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Diseño de funciones heurísticas

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curso-search/8-puzzle-heuristica-07.svg 0 → 100644
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curso-search/8-puzzle-heuristica-08.svg 0 → 100644
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curso-search/8-puzzle-heuristica-09.svg 0 → 100644
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curso-search/8-puzzle-heuristica-10.svg 0 → 100644
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curso-search/8-puzzle-heuristica-11.svg 0 → 100644
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curso-search/8-puzzle-heuristica-12.svg 0 → 100644
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curso-search/8-puzzle-heuristica-13.svg 0 → 100644
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curso-search/8-puzzle-heuristica-14.svg 0 → 100644
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curso-search/8-puzzle-heuristica-15.svg 0 → 100644
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curso-search/heuristicas-diseño.tex 0 → 100644
\documentclass[xcolor=dvipsnames]{beamer}
\documentclass[xcolor=dvipsnames]{beamer}
\usepackage[spanish]{babel}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{pgfpages}
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% descomentar para generar handouts con notas
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\newcommand{\I}[1]{\mathit{#1}}
\newcommand{\cierto}{\I{cierto}}
\newcommand{\falso}{\I{falso}}
\DeclareMathOperator*{\argmax}{argmax}
\spanishdecimal{.}
\title{Diseño de Funciones Heurísticas}
\author{Stalin Muñoz Gutiérrez}
\institute{
Centro de Ciencias de la Complejidad\\
Universidad Nacional Aut\'onoma de Mexico (UNAM)}
\date{}
\begin{document}
\parindent 2em
\frame
{
\titlepage
\note<1>{
Las funciones heurísticas son la base de operación de los algoritmos de búsqueda informada. Su diseño y características tiene un impacto sobre la optimalidad de la solución y el desempeño en tiempo y memoria de los algoritmos.
}
}
\begin{frame}
\frametitle{¿De dónde vienen las heurísticas?}
\begin{block}{Quitando restricciones del problema original}
Una manera común de proponer funciones heurísticas es quitar restricciones al problema original. Esto es, estimar el costo a la meta imaginando que el agente puede realizar acciones que el problema original no permite.
\end{block}
\note{
En muchas ocasiones se puede proponer funciones heurísticas relajando las restricciones del problema original.
}
\end{frame}
\begin{frame}
\frametitle{Distancia euclideana en mapas}
\begin{center}
\includegraphics[scale=0.22]{cdmx-colima-heuristica.pdf}
\end{center}
\note{
En el ejemplo de encontrar rutas en un mapa.
Consideramos la distancia en línea recta como una buena heurística.
En este mapa vemos que la restricción para un vehículo es moverse sobre el sistema carretero.
Esa ruta esta alejada de la línea recta.
Si quitamos esta restricción, estamos considerando que el agente puede viajar en línea recta. A pesar de que esto no es cierto en la realidad,esta heurística es una buena aproximación respecto del costo a la meta.
Cumple además con el criterio de que es facilmente computable.
Como en el mejor de los casos la carretera es una recta entre los puntos de interés, en un espacio Euclideano esta heurística es consistente y admisible.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Distancia de Manhattan en el juego del 8}
\only<1>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-01.pdf}
\end{center}
}
\note<1>{
Otro ejemplo donde podemos proponer una función heurística a partir de relajar las restricciones del problema es el rompecabezas del 8.
}
\only<2>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-02.pdf}
\end{center}
}
\note<2>{
La restricción del juego solo permite el movimiento de las fichas adyacentes al espacio libre.
En esta configuración las fichas 7 y 8.
}
\only<3>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-03.pdf}
\end{center}
}
\note<3>{
Al