcmZn(XbG6$&&atkU^hP_=OjUq$qEA8lWhe{ISh>qbQBB?4JYpsw4cl@D7g8%KnA-a x4?`wHE<++iIzuW$F+)5<4nsbWozGC5QkFMk$@Gm2O#0$\\ -$np$&p&Nombre de processus&$\mathbb{N}, np>2$\\ -$nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ -$ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ -$n$&v&Dimension de l'espace du problème&$\mathbb{N}, n>0$\\ -$m$&v&Dimension de l'espace de solution&$\mathbb{N}, m>0$\\ -$z$&v&Taille de la base de données&$\mathbb{N}, z>0$\\ -$p$&v&Description du problème&$\mathbb{R} ^ n$\\ -$s$&v&Description de la solution&$\mathbb{R} ^ m$\\ -$r_a$&v&Nombre de modèles pour l'étape rétrouver&$\mathbb{N}, r_a>2$\\ -$r_b$&v&Nombre de modèles pour l'étape de réutilisation&$\mathbb{N}, r_b>2$\\ -$at$&v&Identificateur des actions&$[0,2] \in \mathbb{N}$\\ -$nl_i$&v&Nombre de voisins locaux pour le modèle $i$&$\mathbb{N}, nl_i \le nl$\\ -$g$&v&Description de la meilleure solution globale&$\mathbb{R} ^ m$\\ -$v$&v&Évaluation de la meilleure solution globale&$\mathbb{R}$\\ -$d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ -$MP(x_1^z,x_2,a)$&f&Fonction du modèle pour retrouver entre $x_1$ et $x_2$&$\mathbb{R}^{a \times z}$\\ -$MS(x_1^m)$&f&Fonction du modèle pour réutiliser avec $x_1$ &$\mathbb{R}^m$\\ -$f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ -\end{tabular} -\caption{Variables et paramètres du modèle proposé (Type: p - paramètre, v - variable, f - fonction)} -\label{tabVarPar} -\end{table} - -\subsubsection{Rechercher} -La première étape de l'algorithme consiste à trouver les cas les plus similaires à un nouveau cas éventuel\textcolor{red}{supprimer éventuel?}, pour cela un premier modèle de stacking avec différents processus est utilisé comme le montre la figure \ref{figSta1}. Au niveau-0 chaque processus sélectionne et exécute un algorithme de recherche de voisins différent choisi parmi $r_a$ modèles dans le conteneur C3, avec un nombre de voisins $nl_i$ choisi aléatoirement dans l'intervalle $[0,nl]$. Puis au niveau-1 les résultats sont unifiés en construisant un ensemble global de cas similaires. Cinq algorithmes pour le niveau 0 ont été mis en Å“uvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation. - -\begin{figure} -\centering -\includegraphics[width=\textwidth]{./Figures/Stacking1.png} -\caption{\textit{Stacking} pour chercher les plus proches voisins} -\label{figSta1} -\end{figure} - -Formellement, le premier modèle de stacking proposé fonctionne avec deux paramètres : \textcolor{red}{quels sont les 2 paramètres?}une base de données de $z$ cas, un cas est composé de la description du problème et de la description de la solution ${(p^n,s^m)}^{z}$ et un nouveau cas sans solution $p_w^n$. Le but de tous les algorithmes de niveau 0 est de générer une liste locale de cas similaires au nouveau cas en utilisant les informations de la description du problème. C'est-à-dire, pour chaque $j$ modèle effectué, l'ensemble $X_j=\{x_1,x_2,. ..,x_z \; | \; x_i=MP_i((p^n)^z, p_w^n,nl_i) \}$ est généré. Au niveau 1, un ensemble global est créé à l'aide de tous les ensembles locaux $j$ $X_g=\cup_{n=1}^{ng} min \ ; ((\cup_{j=1}^{np} X_j)-X_g)$, puis le résultat du premier modèle d'empilement est l'ensemble $X_g$ avec les $ng$ voisins les plus proches. - -\subsubsection{Réutiliser} - -Une fois la liste globale des cas similaires établie, les informations correspondant aux solutions de chacun de ces cas sont extraites et utilisées pour générer une nouvelle solution qui s'adapte au nouveau cas, comme le montre la figure \ref{figAuto}. La génération est effectuée avec un deuxième modèle de stacking avec différents processus comme le montre la figure \ref{figSta2}. Au niveau 0 chaque processus sélectionne et exécute un algorithme de génération différent à partir des modèles $r_b$ dans le conteneur C2. Au niveau 1 toutes les différentes solutions générées sont stockées dans une mémoire globale. Étant donné que la représentation des solutions est comme un tableau unidimensionnel de multiples cases, alors neuf algorithmes ont été mis en Å“uvre pour l'étape de réutilisation au niveau 0 : moyenne avec probabilité, moyenne sans probabilité, valeurs médianes, sélection aléatoire avec probabilité, copie et changement, vote, interpolation, ACP (analyse en composantes principales) et marche aléatoire. Tous les algorithmes proposés pour générer une nouvelle solution combinent et modifient l'ensemble de solutions construit dans l'étape de récupération. - -\begin{figure}[!ht] -\centering -\includegraphics[width=\textwidth]{./Figures/AutomaticS.png} -\caption{Génération et vérification automatique des solutions} -\label{figAuto} -\end{figure} - -La moyenne pondérée avec probabilité permet de construire une solution selon le calcul de la moyenne avec le poids de chaque solution en fonction de sa proximité au nouveau problème. L'équation \ref{gen00} définit le calcul de la probabilité en fonction de la distance entre les problèmes et l'équation \ref{gen01} construit la solution en calculant chaque case $j$. - -\begin{equation} - \alpha_j=\frac{d(p_j^n,p_w^n)}{\sum_{i=0}^{nl} d(p_i^n,p_w^n)} - \label{gen00} -\end{equation} - -\begin{equation} - s^m_{j,w}= \frac{1}{nl} \sum_{i=0}^{nl} \alpha_j s_{i,j} - \label{gen01} -\end{equation} - -La moyenne sans probabilité copie aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à tous les éléments de toutes les solutions proches. Formellement la génération de la solution est écrite comme l'équation \ref{gen2}, où chaque position $j$ est calculée de la même façon. - -\begin{equation} - s^m_{w,j}= \frac{1}{nl} \sum_{i=0}^{nl} s_{i,j} - \label{gen2} -\end{equation} - -La génération de la solution par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension ou $X_j$ représente l'ensemble des valeurs ordonnées de toutes les solutions $S$ dans la position $j$ - -\begin{equation} - s_{j,w}^m= - \begin{cases} - x_{j,\frac{m+1}{2}}, \; si \; m \in \{{2k+1 : k \in \mathbb{Z}}\}\\ - \frac{x_{j,\frac{m}{2}}+x_{j,\frac{m}{2}+1}}{2}, \; sinon\\ - \end{cases} -\end{equation} - -La sélection aléatoire avec probabilité génère une solution en copiant aléatoirement l'information des solutions dans chaque position ayant une plus grande probabilité vers le cas de problème associé le plus proche. - -\begin{equation} -s_{j,w}^m=s_{j,k}^m; k \sim \left(\frac{d(p_k,p_w)}{\sum_{i=1}^nl(p_k,p_i)} \right) -\end{equation} - -Copie/changement, copie les informations d'une solution aléatoire et change une partie avec les informations d'une autre solution sélectionnée aléatoirement. - -\begin{equation} -s_{j,w}^m=s_{j,k}^m; k \sim \left(\frac{1}{nl} \right) -\end{equation} - -Le vote permet de copier l'information qui se présente avec plus de fréquence entre toutes les solutions. - -\begin{equation} -s_{j,w}^m=s_{j,k}^m; k=argmax_i \; \mathbb{P}(X=s_{j,i}^m), 1\le i \le nl -\end{equation} - -L'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation lineaire 1D calculée. - -\begin{equation} - s_{w,j}^m \sim \left( \left( \frac{y_i-y_{i+1}}{x_i-x_{i+1}} \right) (x-x_i)+y_i \right), \forall i \; 0 \le i < nl -\end{equation} - -Avec ACP (PCA - Principal Component Analysis), si la dimension de l'espace des solutions $m$ est plus petit que la dimension de l'espace des problèmes $n$ ($m0$\\ -$np$&p&Nombre d'agents&$\mathbb{N}, np>2$\\ -$nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ -$ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ -$n$&v&Dimension de l'espace du problème&$\mathbb{N}, n>0$\\ -$m$&v&Dimension de l'espace de solution&$\mathbb{N}, m>0$\\ -$p$&v&Description du problème&$\mathbb{R} ^ n$\\ -$s$&v&Description de la solution&$\mathbb{R} ^ m$\\ -$p_w$&v&Description du nouveau problème&$\mathbb{R} ^ n$\\ -$s_w$&v&Description de la nouvelle solution&$\mathbb{R} ^ m$\\ -$n_{rt}$&v&Nombre d'algorithmes por l'étape de rétrouver&$\mathbb{Z}$\\ -$n_{rs}$&v&Nombre d'algorithmes de réutilisation&$\mathbb{Z}$\\ -$d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ -$rn(x,y)$&f& - -\begin{tabular}{@{}c@{}}Valeur aléatoire avec distribution normale\\ $x$ moyenne, $y$ écart-type -\end{tabular} - -&$\mathbb{R}_+$\\ -$rnp(x,y)$&f& - -\begin{tabular}{@{}c@{}}Valeur aléatoire discrète, $x$ nombre d'options \\ $y$ vecteur discret de probabilités -\end{tabular} -&$\mathbb{Z}$\\ -$f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ -\end{tabular} -\caption{Variables et paramètres du modèle proposé (Type: p - paramètre, v - variable, f - fonction)} -\label{tabVarPar} -\end{table} - -\subsubsection{Algorithmes} -Lors de la première étape de l'empilage\textcolor{red}{empilement?}, chaque agent peut sélectionner l'un des algorithmes mis en Å“uvre pour rechercher des problèmes similaires au nouveau problème posé. Les algorithmes sont les suivants : KNN (K-Nearest Neighbor), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN pondéré. - -Lors de la deuxième étape de l'empilage\textcolor{red}{idem}, les agents peuvent choisir un algorithme parmi les suivants : pondération avec probabilité, pondération sans probabilité, valeurs médianes, Copier/Changer, vote, interpolation, PCA (analyse en composantes principales) et pas aléatoire\textcolor{red}{et pas aléatoire?}. - -La sélection aléatoire pondérée avec l'algorithme de probabilité construit une solution en copiant aléatoirement les informations des solutions ayant une probabilité plus élevée vers le cas de problème associé le plus proche. En revanche, la sélection aléatoire pondérée sans algorithme de probabilité copie aléatoirement les informations des solutions selon la distribution uniforme. Les valeurs médianes utilisent la valeur médiane de toutes les solutions pour chaque dimension. L'algorithme fondé sur la copie/le changement copie les informations d'une solution aléatoire et en modifie une partie avec les informations d'une autre solution sélectionnée de manière aléatoire. L'algorithme fondé sur le vote copie l'information la plus fréquente entre les solutions. L'algorithme fondé sur l'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation calculée. Le générateur avec PCA transforme la description du problème en un espace de description de solutions afin d'établir une relation entre le problème et sa solution. Enfin, l'algorithme de pas aléatoire sélectionne une solution et modifie les valeurs dans une seule dimension de manière aléatoire avec un petit pas dans l'espace des solutions. - -\subsubsection{Structure des agents} - -La structure des agents est similaire pour tous, mais chaque agent effectue un processus cognitif individuel qui lui permet d'obtenir un comportement indépendant et différent de tous les autres. La figure \ref{figAgent} montre les actions et les variables nécessaires à l'exécution de l'ensemble du processus. - -Il y a trois actions possibles à exécuter (« Récupérer et réutiliser », « Réutiliser » et « Échanger ») et huit variables : \textcolor{red}{faire une liste}le nombre de voisins qui définit le nombre de problèmes similaires au nouveau problème posé que l'agent doit rechercher dans la base de données, la liste des voisins les plus proches établit la liste des agents voisins avec lesquels des informations peuvent être échangées, l'algorithme de récupération est l'identifiant de l'algorithme que l'agent va exécuter pour trouver les problèmes similaires au nouveau problème, l'algorithme de réutilisation est l'identifiant de l'algorithme que l'agent va exécuter pour générer une solution candidate au nouveau problème, solution est la description de la solution générée, évaluation de la solution est la valeur numérique décrivant la qualité de la solution générée selon une fonction d'optimisation (eq \ref{eqOpt1} et eq \ref{eqOpt2}), vecteur bayésien pour les algorithmes de récupération contenant les valeurs de probabilité pour chacun des algorithmes de récupération et vecteur bayésien pour les algorithmes de réutilisation contenant les valeurs de probabilité pour chacun des algorithmes de réutilisation. - -\begin{equation} -min \; \left( f_s(p_w^n, s_w^m) \right) = min \left( \sum_{i=1}^{ng} \frac{d(s_w^m,s_i^t)}{d(p_w^n,p_i^n)^2} \right) -\label{eqOpt1} -\end{equation} - -\begin{equation} -s_i^t=s_i^m+rn(0,d(p_w^n,p_i^n)) -\label{eqOpt2} -\end{equation} - -\begin{figure}[!ht] -\centering -\includegraphics[scale=0.7]{Figures/agent.png} -\caption{Structure interne des agents} -\label{figAgent} -\end{figure} - -\subsubsection{Apprentissage des agents} - -Tous les agents contiennent un vecteur bayésien de probabilité pour la phase de récupération (conteneur C3) et un vecteur bayésien de probabilité pour la phase de réutilisation (conteneur C2). Initialement, ces vecteurs sont configurés avec une probabilité uniforme pour tous les algorithmes de récupération et de réutilisation. Il s'agit de la distribution de probabilité \textit{a priori}, mais pour chaque itération, les vecteurs sont mis à jour avec l'équation bayésienne en utilisant les meilleurs résultats du même agent comme paramètre de vraisemblance. Le choix suivant d'algorithmes pour la récupération et la réutilisation calcule la probabilité avec les vecteurs. L'agent apprend ainsi de son expérience et sélectionne les algorithmes les plus susceptibles de fournir les meilleures réponses au regard de l'objectif défini. - -L'apprentissage est fondé sur un raisonnement bayésien où les vecteurs de récupération et de réutilisation sont initialisés avec une probabilité uniforme pour tous les algorithmes, comme le montre la figure \ref{fig:bayev}. Au cours d'une itération, si un algorithme a contribué à la construction de la meilleure solution, il reçoit un point pour chaque agent qui l'a utilisé. Ces informations sont stockées dans un vecteur normalisé qui est ensuite utilisé comme vecteur de vraisemblance $P(A)$ pour calculer les nouvelles probabilités dans l'équation bayésienne \ref{eqBay}, $P(B)$ est le terme de normalisation global. - -\begin{figure} - \centering - \includegraphics[scale=0.5]{Figures/BayesianEvolution.png} - \caption{Exemple d'évolution Bayésienne des vecteurs pour un agent. a) Initialisation des probabilités $P(B|A)$ vecteurs pour Retrieve et Reuse, b) Probabilités après quelques itérations $P(A|B)$ vecteurs pour Retrieve et Reuse} - \label{fig:bayev} -\end{figure} - -\begin{equation} - P(A|B)=\frac{P(B|A)P(A)}{P(B)} - \label{eqBay} -\end{equation} - -La sélection d'un algorithme de recherche $a_{rt}$ se fait au moyen d'une valeur aléatoire tirée du vecteur de distribution de recherche discrète obtenu par raisonnement bayésien, comme le montre l'équation \ref{eqRta}. - -\begin{equation} - a_{rt}=rnp(n_{rt},P(A|B)_{rt}) - \label{eqRta} -\end{equation} - -La sélection d'un algorithme de réutilisation $a_{rs}$ se fait au moyen d'une valeur aléatoire tirée du vecteur de distribution de réutilisation discrète obtenu par raisonnement bayésien, comme le montre l'équation \ref{eqRsa}. - -\begin{equation} - a_{rs}=rnp(n_{rs},P(A|B)_{rs}) - \label{eqRsa} -\end{equation} - -Le processus d'apprentissage est réalisé individuellement par chaque agent, mais comporte un aspect collaboratif puisque les agents communiquent les informations qu'ils ont trouvées, les optimisations locales qu'ils ont réalisées, ainsi que les algorithmes et les paramètres. - -\subsubsection{Échanges entre les agents} - -Les agents peuvent modifier leurs informations au cours d'une itération en choisissant au hasard un voisin dans leur liste de voisins les plus proches. Les changements permettent d'obtenir une grande probabilité de propager les paramètres des agents qui ont obtenu les meilleurs résultats et d'obtenir des effets de rétroaction. Le type d'information qu'ils peuvent modifier est choisi au hasard, il peut s'agir du nombre de voisins, de la liste des voisins les plus proches, de l'algorithme de récupération, de l'algorithme de réutilisation ou même des vecteurs bayésiens. Si un agent décide de modifier ses informations avec un voisin, les informations qu'il possédait à l'origine sont remplacées par une copie des informations obtenues auprès de l'agent sélectionné. - -\subsection{Résultats} - -Afin de comparer la prédiction des performances et le comportement de l'algorithme proposé, onze bases de données de régression présentant des caractéristiques différentes ont été sélectionnées. Les bases de données et leurs caractéristiques sont indiquées dans le tableau \ref{tabBases}. Les valeurs des paramètres de l'algorithme sont les suivantes $it=100$, $np=50$, $nl=10$ et $ng=10$. Les paramètres de tous les autres algorithmes sont présentés dans le tableau \ref{AlgsPar}. - -\begin{table}[!ht] -\footnotesize -\centering -\begin{tabular}{c|ccccccccccc} -&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ -\hline -%DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.263&8.225\\ -DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.225\\ -%DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016&0.016\\ -DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016\\%DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&8.148&7.991\\ -DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&7.991\\ -%DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.628&0.607\\ -DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.607\\ -%DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.690&0.662\\ -DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.662\\ -%DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.413&9.070\\ -DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.070\\ -%DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&3.031&2.941\\ -DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&2.941\\ -%DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.752&2.553\\ -DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.553\\ -%DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.747&2.468\\ -DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.468\\ -%DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.897&3.621\\ -DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.621\\ -DS11&0.625&0.565&0.741&0.56&0.606&0.626&0.626&0.681& -0.541&0.54\\ -\hline -%Avg. Rank&5.8&6.5&7.2&2.3&6.7&5.7&5.6&8.65&1.9&4.65\\ -Avg. Rank&6.4&6.9&8.2&2.6&7.2&6.45&6.35&9.55&2.1&4.75\\ -\end{tabular} -\caption{Résultat de la métrique RMSE (Root Mean Squared Error) pour les bases de données évaluées avec des algorithmes de régression} -\label{tabRes1} -\end{table} - -\begin{table}[!ht] -\scriptsize -\centering -\begin{tabular}{llccp{1.4cm}p{1.2cm}p{1.2cm}} -ID&DataSet&Features&Instances&Output. Dimension&Input. Domain&Output Domain\\ -\hline -DS1&Yatch Hydrodynamics&6&308&1&$\mathbb{R}$&$\mathbb{R}$\\ -DS2&Electrical Grid Stability&12&10000&1&$\mathbb{R}$&$\mathbb{R}$\\ -DS3&Real State Valuation&6&414&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ -DS4&Wine Quality (Red)&11&1598&1&$\mathbb{R_+}$&$\mathbb{N}$\\ -DS5&Wine Quality (White)&11&4897&1&$\mathbb{R_+}$&$\mathbb{N}$\\ -DS6&Concrete Compressive Strength&8&1030&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ -DS7&Energy Efficiency&8&768&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ -DS8&Gas Turbine CO, NOx Emission (2015)&9&7384&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ -DS9&Student Performace Portuguese&30&649&3&$\mathbb{N*}$&$\mathbb{N}$\\ -DS10&Student Performance Math&30&395&3&$\mathbb{N*}$&$\mathbb{N}$\\ -DS11&Generated Student Performance&5&1000&1&$\mathbb{R}_+$&$\mathbb{R}_+$\\ -\end{tabular} -\caption{Description des bases de données évaluées. (* après codification comme -\textit{String})} -\label{tabBases} -\end{table} - -\begin{table}[!ht] -\centering -\begin{tabular}{ccc|ccc} -ID&Parameter&Value&ID&Parameter&Value\\ -\hline -A1&Intercept&True&A6&Degree&4\\ -&Positive&True&&Bias&True\\ -\hline -A2&Neighbors&5&A7&Fit Intercept&True\\ -&Weights&Uniform&&alpha&0.2\\ -&Metric&Minkowsky&&tol&1e-4\\ -&Power Minkowsky&2\\ -\hline -A3&Error&Squared Error&A8&Fit Intercept&True\\ -&Min samples split&2&&alpha&[0.00001, 0.4]\\ -&&&&Max iter&1000\\ -&&&&tol&1e-4\\ -\hline -A4&Estimators&10&A9&Error&Squarred Error\\ -&Error&Squared Error&&Learning Rate&0.1\\ -&Min samples split&2&&Estimators&100\\ -&Bootstrap&True&&Min Split&2\\ -\hline -A5&Hidden Layers&100\\ -&Activation&Relu\\ -&Solver&Adam\\ -&alpha&0.0001\\ -&Learning Rate&0.001\\ -&Max Iter&200\\ -&beta1&0.9\\ -&beta2&0.999\\ -&epsilon&1e-8\\ -\end{tabular} -\caption{Paramètres pour tous les algorithmes comparés} -\label{AlgsPar} -\end{table} - -Le classement moyen de toutes les bases de données en fonction de la mesure RMSE (Root Mean Square Error) est indiqué dans le tableau \ref{tabRes1}. Les résultats détaillés des mêmes algorithmes et des mêmes bases de données, mais comparés avec la métrique MAE (Median Absolute Error), sont présentés dans le tableau \ref{tabRes2}. - -\begin{table}[!ht] -\footnotesize -\centering -\begin{tabular}{c|ccccccccccc} -Dataset&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ -\hline -%DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.193&1.218\\ -DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.218\\ -%DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.011&0.010\\ -DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.010\\ -%DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.90&3.771\\ -DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.771\\ -%DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.154&0.135\\ -DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.135\\ -%DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.113&0.085\\ -DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.085\\ -%DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.439&5.072\\ -DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.072\\ -%DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.008&1.006\\ -DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.006\\ -%DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.861&0.794\\ -DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.794\\ -%DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.721&1.556\\ -DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.556\\ -%DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.602&2.371\\ -DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.371\\ -DS11&0.387&0.35&0.46&0.338&0.384&0.387&0.387&0.453& -0.327&0.347\\ -\hline -Avg. Rank&7.15&6.9&5.35&2.6&7.95&7.25&7.3&9.0&2.5 -&4.5\\ -%Avg. Rank&6.45&6.5&4.35&2.4&7.45&6.55&6.6&8.1&2.4&4.2\\ -\end{tabular} -\caption{Comparaison des résultats MAE (Median Absolute Error) pour les bases de données évaluées avec des algorithmes de régression} -\label{tabRes2} -\end{table} - -La dispersion globale, la médiane et les valeurs aberrantes pour toutes les bases données évaluées sont présentées dans la figure \ref{figBox}, où l'on peut voir que l'algorithme proposé génère dans certains cas plus de valeurs aberrantes que d'autres algorithmes, mais la variance est très faible et la convergence est proche de la valeur réelle, meilleure que la plupart des algorithmes comparés. Les valeurs aberrantes sont plus élevées que les valeurs réelles.\textcolor{red}{plus élevées??, pourquoi?} - -\begin{figure}[!ht] -\includegraphics[width=\textwidth]{Figures/boxplot2.png} -\caption{Résultats de la métrique MAE (Median Absolute Error) pour dix algorithmes} -\label{figBox} -\end{figure} - -Les résultats montrent que l'algorithme est compétitif dans la plupart des bases de données sélectionnées, obtenant les meilleurs résultats dans les bases DS2, DS4, DS5 et DS9. Globalement, d'après le classement moyen, l'algorithme est placé en troisième position, à proximité d'autres algorithmes d'ensemble. Par rapport à l'ESCBR, une amélioration des résultats et une réduction de la variance ont été obtenues, ce qui montre que les systèmes multi-agents et le raisonnement stochastique bayésien contribuent à l'apprentissage et à la convergence de l'algorithme vers des solutions plus proches de la solution réelle. - -\subsection{Conclusion} -L'ECBR proposé avec SMA tente d'utiliser les avantages des systèmes multi-agents pour améliorer la qualité des solutions proposées ainsi que pour améliorer le processus d'apprentissage global \textcolor{red}{revoir fin de al phrase}afin d'augmenter la performance de l'algorithme à chaque nouvelle exécution et ce même sur des données différentes. Il utilise également le raisonnement bayésien qui permet d'obtenir de bonnes approximations et un apprentissage optimal avec peu de données. - -Ce travail a démontré la capacité du modèle à trouver des solutions proches de l'optimum global pour la majorité des ensembles de données analysés, y compris avec des ensembles de données divers, déséquilibrés et de tailles différentes. Les résultats montrent en effet une amélioration de l'ECBR de base, qui peut être due \textcolor{red}{grace à ?}à la combinaison du potentiel de l'ECBR et des caractéristiques des systèmes multi-agents tels que les effets de rétroaction, les effets émergents et le comportement de raisonnement bayésien cognitif mis en Å“uvre. +\chapter{Le raisonnement à partir de cas (RàPC) pour la régression} +\chaptermark{RàPC POUR RÉGRESSION} + +\section{Introduction} + +Ce chapitre est divisé en deux parties. La première partie présente un modèle fondé sur le raisonnement à partir de cas et les méthodes d'ensemble avec un double empilement itératif. Nous l'avons baptisé \textit{ESCBR} (\textit{Ensemble Stacking Case Based Reasoning}). Ce processus se fait en deux étapes pour trouver des solutions approximatives à des problèmes de régression unidimensionnels et multidimensionnels. Une partie de cette proposition est publiée dans \cite{10.1007/978-3-031-63646-2_11}. La seconde partie montre la conception et l'implémentation d'un SMA intégré à l'ESCBR présenté dans la première partie. Nous considérons dans ce chapitre que le choix des exercices les plus adaptés revient à résoudre un problème de régression. C'est la raison pour laquelle nous testons notre approche sur des jeux de données classiques de régression. +Le modèle présenté dans cette seconde partie associe un raisonnement à partir de cas à des systèmes multi-agents cognitifs implémentant un raisonnement Bayésien. Cette association, combinant échange d'informations entre agents et apprentissage par renforcement, permet l'émergence de prédictions plus précises et améliore ainsi les performances d'ESCBR \cite{10.1007/978-3-031-63646-2_11}.\\ + +Avant de présenter nos propositions, rappelons quelques caractéristiques importantes des outils combinés dans notre approche. + +Le système de raisonnement à partir de cas ne nécessite pas d'entrainement, et peut fonctionner avec des données dynamiques au moment de l'exécution. Les solutions proposées par notre système de RàPC sont générées à l'aide d'algorithmes stochastiques guidant l'exploration de l'espace des solutions. L'évaluation des solutions possibles est effectuée en transformant le problème de régression en un problème d'optimisation et utilise une fonction \textit{objectif}. +\\ \colorbox{yellow}{Il faut expliquer en quelques mots ce que fait cette fonction objectif}\\ +Les prédictions de ce nouvel algorithme ont été comparées à celles de neuf algorithmes de régression classiques sur dix jeux de données pour la régression extraits du site de l'UCI\textcolor{red}{ref?}. En évaluant les résultats obtenus avec la métrique RMSE, ce nouvel algorithme se classe parmi les six meilleurs. Avec la métrique MAE il est le troisième meilleur algorithme des dix évalués, ce qui suggère que les résultats produits par ESCBR sont raisonnablement saitsfaisants. + +Les méthodes d'ensemble permettent de résoudre des problèmes de classification et de régression en combinant les résultats de plusieurs modèles exécutés indépendamment. Certaines de ces méthodes utilisent des modèles différents et des ensembles de données différents tandis que d'autres utilisent les mêmes modèles avec des paramètres différents. La combinaison des résultats provenant de multiples modèles peut être réalisée selon différentes stratégies comme l'application de règles simples ou des approches plus complexes \cite{BAKUROV2021100913}. Plusieurs travaux de recherche explorent la possibilité d'utiliser cette méthode d'ensemble en la combinant à des outils d'apprentissage automatique. + +Les méthodes d'apprentissage automatique appliquées à la régression permettent quant à elles de prédire des valeurs pour différents types de problèmes en construisant, évaluant et formant des modèles linéaires et non linéaires complexes. Mais s'il est possible d'en améliorer la précision en les associant. Les stratégies d'intégration les plus courantes utilisées pour l'apprentissage d'ensemble sont le \textit{Stacking} (empilement), le \textit{Boosting} et le \textit{Bagging} \cite{Liang}. Le \textit{Stacking} est un type de méta-modèle d'apprentissage profond d'ensemble dont l'objectif est d'utiliser diverses techniques d'apprentissage automatique pour surmonter les limites des modèles individuels. Plusieurs études démontrent que l'association de ces techniques permet d'améliorer la précision des résultats \cite{cmc.2023.033417}. Dans ces méthodes d'empilement, les algorithmes de base sont appelés \textit{niveau-0}. Il s'agit généralement de modèles ou d'algorithmes d'apprentissage automatique hétérogènes qui travaillent tous avec les mêmes données. Le méta-algorithme (appelé \textit{niveau-1}) qui unifie les résultats peut être une autre technique d'apprentissage automatique ou un ensemble de règles qui reçoit en entrée les résultats des algorithmes de \textit{niveau-0} \cite{10.3389/fgene.2021.600040}. + +La modélisation de systèmes implémentant différentes techniques d'apprentissage nous amène tout naturellement à considérer les avantages et inconvénients proposés par un système multi-agents. Un SMA est système décentralisé composé de plusieurs entités appelées agents qui ont la capacité d'effectuer des actions spécifiques et de réagir à l'environnement en fonction des informations partielles à leur disposition. Ils peuvent également collaborer les uns avec les autres et coopérer pour atteindre un objectif spécifique. À partir des informations qu'ils perçoivent et échangent, les agents peuvent apprendre de manière autonome et atteindre leurs objectifs efficacement \cite{KAMALI2023110242}. Les actions d'un système multi-agents peuvent être exécutées en parallèle grâce à l'indépendance des agents. Ils sont également robustes aux problèmes présentant une incertitude \cite{DIDDEN2023338}. + +Le raisonnement Bayésien clos ce premier tour d'horizon des techniques implémentées dans l'approche présentée dans ce chapitre. Celui-ci est fondé sur l'observation du raisonnement humain et la relation de l'humain avec l'environnement. Son principe repose sur le postulat que les expériences passées permettent de déduire les états futurs, guidant ainsi ses actions et ses décisions \cite{HIPOLITO2023103510}. Des informations peuvent également être déduites à partir d'informations incomplètes \cite{ZHANG2023110564}. + +\section{Apprentissage par empilement et raisonnement à partir de cas} + +Cette section présente la première version de l'algorithme que nous avons conçu pour résoudre des problèmes de régression. Celui-ci est fondé sur le raisonnement à partir de cas et l'empilement. + +\subsection{Modèle Proposé} + +L'algorithme proposé, ESCBR (\textit{Ensemble Stacking Case-Based Reasoning}), est fondé sur le paradigme générique du RàPC combiné à plusieurs algorithmes de recherche de voisins et de génération de solutions. Ces algorithmes ont été intégrés selon une variation du modèle d'empilement en deux étapes itératives. Cette intégration donne à l'algorithme la capacité de s'adapter à différents types de problèmes, d'éviter les biais et le surentraînement. Les résultats de l'exécution des niveaux d'empilement stockent dans la mémoire des conteneurs de connaissances du système de RàPC des informations qui aident non seulement à l'apprentissage de l'algorithme au fil des itérations, mais facilitent également la génération de solutions à divers problèmes sur différents ensembles de données sans nécessité d'entraînement préalable. La conception itérative en deux cycles améliore la capacité du système de RàPC à travailler et à s'adapter à des problèmes dynamiques en cours d'exécution, comme le montre la figure \ref{figNCBR1}. + +\begin{figure}[!ht] +\centering +\includegraphics[width=\textwidth]{./Figures/NCBR0.png} +\caption{Les deux cycles proposés pour le RàPC} +\label{figNCBR1} +\end{figure} +\colorbox{yellow}{Attention, cette figure apparaît deux fois dans ce chapitre.}\\ +\colorbox{yellow}{J'ai l'impression que ce n'est pas la seule.} + +L'étape de récupération utilise les algorithmes de recherche et la base de données de cas (conteneurs $C1$ et $C3$ de la figure \ref{figNCBR1}) pour trouver les voisins les plus proches d'un problème cible. Puis l'étape de réutilisation utilise les algorithmes de génération de solutions (conteneur $C2$). L'étape de révision évalue ensuite les solutions générées et permet d'en générer de nouvelles itérativement en fonction des paramètres stockés dans le conteneur $C4$. Vient ensuite l'étape de révision prenant en considération la solution sélectionnée. Faisant suite à cette révision, l'étape de renouvellement met à jour les paramètres et les données du conteneur. Enfin, dans l'étape de capitalisation, la base de cas est mise à jour avec l'intégration du nouveau cas. Les flux d'information de l'algorithme proposé sont présentés sur la figure~\ref{figFlowCBR}, tandis que le tableau~\ref{tabVarPar} présente l'ensemble des variables et paramètres de l'algorithme proposé. + +\begin{figure}[!ht] +\centering +\includegraphics[scale=0.6]{./Figures/FlowCBR0.png} +\caption{Flux du \textit{Stacking} RàPC} +\label{figFlowCBR} +\end{figure} + +\begin{table}[!ht] +\centering +\begin{tabular}{cccc} +ID&Type&Description&Domain\\ +\hline +$it$&p&Nombre d'itérations&$\mathbb{N}, it>0$\\ +$np$&p&Nombre de processus&$\mathbb{N}, np>2$\\ +$nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ +$ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ +$n$&v&Dimension de l'espace du problème&$\mathbb{N}, n>0$\\ +$m$&v&Dimension de l'espace de solution&$\mathbb{N}, m>0$\\ +$z$&v&Taille de la base de données&$\mathbb{N}, z>0$\\ +$p$&v&Description du problème&$\mathbb{R} ^ n$\\ +$s$&v&Description de la solution&$\mathbb{R} ^ m$\\ +$r_a$&v&Nombre de modèles pour l'étape rétrouver&$\mathbb{N}, r_a>2$\\ +$r_b$&v&Nombre de modèles pour l'étape de réutilisation&$\mathbb{N}, r_b>2$\\ +$at$&v&Identificateur des actions&$[0,2] \in \mathbb{N}$\\ +$nl_i$&v&Nombre de voisins locaux pour le modèle $i$&$\mathbb{N}, nl_i \le nl$\\ +$g$&v&Description de la meilleure solution globale&$\mathbb{R} ^ m$\\ +$v$&v&Évaluation de la meilleure solution globale&$\mathbb{R}$\\ +$d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ +$MP(x_1^z,x_2,a)$&f&Fonction du modèle pour retrouver entre $x_1$ et $x_2$&$\mathbb{R}^{a \times z}$\\ +$MS(x_1^m)$&f&Fonction du modèle pour réutiliser avec $x_1$ &$\mathbb{R}^m$\\ +$f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ +\end{tabular} +\caption{Variables et paramètres du modèle proposé (Type: p - paramètre, v - variable, f - fonction)} +\label{tabVarPar} +\end{table} + +\subsubsection{Rechercher} +La première étape de l'algorithme consiste à trouver les cas les plus similaires à un nouveau cas (appelé \textit{cas cible}). Pour ce faire, le modèle d'empilement de différents processus présenté sur la figure \ref{figSta1} est utilisé. Au niveau-0, chaque processus sélectionne et exécute un algorithme de recherche de voisins différents choisi parmi $r_a$ modèles dans le conteneur $C3$, avec un nombre de voisins $nl_i$ choisi aléatoirement dans l'intervalle $[0,nl]$. Puis au niveau-1, les résultats sont unifiés en construisant un ensemble global de cas similaires. Cinq algorithmes pour le niveau-0 ont été mis en Å“uvre pour l'étape de récupération : KNN (\textit{K Nearest Neighbors} - K plus proches voisins), KMeans, GMM (\textit{Gaussian Mixture Model}), FuzzyC et KNN Ponderation. + +\begin{figure} +\centering +\includegraphics[width=\textwidth]{./Figures/Stacking1.png} +\caption{\textit{Stacking} pour chercher les plus proches voisins} +\label{figSta1} +\end{figure} + +Formellement, le premier modèle d'empilement proposé fonctionne avec deux paramètres : \textcolor{red}{quels sont les 2 paramètres?}une base de données de $z$ cas, un cas est composé de la description du problème et de la description de la solution ${(p^n,s^m)}^{z}$ et un nouveau cas sans solution $p_w^n$. Le but de tous les algorithmes de niveau-0 est de générer une liste locale de cas similaires au cas cible. Ainsi, pour chaque algorithme $j$ exécuté, l'ensemble $X_j=\{x_1,x_2,. ..,x_z \; | \; x_i=MP_i((p^n)^z, p_w^n,nl_i) \}$ est généré. Au niveau-1, un ensemble global est créé à l'aide de tous les ensembles locaux $j$ $X_g=\cup_{n=1}^{ng} min \ ; ((\cup_{j=1}^{np} X_j)-X_g)$. Le résultat du premier modèle d'empilement est l'ensemble $X_g$ avec les $ng$ voisins les plus proches. + +\subsubsection{Réutiliser} + +Une fois la liste globale des cas similaires établie, les informations correspondant aux solutions de chacun de ces cas sont extraites et utilisées pour générer une nouvelle solution qui s'adapte au cas cible, en suivant le processus et les flux d'informations représentés sur la figure \ref{figAuto}. La génération est effectuée avec un deuxième modèle d'empilement de différents processus. Ce modèle d'empilement est représenté sur la figure \ref{figSta2}. Au niveau-0, chaque processus sélectionne et exécute un algorithme de génération différent à partir des modèles $r_b$ dans le conteneur $C2$. Au niveau-1, toutes les solutions générées sont stockées dans une mémoire globale. + +Neuf algorithmes ont été mis en Å“uvre pour l'étape de réutilisation au niveau-0 : moyenne avec probabilité, moyenne sans probabilité, valeurs médianes, sélection aléatoire avec probabilité, copie et changement, vote, interpolation, ACP (analyse en composantes principales) et marche aléatoire. Tous les algorithmes proposés pour générer une nouvelle solution combinent et modifient l'ensemble de solutions construit dans l'étape de récupération. + +\begin{figure}[!ht] +\centering +\includegraphics[width=\textwidth]{./Figures/AutomaticS.png} +\caption{Génération et vérification automatique des solutions} +\label{figAuto} +\end{figure} + +\colorbox{yellow}{Il faut revoir ce qui suit car ne comprenant pas, j'ai complètement ré-écrit.} +La moyenne pondérée avec probabilité permet de construire une solution. La pondération est calculée en fonction de la proximité \colorbox{yellow}{du cas ? lequel ? de la solution ? On la connait ?} avec le cas cible. La probabilité est calculée en fonction de la distance entre les problèmes selon l'équation \ref{gen00} et la solution globale est construite à partir des solutions proposées par les $nl$ algorithmes selon l'équation \ref{gen01}. + +\begin{equation} + \alpha_j=\frac{d(p_j^n,p_w^n)}{\sum_{i=0}^{nl} d(p_i^n,p_w^n)} + \label{gen00} +\end{equation} + +\begin{equation} + s^m_{j,w}= \frac{1}{nl} \sum_{i=0}^{nl} \alpha_j s_{i,j} + \label{gen01} +\end{equation} + +La moyenne sans probabilité copie \colorbox{yellow}{copie ?} aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à tous les éléments de toutes les solutions proches. Formellement la génération de la solution est calculée selon l'équation \ref{gen2}, où chaque position $j$ est calculée de la même façon \colorbox{yellow}{?}. + +\begin{equation} + s^m_{w,j}= \frac{1}{nl} \sum_{i=0}^{nl} s_{i,j} + \label{gen2} +\end{equation} + +La génération par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension. $X_j$ représente l'ensemble des valeurs ordonnées de toutes les solutions $S$ dans la position $j$ \colorbox{yellow}{position ?}. + +\begin{equation} + s_{j,w}^m= + \begin{cases} + x_{j,\frac{m+1}{2}}, \; si \; m \in \{{2k+1 : k \in \mathbb{Z}}\}\\ + \frac{x_{j,\frac{m}{2}}+x_{j,\frac{m}{2}+1}}{2}, \; sinon\\ + \end{cases} +\end{equation} + +La sélection aléatoire avec probabilité génère une solution en copiant aléatoirement l'information des solutions dans chaque position ayant une plus grande probabilité vers le cas de problème associé le plus proche. +\colorbox{yellow}{Il est difficile à comprendre à quel moment intervient l'aléatoire dans ce processus}\\ +\colorbox{yellow}{À ce stade, les équations ne sont plus citées.} + +\begin{equation} +s_{j,w}^m=s_{j,k}^m; k \sim \left(\frac{d(p_k,p_w)}{\sum_{i=1}^nl(p_k,p_i)} \right) +\end{equation} + +"Copie/changement" copie les informations d'une solution aléatoire et en remplace une partie par celles d'une autre solution sélectionnée aléatoirement. + +\begin{equation} +s_{j,w}^m=s_{j,k}^m; k \sim \left(\frac{1}{nl} \right) +\end{equation} + +Le vote permet de copier l'information la plus fréquente de toutes. + +\begin{equation} +s_{j,w}^m=s_{j,k}^m; k=argmax_i \; \mathbb{P}(X=s_{j,i}^m), 1\le i \le nl +\end{equation} + +L'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation lineaire 1D calculée. +\\ \colorbox{yellow}{Pourquoi aléatoire ? Une interpolation ne rend pas un résultat aléatoire} + +\begin{equation} + s_{w,j}^m \sim \left( \left( \frac{y_i-y_{i+1}}{x_i-x_{i+1}} \right) (x-x_i)+y_i \right), \forall i \; 0 \le i < nl +\end{equation} + +Dans l'analyse en composantes principales (ACP), si la dimension de l'espace des solutions $m$ est plus petit que la dimension de l'espace des problèmes $n$ ($m0$\\ +$np$&p&Nombre d'agents&$\mathbb{N}, np>2$\\ +$nl$&p&Nombre maximal de voisins locaux&$\mathbb{N}, nl>0$\\ +$ng$&p&Nombre de voisins globaux&$\mathbb{N}, ng>2$\\ +$n$&v&Dimension de l'espace du problème&$\mathbb{N}, n>0$\\ +$m$&v&Dimension de l'espace de solution&$\mathbb{N}, m>0$\\ +$p$&v&Description du problème&$\mathbb{R} ^ n$\\ +$s$&v&Description de la solution&$\mathbb{R} ^ m$\\ +$p_w$&v&Description du nouveau problème&$\mathbb{R} ^ n$\\ +$s_w$&v&Description de la nouvelle solution&$\mathbb{R} ^ m$\\ +$n_{rt}$&v&Nombre d'algorithmes por l'étape de rétrouver&$\mathbb{Z}$\\ +$n_{rs}$&v&Nombre d'algorithmes de réutilisation&$\mathbb{Z}$\\ +$d(x_1,x_2)$&f&Fonction de distance entre $x_1$ et $x_2$ &$\mathbb{R}$\\ +$rn(x,y)$&f& + +\begin{tabular}{@{}c@{}}Valeur aléatoire avec distribution normale\\ $x$ moyenne, $y$ écart-type +\end{tabular} + +&$\mathbb{R}_+$\\ +$rnp(x,y)$&f& + +\begin{tabular}{@{}c@{}}Valeur aléatoire discrète, $x$ nombre d'options \\ $y$ vecteur discret de probabilités +\end{tabular} +&$\mathbb{Z}$\\ +$f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ +\end{tabular} +\caption{Variables et paramètres du modèle proposé (Type: p - paramètre, v - variable, f - fonction)} +\label{tabVarPar} +\end{table} + +\subsubsection{Algorithmes} + +Cette section présente de manière plus détaillée les comportements des agents d'ESCBR-SMA. + +Lors de la première étape de l'empilement, chaque agent peut sélectionner l'un des algorithmes à mettre en Å“uvre pour rechercher des problèmes similaires au nouveau problème posé. Les algorithmes possibles sont les suivants : KNN (K-Nearest Neighbor), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN pondéré. + +Lors de la deuxième étape de l'empilement, les agents peuvent choisir un algorithme parmi les suivants : pondération avec probabilité, pondération sans probabilité, valeurs médianes, Copier/Changer, vote, interpolation, PCA (analyse en composantes principales) et pas aléatoire\textcolor{red}{et non aléatoire?}. + +L'algorithme de construction de solution par pondération avec probabilité utilise la probabilité que le problème considéré soit le plus proche du problème cible. Cet algorithme construit une solution en copiant certaines informations de la ou des solutions ayant la probabilité la plus élevée. Le choix des informations à copier est aléatoire. Pour sa part, la sélection aléatoire pondérée sans probabilité copie certaines informations (choisies aléatoirement) des solutions sans tenir compte de la probabilité que le problème associé soit le plus proche du problème cible. + +Les valeurs médianes construisent une solution à partir des valeurs médianes des informations de toutes les solutions. + +L'algorithme Copie/Changer copie les informations d'une solution aléatoire +\\ \colorbox{yellow}{c'est le contenu de la solution qui est généré avec des valeurs aléatoires ou} +\\ \colorbox{yellow}{cette solution est choisie aléatoirement ?} +\\et en modifie une partie avec les informations d'une autre solution sélectionnée de manière aléatoire. + +L'algorithme fondé sur le vote construit une solution en considérant les informations indépendemment. Chaque information aura la valeur apparaissant leplus fréquemment dans l'ensemble des solutions possibles. + +L'algorithme fondé sur l'interpolation utilise des informations aléatoires à partir d'une fonction d'interpolation calculée. +\\ \colorbox{yellow}{Qu'est-ce qui est aléatoire ?} +\\ \colorbox{yellow}{Qu'est-ce qui est interpolé ?} +\\ \colorbox{yellow}{Qu'est-ce qui est calculé ?} + +Le générateur avec PCA transforme la description du problème en une description de la solution et établit ainsi une relation entre les valeurs des descripteurs de la partie problème et celles des descripteurs de la patie solution. + +Enfin, l'algorithme de pas aléatoire sélectionne une solution et modifie la valeur d'une seule de ses composantes choisie au hasard selon un certain pas. + +\subsubsection{Structure des agents} + +Tous les agents ont une structure siùilaire, mais chaque agent suit un processus cognitif individuel qui lui permet d'obtenir un comportement indépendant et différent de tous les autres. La figure \ref{figAgent} montre les actions et les variables nécessaires à l'exécution de l'ensemble du processus. + +Chaque agent peut exécuter trois actions différentes : +\begin{itemize} + \item « Récupérer et réutiliser », + \item « Réutiliser » et + \item « Échanger ». +\end{itemize} + +Chaque agent accède aux valeurs de huit variables qui lui sont propres : +\begin{itemize} + \item le nombre de voisins définissant le nombre de problèmes similaires au nouveau problème posé que l'agent doit rechercher dans la base de connaissancesÃ’, + \item la liste des voisins les plus proches établit la liste des agents avec lesquels des informations peuvent être échangées, + \item l'identifiant de l'algorithme de récupération que l'agent exécutera pour trouver les problèmes similaires au nouveau problème, + \item l'identifiant de l'algorithme de réutilisation que l'agent exécutera pour générer une solution candidate au cas cible, + \item la description de la solution générée, + \item l'évaluation de la solution renseignant sur la qualité de la solution générée et calculée selon une fonction d'optimisation (eq \ref{eqOpt1} et eq \ref{eqOpt2}), + \item le vecteur bayésien nécessaire aux algorithmes de récupération contenant les valeurs de probabilité, et + \item le vecteur bayésien nécessaire aux algorithmes de réutilisation contenant les valeurs de probabilité. +\end{itemize} + +\begin{equation} +min \; \left( f_s(p_w^n, s_w^m) \right) = min \left( \sum_{i=1}^{ng} \frac{d(s_w^m,s_i^t)}{d(p_w^n,p_i^n)^2} \right) +\label{eqOpt1} +\end{equation} + +\begin{equation} +s_i^t=s_i^m+rn(0,d(p_w^n,p_i^n)) +\label{eqOpt2} +\end{equation} + +\begin{figure}[!ht] +\centering +\includegraphics[scale=0.7]{Figures/agent.png} +\caption{Structure interne des agents} +\label{figAgent} +\end{figure} + +\subsubsection{Apprentissage des agents} + +Tous les agents considèrent un vecteur bayésien de probabilité pour la phase de récupération (conteneur $C3$) et un vecteur bayésien de probabilité pour la phase de réutilisation (conteneur $C2$). Initialement, ces vecteurs sont configurés avec une probabilité uniforme pour tous les algorithmes de récupération et de réutilisation (probabilité \textit{a priori}). À chaque itération, les vecteurs sont mis à jour selon l'équation bayésienne \colorbox{yellow}{ref ? Numéro d'équation ?} en utilisant les meilleurs résultats du même agent comme paramètre de vraisemblance. L'agent apprend ainsi de son expérience et sélectionne les algorithmes les plus aptes à fournir les meilleures réponses au regard de l'objectif défini. + +Par conséquent, d'un point plus global au niveau du SMA, l'apprentissage est fondé sur un raisonnement bayésien où les vecteurs de récupération et de réutilisation évoluent. Un exemple d'évolution est présenté sur la figure \ref{fig:bayev}. Au cours d'une itération, si un algorithme a contribué à la construction de la meilleure solution, il reçoit un point pour chaque agent qui l'a utilisé. Ces informations sont stockées dans un vecteur normalisé qui est ensuite utilisé comme vecteur de vraisemblance $P(A)$ pour calculer les nouvelles probabilités dans l'équation bayésienne \ref{eqBay} (dans cette équation, $P(B)$ est le terme de normalisation global). + +\begin{figure} + \centering + \includegraphics[scale=0.5]{Figures/BayesianEvolution.png} + \caption{Exemple d'évolution Bayésienne des vecteurs pour un agent. a) Initialisation des probabilités $P(B|A)$ vecteurs pour Retrieve et Reuse, b) Probabilités après quelques itérations $P(A|B)$ vecteurs pour Retrieve et Reuse} + \label{fig:bayev} +\end{figure} + +\begin{equation} + P(A|B)=\frac{P(B|A)P(A)}{P(B)} + \label{eqBay} +\end{equation} + +La sélection d'un algorithme de recherche $a_{rt}$ se fait au moyen d'une valeur aléatoire +\\ \colorbox{yellow}{La valeur est aléatoire ? Ou le choix de la valeur est aléatoire ?} \\ +tirée du vecteur de distribution de recherche discrète obtenu par raisonnement bayésien et calculé selon l'équation \ref{eqRta}. + +\begin{equation} + a_{rt}=rnp(n_{rt},P(A|B)_{rt}) + \label{eqRta} +\end{equation} + +La sélection d'un algorithme de réutilisation $a_{rs}$ se fait au moyen d'une valeur aléatoire +\\ \colorbox{yellow}{La valeur est aléatoire ? Ou le choix de la valeur est aléatoire ?} \\ +tirée du vecteur de distribution de réutilisation discrète obtenu par raisonnement bayésien et calculé selon l'équation \ref{eqRsa}. + +\begin{equation} + a_{rs}=rnp(n_{rs},P(A|B)_{rs}) + \label{eqRsa} +\end{equation} + +Le processus d'apprentissage est réalisé individuellement par chaque agent, mais comporte un aspect collaboratif puisque les agents échangent les informations qu'ils ont calculées, les optimisations locales qu'ils ont réalisées, ainsi que les algorithmes et les paramètres qu'ils ont utilisés. + +\subsubsection{Échanges entre les agents} + +Un agent peut modifier ses informations et leur affecter les valeurs de celles d'un voisin au cours de chaque itération en choisissant au hasard un voisin dans sa liste de voisins les plus proches. L'ensemble de ces changements permettent de propager les paramètres menant aux meilleurs résultats et d'effectuer des actions rétrospectivement. Les informations modifables sont choisies aléatoirement : il peut s'agir du nombre de voisins, de la liste des voisins les plus proches, de l'algorithme de récupération, de l'algorithme de réutilisation ou même des vecteurs bayésiens. + +\subsection{Résultats} + +Des expérimentations sur onze jeux de données relatifs à des problèmes de régression et présentant des caractéristiques différentes ont été réalisées. Les jeux de données et leurs caractéristiques sont consignés dans le tableau \ref{tabBases}. Les valeurs des paramètres de l'algorithme sont les suivantes $it=100$, $np=50$, $nl=10$ et $ng=10$. +\\ \colorbox{yellow}{Quel algorithme ?} +\\ \colorbox{yellow}{À quoi correspondent ces paramètres ? Quelles sont les unités ?}\\ +Le tableau \ref{AlgsPar} présente les valeurs des paramètres de tous les autres algorithmes. + +\begin{table}[!ht] +\footnotesize +\centering +\begin{tabular}{c|ccccccccccc} +&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ +\hline +%DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.263&8.225\\ +DS1&9.081&12.301&1.228&1.066&7.763&9.081&9.078&9.764&0.750&8.225\\ +%DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016&0.016\\ +DS2&0.022&0.025&0.019&0.013&0.017&0.022&0.022&0.037&0.011&0.016\\%DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&8.148&7.991\\ +DS3&8.756&8.465&9.656&7.665&8.716&8.756&9.005&9.177&7.369&7.991\\ +%DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.628&0.607\\ +DS4&0.647&0.752&0.794&0.602&0.688&0.647&0.646&0.798&0.616&0.607\\ +%DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.690&0.662\\ +DS5&0.767&0.824&0.877&0.66&0.826&0.767&0.775&0.87&0.703&0.662\\ +%DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.413&9.070\\ +DS6&10.525&9.174&6.93&5.372&6.662&10.525&10.525&10.527&5.131&9.070\\ +%DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&3.031&2.941\\ +DS7&2.961&2.451&0.589&0.528&3.955&2.961&3.009&4.083&0.490&2.941\\ +%DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.752&2.553\\ +DS8&1.298&1.125&1.360&1.197&1.486&1.298&1.298&1.306&1.128&2.553\\ +%DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.747&2.468\\ +DS9&2.256&2.565&3.174&2.377&2.817&2.256&2.255&2.468&2.293&2.468\\ +%DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.897&3.621\\ +DS10&3.136&3.415&4.173&3.165&3.710&3.136&3.135&3.161&3.108&3.621\\ +DS11&0.625&0.565&0.741&0.56&0.606&0.626&0.626&0.681& +0.541&0.54\\ +\hline +%Avg. Rank&5.8&6.5&7.2&2.3&6.7&5.7&5.6&8.65&1.9&4.65\\ +Avg. Rank&6.4&6.9&8.2&2.6&7.2&6.45&6.35&9.55&2.1&4.75\\ +\end{tabular} +\caption{Résultat selon la métrique RMSE (Root Mean Squared Error) pour les jeux de données évalués avec les différents algorithmes de régression considérés.} +\label{tabRes1} +\end{table} + +\begin{table}[!ht] +\scriptsize +\centering +\begin{tabular}{llccp{1.4cm}p{1.2cm}p{1.2cm}} +ID&DataSet&Features&Instances&Output. Dimension&Input. Domain&Output Domain\\ +\hline +DS1&Yatch Hydrodynamics&6&308&1&$\mathbb{R}$&$\mathbb{R}$\\ +DS2&Electrical Grid Stability&12&10000&1&$\mathbb{R}$&$\mathbb{R}$\\ +DS3&Real State Valuation&6&414&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS4&Wine Quality (Red)&11&1598&1&$\mathbb{R_+}$&$\mathbb{N}$\\ +DS5&Wine Quality (White)&11&4897&1&$\mathbb{R_+}$&$\mathbb{N}$\\ +DS6&Concrete Compressive Strength&8&1030&1&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS7&Energy Efficiency&8&768&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS8&Gas Turbine CO, NOx Emission (2015)&9&7384&2&$\mathbb{R_+}$&$\mathbb{R_+}$\\ +DS9&Student Performace Portuguese&30&649&3&$\mathbb{N*}$&$\mathbb{N}$\\ +DS10&Student Performance Math&30&395&3&$\mathbb{N*}$&$\mathbb{N}$\\ +DS11&Generated Student Performance&5&1000&1&$\mathbb{R}_+$&$\mathbb{R}_+$\\ +\end{tabular} +\caption{Description des jeux de données évalués. (* après codification comme +\textit{String})} +\label{tabBases} +\end{table} + +\begin{table}[!ht] +\centering +\begin{tabular}{ccc|ccc} +ID&Parameter&Value&ID&Parameter&Value\\ +\hline +A1&Intercept&True&A6&Degree&4\\ +&Positive&True&&Bias&True\\ +\hline +A2&Neighbors&5&A7&Fit Intercept&True\\ +&Weights&Uniform&&alpha&0.2\\ +&Metric&Minkowsky&&tol&1e-4\\ +&Power Minkowsky&2\\ +\hline +A3&Error&Squared Error&A8&Fit Intercept&True\\ +&Min samples split&2&&alpha&[0.00001, 0.4]\\ +&&&&Max iter&1000\\ +&&&&tol&1e-4\\ +\hline +A4&Estimators&10&A9&Error&Squarred Error\\ +&Error&Squared Error&&Learning Rate&0.1\\ +&Min samples split&2&&Estimators&100\\ +&Bootstrap&True&&Min Split&2\\ +\hline +A5&Hidden Layers&100\\ +&Activation&Relu\\ +&Solver&Adam\\ +&alpha&0.0001\\ +&Learning Rate&0.001\\ +&Max Iter&200\\ +&beta1&0.9\\ +&beta2&0.999\\ +&epsilon&1e-8\\ +\end{tabular} +\caption{Paramètres de tous les algorithmes comparés} +\label{AlgsPar} +\end{table} + +\begin{table}[!ht] +\footnotesize +\centering +\begin{tabular}{c|ccccccccccc} +Dataset&A1&A2&A3&A4&A5&A6&A7&A8&A9&A10\\ +\hline +%DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.193&1.218\\ +DS1&6.776&2.385&0.231&0.207&3.632&6.778&6.307&5.186&0.162&1.218\\ +%DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.011&0.010\\ +DS2&0.015&0.017&0.012&0.008&0.012&0.015&0.015&0.030&0.007&0.010\\ +%DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.90&3.771\\ +DS3&5.092&4.320&4.1&3.632&4.435&5.092&5.20&5.132&3.504&3.771\\ +%DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.154&0.135\\ +DS4&0.413&0.495&0.18&0.325&0.451&0.413&0.412&0.544&0.387&0.135\\ +%DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.113&0.085\\ +DS5&0.509&0.548&0.285&0.374&0.550&0.509&0.509&0.633&0.456&0.085\\ +%DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.439&5.072\\ +DS6&6.989&5.709&3.134&2.839&4.306&6.989&6.989&6.986&3.084&5.072\\ +%DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.008&1.006\\ +DS7&1.393&1.372&0.217&0.218&2.523&1.393&1.529&2.346&0.243&1.006\\ +%DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.861&0.794\\ +DS8&0.549&0.297&0.365&0.289&0.742&0.549&0.549&0.540&0.309&0.794\\ +%DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.721&1.556\\ +DS9&1.496&1.788&2.080&1.612&2.005&1.496&1.496&1.714&1.538&1.556\\ +%DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.602&2.371\\ +DS10&2.344&2.534&2.910&2.331&2.543&2.344&2.344&2.481&2.258&2.371\\ +DS11&0.387&0.35&0.46&0.338&0.384&0.387&0.387&0.453& +0.327&0.347\\ +\hline +Avg. Rank&7.15&6.9&5.35&2.6&7.95&7.25&7.3&9.0&2.5 +&4.5\\ +%Avg. Rank&6.45&6.5&4.35&2.4&7.45&6.55&6.6&8.1&2.4&4.2\\ +\end{tabular} +\caption{Comparaison des résultats MAE (Median Absolute Error) pour les bases de données évaluées avec des algorithmes de régression} +\label{tabRes2} +\end{table} + +Les tableaux \ref{tabRes1} et \ref{tabRes2} présentent respectivement les RMSE et les MAE obtenues pour chaque jeu de données et chaque algorithme testé. + +La figure \ref{figBox} représente graphiquement la dispersion globale, la médiane et les valeurs aberrantes obtenues durant ces tests. Cette figure montre qu'ESCBR-SMA génère parfois plus de valeurs aberrantes que d'autres algorithmes. Toutefois, la variance est très faible. De plus, la convergence est proche de la valeur réelle et même meilleure que celle de la plupart des autres algorithmes testés. Il est également possible de remarquer que les valeurs aberrantes sont plus élevées que les valeurs réelles.\textcolor{red}{plus élevées??, pourquoi?} + +\begin{figure}[!ht] +\includegraphics[width=\textwidth]{Figures/boxplot2.png} +\caption{Résultats selon la métrique MAE (Median Absolute Error) pour les dix algorithmes testés} +\label{figBox} +\end{figure} + +Les résultats montrent que l'algorithme ESCBR-SMA est compétitif pour la plupart des jeux de données considérés dans cette étude. Il obtient en effet les meilleurs résultats sur $DS2$, $DS4$, $DS5$ et $DS9$. Globalement, ESCBR-SMA est le troisième meilleur algorithme. Il se classe donc à proximité d'autres algorithmes d'ensemble. Par rapport à l'ESCBR, une amélioration des résultats et une réduction de la variance ont été obtenues, démontrant ainsi que les systèmes multi-agents et le raisonnement stochastique bayésien contribuent à l'apprentissage et à la convergence vers des solutions plus proches de la solution réelle. + +\subsection{Conclusion} +L'ECBR intégrant un SMA propose d'utiliser les avantages des systèmes multi-agents pour améliorer la qualité des solutions proposées et également le processus d'apprentissage global en couvrant un plus large spectre de possibilités et en le couvrant de manière intelligente à l'aide d'un raisonnement bayésien. ESCBR-SMA permet ainsi d'obtenir de bonnes approximations avec peu de données. + +Ce travail a démontré la capacité d'ESCBR-SMA à trouver des solutions proches de l'optimum global pour la majorité des ensembles de données analysés. Ces jeux de données présentent une certaine diversité, ils peuvent être déséquilibrés et ils sont de tailles différentes. Grâce aux caractéristiques inhérentes aux systèmes multi-agents (possibilités de rétroactions, d'échanges d'informations, l'émergence d'une intelligence collective, utilisation d'un raisonnement cognitif), les performances d'ESCBR-SMA sont meilleures que celles d'ESCBR. diff --git a/chapters/ESCBR0.tex b/chapters/ESCBR0.tex index 24c50dd..9ea9631 100644 --- a/chapters/ESCBR0.tex +++ b/chapters/ESCBR0.tex @@ -1,27 +1,29 @@ -\chapter{Raisonnement à partir de cas (RàPC) pour Régression} +\chapter{Le raisonnement à partir de cas (RàPC) pour la régression} \chaptermark{RàPC POUR RÉGRESSION} \section{Introduction} -Ce chapitre est divisé en deux parties, la première partie présente un modèle fondé sur le raisonnement à partir de cas et les méthodes d'ensemble avec un double empilement itératif en deux étapes pour trouver des solutions approximatives à des problèmes de régression unidimensionnels et multidimensionnels. Une partie du contenu est extrait et traduit de l'article Soto \textit{et al.} \cite{10.1007/978-3-031-63646-2_11}. La deuxième partie montre comme a été conçu et implémenté un algorithme pour intégrer l'algorithme de raisonnement à partir de cas explicité dans la première partie avec les systèmes multi-agents pour améliorer la performance et les résultats pour traiter des problèmes de régression. +Ce chapitre est divisé en deux parties. La première partie présente un modèle fondé sur le raisonnement à partir de cas et les méthodes d'ensemble avec un double empilement \textcolor{red}{empilement?}itératif en deux étapes pour trouver des solutions approximatives à des problèmes de régression unidimensionnels et multidimensionnels. Une partie de cette proposition est publiée dans \textit{et al.} \cite{10.1007/978-3-031-63646-2_11}. La seconde partie montre la conception et l'implémentation de SMA intégré à celui du ESCBR(explicité dans la première partie). L'objectif étant d'améliorer la performance et les résultats en appliquant et en testant des problèmes de régression\textcolor{red}{revoir cette phrase que j'ai modifiée}. +\textcolor{red}{revoir cette phrase en la coupant}Nous proposons dans la seconde partie un modèle qui intègre un algorithme de raisonnement à partir de cas avec des systèmes multi-agents cognitifs qui utilisent le raisonnement Bayésien afin d'améliorer les processus de recherche de voisins et de génération de solutions en utilisant l'échange d'informations inter-agents et l'apprentissage par renforcement, obtenant ainsi des effets émergents dans le comportement global de l'algorithme, ce qui peut conduire à l'amélioration des prédictions de l'algorithme ESCBR \cite{10.1007/978-3-031-63646-2_11}.\\\\ -Le modèle fondé sur le raisonnement à partir de cas ne nécessite pas d'entrainement, et peut fonctionner avec des données dynamiques au moment de l'exécution. Les solutions sont générées à l'aide d'algorithmes stochastiques afin de permettre l'exploration de l'espace des solutions, l'évaluation est effectuée en transformant le problème de régression en un problème d'optimisation avec une fonction objectif associée. L'algorithme a été testé en comparaison avec neuf algorithmes de régression classiques sur dix bases de données de régression différentes extraites du site de l'UCI, les résultats montrent que l'algorithme proposé génère dans la plupart des cas des solutions assez proches des solutions réelles, selon le RMSE l'algorithme se trouve globalement parmi les six meilleurs algorithmes et avec MAE au troisième meilleur algorithmes des dix évalués, suggérant que les résultats sont raisonnablement bons. +\textcolor{red}{attention la suite fait un peu catalogue} +Le \textcolor{red}{Un modèle?}modèle fondé sur le raisonnement à partir de cas ne nécessite pas d'entrainement, et peut fonctionner avec des données dynamiques au moment de l'exécution. Les solutions sont générées à l'aide d'algorithmes stochastiques afin de permettre l'exploration de l'espace des solutions. L'évaluation est effectuée en transformant le problème de régression en un problème d'optimisation avec une fonction objectif associée \textcolor{red}{fonction objectif associée?}. L'algorithme a été testé par comparaison à neuf algorithmes de régression classiques sur dix bases de données de régression différentes extraites du site de l'UCI\textcolor{red}{ref?}. Les résultats montrent que l'algorithme proposé génère dans la plupart des cas des solutions assez proches des solutions réelles. \textcolor{red}{En utilisant la métrique ? RMSE?} selon le RMSE l'algorithme se trouve globalement parmi les six meilleurs algorithmes. \textcolor{red}{Avec la métrique MAE il est le ?} et avec MAE le troisième meilleur algorithme des dix évalués, ce qui suggère que les résultats sont raisonnablement bons. -Les méthodes d'ensemble utilisent plusieurs modèles multiples exécutés indépendamment et leurs résultats sont combinés pour obtenir une prédiction globale finale. L'idée principale est d'améliorer les résultats et la capacité de généralisation des modèles individuels. Certaines méthodes d'ensemble utilisent différents modèles avec différents ensembles de données, d'autres utilisent les mêmes modèles avec des paramètres différents, la combinaison des résultats des multiples modèles peut utiliser différentes stratégies comme des règles simples ou des approches plus complexes \cite{BAKUROV2021100913}. Les méthodes d'ensemble sont utiles dans les problèmes de classification et de régression. +Les méthodes d'ensemble utilisent plusieurs modèles multiples exécutés indépendamment et leurs résultats sont combinés pour obtenir une prédiction globale finale. L'idée principale est d'améliorer les résultats ainsi que la capacité de généralisation des modèles individuels \textcolor{red}{vérifier la phrase précédente}. Certaines méthodes d'ensemble utilisent différents modèles avec différents ensembles de données, d'autres utilisent les mêmes modèles avec des paramètres différents. La combinaison des résultats des multiples modèles peut utiliser différentes stratégies comme des règles simples ou des approches plus complexes \cite{BAKUROV2021100913}. Les méthodes d'ensemble sont utiles dans \textcolor{red}{dans la résolution des problèmes?}les problèmes de classification et de régression. -Les méthodes d'apprentissage automatique appliquées à la régression permettent de prédire des valeurs pour différents types de problèmes en construisant, évaluant et formant des modèles linéaires et non linéaires complexes, mais s'il est possible d'améliorer la précision en les intégrant, les stratégies d'intégration les plus courantes utilisées pour l'apprentissage d'ensemble sont les suivantes : Stacking, Boosting et Bagging \cite{Liang}. Le Stacking est un type de méta-modèle d'apprentissage profond d'ensemble, dont l'objectif est d'utiliser diverses techniques d'apprentissage automatique pour surmonter les limites des modèles individuels, l'intégration générant un résultat final avec une précision améliorée \cite{cmc.2023.033417}. Dans les méthodes d'empilage, les algorithmes de base sont appelés niveau-0, il s'agit généralement de modèles ou d'algorithmes d'apprentissage automatique hétérogènes qui travaillent tous avec la même base de données. Le méta-algorithme qui unifie les résultats peut être une autre technique d'apprentissage automatique ou un ensemble de règles qui reçoit comme données d'entrée les résultats des algorithmes de niveau-0 est appelé niveau-1 \cite{10.3389/fgene.2021.600040}. +Les méthodes d'apprentissage automatique appliquées à la régression permettent de prédire des valeurs pour différents types de problèmes en construisant, évaluant et formant des modèles linéaires et non linéaires complexes. Mais s'il est possible d'améliorer la précision en les intégrant, les stratégies d'intégration les plus courantes, utilisées pour l'apprentissage d'ensemble, sont les suivantes : Stacking, Boosting et Bagging \cite{Liang}. Le Stacking est un type de méta-modèle d'apprentissage profond d'ensemble dont l'objectif est d'utiliser diverses techniques d'apprentissage automatique pour surmonter les limites des modèles individuels, l'intégration \textcolor{red}{de ces techniques?}générant un résultat final avec une précision améliorée \cite{cmc.2023.033417}. Dans les méthodes d'empilage\textcolor{red}{empilement, choisir}, les algorithmes de base sont appelés niveau-0, il s'agit généralement de modèles ou d'algorithmes d'apprentissage automatique hétérogènes qui travaillent tous avec la même base de données. Le méta-algorithme qui unifie les résultats peut être une autre technique d'apprentissage automatique ou un ensemble de règles qui reçoit comme données d'entrée les résultats des algorithmes de niveau-0 est appelé niveau-1 \cite{10.3389/fgene.2021.600040}. -Un système multi-agents est un système décentralisé composé de plusieurs entités appelées agents qui ont la capacité d'effectuer des actions spécifiques et de réagir à l'environnement en fonction des informations partielles qu'ils peuvent obtenir, ils peuvent également collaborer les uns avec les autres et coopérer pour atteindre un objectif spécifique. À partir des informations qu'ils perçoivent et échangent, les agents peuvent apprendre de manière autonome et atteindre leurs objectifs de manière efficace \cite{KAMALI2023110242}. Les systèmes multi-agents peuvent être exécutés en parallèle étant donné l'indépendance des agents, ils sont robustes aux problèmes qui présentent une incertitude \cite{DIDDEN2023338}. +Un système multi-agents est un système décentralisé composé de plusieurs entités appelées agents qui ont la capacité d'effectuer des actions spécifiques et de réagir à l'environnement en fonction des informations partielles qu'ils peuvent obtenir. Ils peuvent également collaborer les uns avec les autres et coopérer pour atteindre un objectif spécifique. À partir des informations qu'ils perçoivent et échangent, les agents peuvent apprendre de manière autonome et atteindre leurs objectifs de manière efficace \cite{KAMALI2023110242}. Les systèmes multi-agents peuvent être exécutés en parallèle étant donné l'indépendance des agents. Ils sont également robustes aux problèmes qui présentent une incertitude \cite{DIDDEN2023338}. + +Le raisonnement Bayésien est une hypothèse sur le fonctionnement du cerveau humain et sa relation avec l'environnement. Le principe est que les expériences passées permettent de déduire les états futurs, ce qui permet d'agir et de prendre des décisions \cite{HIPOLITO2023103510}. Des informations peuvent également être déduites et d'apprendre \textcolor{red}{qui peut apprendre?}à partir d'informations incomplètes \cite{ZHANG2023110564}. -Le raisonnement Bayésien est une hypothèse sur le fonctionnement du cerveau humain et sa relation avec l'environnement, dont le principe est que les expériences passées permettent de déduire les états futurs, ce qui permet d'agir et de prendre des décisions \cite{HIPOLITO2023103510}, également des informations peuvent être deduites et d'apprendre à partir d'informations incomplètes \cite{ZHANG2023110564}. -Nous proposons dans la seconde partie un modèle qui intègre un algorithme de raisonnement à partir de cas avec des systèmes multi-agents cognitifs qui utilisent le raisonnement Bayésien afin d'améliorer les processus de recherche de voisins et de génération de solutions en utilisant l'échange d'informations inter-agents et l'apprentissage par renforcement, obtenant ainsi des effets émergents dans le comportement global de l'algorithme, ce qui peut conduire à l'amélioration des prédictions de l'algorithme ESCBR \cite{10.1007/978-3-031-63646-2_11}.\\\\ \section{PREMIÈRE PARTIE} \subsection{Modèle Proposé} -L'algorithme proposé ESCBR (Ensemble Stacking Case-Based Reasoning) est fondé sur le paradigme générique CBR avec plusieurs algorithmes de recherche de voisins et de génération de solutions qui ont été intégrés selon une variation du modèle de stacking en deux étapes itératives, cette intégration donne à l'algorithme la capacité de s'adapter à différents types de problèmes, d'éviter les biais et le surentraînement. Les résultats de l'exécution des niveaux de stacking stockent dans la mémoire des conteneurs CBR des informations qui aident à l'apprentissage de l'algorithme au fil des itérations, en plus de faciliter la génération de solutions à divers problèmes sur différentes bases de données sans avoir besoin d'une phase d'entraînement. La conception itérative en deux cycles améliore la capacité de la CBR à travailler et à s'adapter à des problèmes dynamiques en cours d'exécution, comme le montre la figure \ref{figNCBR}. +L'algorithme proposé ESCBR (Ensemble Stacking Case-Based Reasoning) est fondé sur le paradigme générique CBR avec plusieurs algorithmes de recherche de voisins et de génération de solutions. Ces algorithmes ont été intégrés selon une variation du modèle de stacking en deux étapes itératives. Cette intégration donne à l'algorithme la capacité de s'adapter à différents types de problèmes, d'éviter les biais et le surentraînement. Les résultats de l'exécution des niveaux de stacking stockent dans la mémoire des conteneurs CBR des informations qui non seulement aident à l'apprentissage de l'algorithme au fil des itérations, mais aussi facilitent la génération de solutions à divers problèmes sur différentes bases de données sans avoir besoin d'une phase d'entraînement \textcolor{red}{vérifier la phrase précédent que j'ai modifiée}. La conception itérative en deux cycles améliore la capacité du CBR à travailler et à s'adapter à des problèmes dynamiques en cours d'exécution, comme le montre la figure \ref{figNCBR}. \begin{figure}[!ht] \centering @@ -30,7 +32,7 @@ L'algorithme proposé ESCBR (Ensemble Stacking Case-Based Reasoning) est fondé \label{figNCBR} \end{figure} -L'étape de récupération utilise les algorithmes de recherche et la base de données de cas (conteneurs C1 et C3) pour trouver les voisins les plus proches d'un nouveau problème donné, l'étape de réutilisation utilise les algorithmes de génération de solutions (conteneur C2), l'étape de révision évalue les solutions générées et permet de générer de nouvelles solutions itérativement en fonction des paramètres stockés dans le conteneur C4 et en invoquant l'étape de reconfiguration, avec une solution sélectionnée, l'étape de renouvellement met à jour les paramètres et les données du conteneur, enfin, dans l'étape de conservation, la base de cas est mise à jour avec le nouveau cas et la solution générée. Le flux complet de l'algorithme proposé est présenté dans la figure \ref{figFlowCBR}. Les variables et paramètres complets de l'algorithme proposé sont indiqués dans le tableau~\ref{tabVarPar}. +L'étape de récupération utilise les algorithmes de recherche et la base de données de cas (conteneurs C1 et C3) pour trouver les voisins les plus proches d'un nouveau problème donné. L'étape de réutilisation utilise les algorithmes de génération de solutions (conteneur C2). L'étape de révision évalue les solutions générées et permet de générer de nouvelles solutions itérativement en fonction des paramètres stockés dans le conteneur C4 et en invoquant l'étape de reconfiguration, avec une solution sélectionnée. Puis l'étape de renouvellement met à jour les paramètres et les données du conteneur. Enfin, dans l'étape de conservation, la base de cas est mise à jour avec le nouveau cas et la solution générée. Le flux complet de l'algorithme proposé est présenté dans la figure \ref{figFlowCBR}. Les variables et paramètres complets de l'algorithme proposé sont indiqués dans le tableau~\ref{tabVarPar}. \begin{figure}[!ht] \centering @@ -69,7 +71,7 @@ $f_s(p^n,s^m)$&f&Évaluation des solutions&$\mathbb{R}$\\ \end{table} \subsubsection{Rechercher} -La première étape de l'algorithme consiste à trouver les cas les plus similaires à un nouveau cas éventuel, pour cela un premier modèle de stacking avec différents processus est utilisé comme le montre la figure \ref{figSta1}, au niveau-0 chaque processus sélectionne et exécute un algorithme de recherche de voisins différent choisit parmi $r_a$ modèles dans le conteneur C3, avec un nombre de voisins $nl_i$ choisi aléatoirement dans l'intervalle $[0,nl]$, puis au niveau-1 les résultats sont unifiés en construisant un ensemble global de cas similaires. Cinq algorithmes pour le niveau 0 ont été mis en Å“uvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation. +La première étape de l'algorithme consiste à trouver les cas les plus similaires à un nouveau cas éventuel\textcolor{red}{supprimer éventuel?}, pour cela un premier modèle de stacking avec différents processus est utilisé comme le montre la figure \ref{figSta1}. Au niveau-0 chaque processus sélectionne et exécute un algorithme de recherche de voisins différent choisi parmi $r_a$ modèles dans le conteneur C3, avec un nombre de voisins $nl_i$ choisi aléatoirement dans l'intervalle $[0,nl]$. Puis au niveau-1 les résultats sont unifiés en construisant un ensemble global de cas similaires. Cinq algorithmes pour le niveau 0 ont été mis en Å“uvre pour l'étape de récupération : KNN (K Nearest Neighbors), KMeans, GMM (Gaussian Mixture Model), FuzzyC et KNN Ponderation. \begin{figure} \centering @@ -78,11 +80,11 @@ La première étape de l'algorithme consiste à trouver les cas les plus similai \label{figSta1} \end{figure} -Formellement, le premier modèle de stacking proposé fonctionne avec deux paramètres : une base de données de $z$ cas, un cas est composé de la description du problème et de la description de la solution ${(p^n,s^m)}^{z}$ et un nouveau cas sans solution $p_w^n$, le but de tous les algorithmes de niveau 0 est de générer une liste locale de cas similaires au nouveau cas en utilisant les informations de la description du problème, c'est-à-dire que pour chaque $j$ modèle effectué, est généré l'ensemble $X_j=\{x_1,x_2,. ..,x_z \; | \; x_i=MP_i((p^n)^z, p_w^n,nl_i) \}$. Au niveau 1, un ensemble global est créé à l'aide de tous les ensembles locaux $j$ $X_g=\cup_{n=1}^{ng} min \ ; ((\cup_{j=1}^{np} X_j)-X_g)$, puis le résultat du premier modèle d'empilement est l'ensemble $X_g$ avec les $ng$ voisins les plus proches. +Formellement, le premier modèle de stacking proposé fonctionne avec deux paramètres : \textcolor{red}{quels sont les 2 paramètres?}une base de données de $z$ cas, un cas est composé de la description du problème et de la description de la solution ${(p^n,s^m)}^{z}$ et un nouveau cas sans solution $p_w^n$. Le but de tous les algorithmes de niveau 0 est de générer une liste locale de cas similaires au nouveau cas en utilisant les informations de la description du problème. C'est-à-dire, pour chaque $j$ modèle effectué, l'ensemble $X_j=\{x_1,x_2,. ..,x_z \; | \; x_i=MP_i((p^n)^z, p_w^n,nl_i) \}$ est généré. Au niveau 1, un ensemble global est créé à l'aide de tous les ensembles locaux $j$ $X_g=\cup_{n=1}^{ng} min \ ; ((\cup_{j=1}^{np} X_j)-X_g)$, puis le résultat du premier modèle d'empilement est l'ensemble $X_g$ avec les $ng$ voisins les plus proches. \subsubsection{Réutiliser} -Une fois la liste globale des cas similaires établie, les informations correspondant aux solutions de chacun de ces cas sont extraites et utilisées pour générer une nouvelle solution qui s'adapte au nouveau cas en utilisant des cas similaires et des solutions similaires, comme le montre la figure \ref{figAuto}. La génération est effectuée avec un deuxième modèle de stacking avec différents processus comme le montre la figure \ref{figSta2}, au niveau 0 chaque processus sélectionne et exécute un algorithme de génération différent à partir des modèles $r_b$ dans le conteneur C2 et au niveau 1 toutes les différentes solutions générées sont stockées dans une mémoire globale. Étant donné que la représentation des solutions est comme un tableau unidimensionnel de multiples cases, alors neuf algorithmes ont été mis en Å“uvre pour l'étape de réutilisation au niveau 0 : moyenne avec probabilité, moyenne sans probabilité, valeurs médianes, sélection aléatoire avec probabilité, copie et changement, vote, interpolation, ACP (analyse en composantes principales) et marche aléatoire. Tous les algorithmes proposées pour générer une nouvelle solution combinent et modifient l'ensemble de solutions construit dans l'étape de récupération. +Une fois la liste globale des cas similaires établie, les informations correspondant aux solutions de chacun de ces cas sont extraites et utilisées pour générer une nouvelle solution qui s'adapte au nouveau cas, comme le montre la figure \ref{figAuto}. La génération est effectuée avec un deuxième modèle de stacking avec différents processus comme le montre la figure \ref{figSta2}. Au niveau 0 chaque processus sélectionne et exécute un algorithme de génération différent à partir des modèles $r_b$ dans le conteneur C2. Au niveau 1 toutes les différentes solutions générées sont stockées dans une mémoire globale. Étant donné que la représentation des solutions est comme un tableau unidimensionnel de multiples cases, alors neuf algorithmes ont été mis en Å“uvre pour l'étape de réutilisation au niveau 0 : moyenne avec probabilité, moyenne sans probabilité, valeurs médianes, sélection aléatoire avec probabilité, copie et changement, vote, interpolation, ACP (analyse en composantes principales) et marche aléatoire. Tous les algorithmes proposés pour générer une nouvelle solution combinent et modifient l'ensemble de solutions construit dans l'étape de récupération. \begin{figure}[!ht] \centering @@ -91,7 +93,7 @@ Une fois la liste globale des cas similaires établie, les informations correspo \label{figAuto} \end{figure} -La moyenne pondérée avec probabilité permet de construire une solution selon le calcul de la moyenne avec le poids de chaque solution en fonction de sa proximité au nouveau problème. L'équation \ref{gen00} define le calcul de la probabilité en fonction de la distance entre les problèmes et l'équation \ref{gen01} construit la solution en calculant chaque case $j$. +La moyenne pondérée avec probabilité permet de construire une solution selon le calcul de la moyenne avec le poids de chaque solution en fonction de sa proximité au nouveau problème. L'équation \ref{gen00} définit le calcul de la probabilité en fonction de la distance entre les problèmes et l'équation \ref{gen01} construit la solution en calculant chaque case $j$. \begin{equation} \alpha_j=\frac{d(p_j^n,p_w^n)}{\sum_{i=0}^{nl} d(p_i^n,p_w^n)} @@ -103,14 +105,14 @@ La moyenne pondérée avec probabilité permet de construire une solution selon \label{gen01} \end{equation} -La moyenne sans probabilité copie aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à toutes les éléments de toutes les solutions proches. Formellement la génération de la solution est écrite comme l'équation \ref{gen2}, où chaque position $j$ est calculée de la même façon. +La moyenne sans probabilité copie aléatoirement les informations des solutions selon la distribution uniforme en donnant la même probabilité à tous les éléments de toutes les solutions proches. Formellement la génération de la solution est écrite comme l'équation \ref{gen2}, où chaque position $j$ est calculée de la même façon. \begin{equation} s^m_{w,j}= \frac{1}{nl} \sum_{i=0}^{nl} s_{i,j} \label{gen2} \end{equation} -La génération de la solution par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension ou $X_j$ représente l'ensemble des valeurs ordonnées de toutes le solutions $S$ dans la position $j$ +La génération de la solution par valeurs médianes construit la solution en utilisant la valeur médiane de toutes les solutions pour chaque dimension ou $X_j$ représente l'ensemble des valeurs ordonnées de toutes les solutions $S$ dans la position $j$ \begin{equation} s_{j,w}^m= @@ -132,7 +134,7 @@ Copie/changement, copie les informations d'une solution aléatoire et change une s_{j,w}^m=s_{j,k}^m; k \sim \left(\frac{1}{nl} \right) \end{equation} -Le vote permet de copier l'information qui se présente avec plus de fréquence entre toutes les solutions, . +Le vote permet de copier l'information qui se présente avec plus de fréquence entre toutes les solutions. \begin{equation} s_{j,w}^m=s_{j,k}^m; k=argmax_i \; \mathbb{P}(X=s_{j,i}^m), 1\le i \le nl @@ -144,7 +146,7 @@ L'interpolation utilise des informations aléatoires à partir d'une fonction d' s_{w,j}^m \sim \left( \left( \frac{y_i-y_{i+1}}{x_i-x_{i+1}} \right) (x-x_i)+y_i \right), \forall i \; 0 \le i < nl \end{equation} -Avec ACP (PCA - Principal Component Analysis), si la dimension de l'espace des solutions $m$ est plus petit que la dimension de l'espace des problèmes $n$ ($m not available [5 ] [6] -Overfull \hbox (1.29184pt too wide) detected at line 89 +Overfull \hbox (1.29184pt too wide) detected at line 86 + [][]\T1/phv/m/n/10.95 100[] + [] + + +Overfull \hbox (1.29184pt too wide) detected at line 87 + [][]\T1/phv/m/n/10.95 100[] + [] + + +Overfull \hbox (1.29184pt too wide) detected at line 88 [][]\T1/phv/m/n/10.95 100[] [] + +Overfull \hbox (1.29184pt too wide) detected at line 89 + [][]\T1/phv/m/n/10.95 102[] + [] + [7] Overfull \hbox (1.29184pt too wide) detected at line 91 - [][]\T1/phv/m/n/10.95 103[] + [][]\T1/phv/m/n/10.95 105[] [] Overfull \hbox (1.29184pt too wide) detected at line 92 - [][]\T1/phv/m/n/10.95 103[] + [][]\T1/phv/m/n/10.95 105[] [] Overfull \hbox (1.29184pt too wide) detected at line 94 - [][]\T1/phv/m/n/10.95 105[] + [][]\T1/phv/m/n/10.95 107[] [] Overfull \hbox (1.29184pt too wide) detected at line 95 - [][]\T1/phv/m/n/10.95 106[] + [][]\T1/phv/m/n/10.95 108[] [] ) @@ -1410,7 +1422,10 @@ Package pdftex.def Info: ./Figures/architecture.png used on input line 37. 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E05S#7PXGV_ diff --git a/main.toc b/main.toc index c8dfe2e..9240eee 100644 --- a/main.toc +++ b/main.toc @@ -48,48 +48,48 @@ \contentsline {section}{\numberline {5.4}Conclusion}{49}{section.5.4}% \contentsline {chapter}{\numberline {6}Le raisonnement à partir de cas (RàPC) pour la régression}{51}{chapter.6}% \contentsline {section}{\numberline {6.1}Introduction}{51}{section.6.1}% -\contentsline {section}{\numberline {6.2}PREMIÈRE PARTIE}{52}{section.6.2}% -\contentsline {subsection}{\numberline {6.2.1}Modèle Proposé}{52}{subsection.6.2.1}% -\contentsline {subsubsection}{\numberline {6.2.1.1}Rechercher}{54}{subsubsection.6.2.1.1}% -\contentsline {subsubsection}{\numberline {6.2.1.2}Réutiliser}{55}{subsubsection.6.2.1.2}% +\contentsline {section}{\numberline {6.2}Apprentissage par empilement et raisonnement à partir de cas}{53}{section.6.2}% +\contentsline {subsection}{\numberline {6.2.1}Modèle Proposé}{53}{subsection.6.2.1}% +\contentsline {subsubsection}{\numberline {6.2.1.1}Rechercher}{55}{subsubsection.6.2.1.1}% +\contentsline {subsubsection}{\numberline {6.2.1.2}Réutiliser}{56}{subsubsection.6.2.1.2}% \contentsline {subsubsection}{\numberline {6.2.1.3}Révision}{59}{subsubsection.6.2.1.3}% \contentsline {subsubsection}{\numberline {6.2.1.4}Mémorisation}{60}{subsubsection.6.2.1.4}% -\contentsline {subsection}{\numberline {6.2.2}Résultats}{60}{subsection.6.2.2}% -\contentsline {subsection}{\numberline {6.2.3}Discussion}{62}{subsection.6.2.3}% -\contentsline {subsection}{\numberline {6.2.4}Conclusion}{63}{subsection.6.2.4}% -\contentsline {section}{\numberline {6.3}SECONDE PARTIE}{63}{section.6.3}% -\contentsline {subsection}{\numberline {6.3.1}Modèle Proposé}{63}{subsection.6.3.1}% +\contentsline {subsection}{\numberline {6.2.2}Résultats}{61}{subsection.6.2.2}% +\contentsline {subsection}{\numberline {6.2.3}Discussion}{63}{subsection.6.2.3}% +\contentsline {subsection}{\numberline {6.2.4}Conclusion}{64}{subsection.6.2.4}% +\contentsline {section}{\numberline {6.3}ESCBR-SMA : Introduction des systèmes multi-agents dans ESCBR}{64}{section.6.3}% +\contentsline {subsection}{\numberline {6.3.1}Modèle Proposé}{64}{subsection.6.3.1}% \contentsline {subsubsection}{\numberline {6.3.1.1}Algorithmes}{66}{subsubsection.6.3.1.1}% -\contentsline {subsubsection}{\numberline {6.3.1.2}Structure des agents}{67}{subsubsection.6.3.1.2}% -\contentsline {subsubsection}{\numberline {6.3.1.3}Apprentissage des agents}{67}{subsubsection.6.3.1.3}% -\contentsline {subsubsection}{\numberline {6.3.1.4}Échanges entre les agents}{68}{subsubsection.6.3.1.4}% -\contentsline {subsection}{\numberline {6.3.2}Résultats}{69}{subsection.6.3.2}% -\contentsline {subsection}{\numberline {6.3.3}Conclusion}{72}{subsection.6.3.3}% -\contentsline {chapter}{\numberline {7}Système de Recommandation dans AI-VT}{73}{chapter.7}% -\contentsline {section}{\numberline {7.1}Introduction}{73}{section.7.1}% -\contentsline {section}{\numberline {7.2}PREMIÈRE PARTIE}{74}{section.7.2}% -\contentsline {subsection}{\numberline {7.2.1}Modèle Proposé}{74}{subsection.7.2.1}% -\contentsline {subsection}{\numberline {7.2.2}Résultats}{76}{subsection.7.2.2}% -\contentsline {subsection}{\numberline {7.2.3}Discussion et Conclusions}{83}{subsection.7.2.3}% -\contentsline {section}{\numberline {7.3}DEUXIÈME PARTIE}{84}{section.7.3}% -\contentsline {subsection}{\numberline {7.3.1}Concepts Associés}{84}{subsection.7.3.1}% -\contentsline {subsection}{\numberline {7.3.2}Modèle Proposé}{87}{subsection.7.3.2}% -\contentsline {subsection}{\numberline {7.3.3}Résultats et Discussion}{88}{subsection.7.3.3}% -\contentsline {subsubsection}{\numberline {7.3.3.1}Régression dans la base de données des apprenants avec ESCBR-SMA}{89}{subsubsection.7.3.3.1}% -\contentsline {subsubsection}{\numberline {7.3.3.2}Progression des connaissances}{90}{subsubsection.7.3.3.2}% -\contentsline {subsubsection}{\numberline {7.3.3.3}Comparaison entre TS et BKT}{91}{subsubsection.7.3.3.3}% -\contentsline {subsubsection}{\numberline {7.3.3.4}Système de recommandation avec ESCBR-SMA}{92}{subsubsection.7.3.3.4}% -\contentsline {subsubsection}{\numberline {7.3.3.5}Progression des connaissances TS vs TS et ESCBR-SMA}{93}{subsubsection.7.3.3.5}% -\contentsline {subsection}{\numberline {7.3.4}Conclusion}{94}{subsection.7.3.4}% -\contentsline {section}{\numberline {7.4}TROISIÈME PARTIE}{95}{section.7.4}% -\contentsline {subsection}{\numberline {7.4.1}Modèle Proposé}{95}{subsection.7.4.1}% -\contentsline {subsection}{\numberline {7.4.2}Résultats et Discussion}{98}{subsection.7.4.2}% -\contentsline {subsubsection}{\numberline {7.4.2.1}Système de recommandation avec une base de données d'étudiants réels (TS avec Hawkes)}{98}{subsubsection.7.4.2.1}% -\contentsline {subsubsection}{\numberline {7.4.2.2}Base de données simulée (ESCBR, TS avec Hawkes)}{98}{subsubsection.7.4.2.2}% -\contentsline {subsection}{\numberline {7.4.3}Conclusion}{100}{subsection.7.4.3}% -\contentsline {chapter}{\numberline {8}Conclusions et Perspectives}{103}{chapter.8}% -\contentsline {section}{\numberline {8.1}Conclusion générale}{103}{section.8.1}% -\contentsline {section}{\numberline {8.2}Perspectives}{103}{section.8.2}% -\contentsline {chapter}{\numberline {9}Publications}{105}{chapter.9}% -\contentsline {section}{\numberline {9.1}Publications par rapport au sujet de thèse}{105}{section.9.1}% -\contentsline {section}{\numberline {9.2}Autres publications}{106}{section.9.2}% +\contentsline {subsubsection}{\numberline {6.3.1.2}Structure des agents}{68}{subsubsection.6.3.1.2}% +\contentsline {subsubsection}{\numberline {6.3.1.3}Apprentissage des agents}{69}{subsubsection.6.3.1.3}% +\contentsline {subsubsection}{\numberline {6.3.1.4}Échanges entre les agents}{70}{subsubsection.6.3.1.4}% +\contentsline {subsection}{\numberline {6.3.2}Résultats}{71}{subsection.6.3.2}% +\contentsline {subsection}{\numberline {6.3.3}Conclusion}{73}{subsection.6.3.3}% +\contentsline {chapter}{\numberline {7}Système de Recommandation dans AI-VT}{75}{chapter.7}% +\contentsline {section}{\numberline {7.1}Introduction}{75}{section.7.1}% +\contentsline {section}{\numberline {7.2}PREMIÈRE PARTIE}{76}{section.7.2}% +\contentsline {subsection}{\numberline {7.2.1}Modèle Proposé}{76}{subsection.7.2.1}% +\contentsline {subsection}{\numberline {7.2.2}Résultats}{78}{subsection.7.2.2}% +\contentsline {subsection}{\numberline {7.2.3}Discussion et Conclusions}{85}{subsection.7.2.3}% +\contentsline {section}{\numberline {7.3}DEUXIÈME PARTIE}{86}{section.7.3}% +\contentsline {subsection}{\numberline {7.3.1}Concepts Associés}{86}{subsection.7.3.1}% +\contentsline {subsection}{\numberline {7.3.2}Modèle Proposé}{89}{subsection.7.3.2}% +\contentsline {subsection}{\numberline {7.3.3}Résultats et Discussion}{90}{subsection.7.3.3}% +\contentsline {subsubsection}{\numberline {7.3.3.1}Régression dans la base de données des apprenants avec ESCBR-SMA}{91}{subsubsection.7.3.3.1}% +\contentsline {subsubsection}{\numberline {7.3.3.2}Progression des connaissances}{92}{subsubsection.7.3.3.2}% +\contentsline {subsubsection}{\numberline {7.3.3.3}Comparaison entre TS et BKT}{93}{subsubsection.7.3.3.3}% +\contentsline {subsubsection}{\numberline {7.3.3.4}Système de recommandation avec ESCBR-SMA}{94}{subsubsection.7.3.3.4}% +\contentsline {subsubsection}{\numberline {7.3.3.5}Progression des connaissances TS vs TS et ESCBR-SMA}{95}{subsubsection.7.3.3.5}% +\contentsline {subsection}{\numberline {7.3.4}Conclusion}{96}{subsection.7.3.4}% +\contentsline {section}{\numberline {7.4}TROISIÈME PARTIE}{97}{section.7.4}% +\contentsline {subsection}{\numberline {7.4.1}Modèle Proposé}{97}{subsection.7.4.1}% +\contentsline {subsection}{\numberline {7.4.2}Résultats et Discussion}{100}{subsection.7.4.2}% +\contentsline {subsubsection}{\numberline {7.4.2.1}Système de recommandation avec une base de données d'étudiants réels (TS avec Hawkes)}{100}{subsubsection.7.4.2.1}% +\contentsline {subsubsection}{\numberline {7.4.2.2}Base de données simulée (ESCBR, TS avec Hawkes)}{100}{subsubsection.7.4.2.2}% +\contentsline {subsection}{\numberline {7.4.3}Conclusion}{102}{subsection.7.4.3}% +\contentsline {chapter}{\numberline {8}Conclusions et Perspectives}{105}{chapter.8}% +\contentsline {section}{\numberline {8.1}Conclusion générale}{105}{section.8.1}% +\contentsline {section}{\numberline {8.2}Perspectives}{105}{section.8.2}% +\contentsline {chapter}{\numberline {9}Publications}{107}{chapter.9}% +\contentsline {section}{\numberline {9.1}Publications par rapport au sujet de thèse}{107}{section.9.1}% +\contentsline {section}{\numberline {9.2}Autres publications}{108}{section.9.2}% diff --git a/submit.sh b/submit.sh index 125804e..14d13fb 100755 --- a/submit.sh +++ b/submit.sh @@ -1,5 +1,5 @@ #!/bin/bash git add . -git commit -m 'version correction to chapter 7' +git commit -m 'version correct to chapter 5 and corrections to do in chapter 6' git push origin main

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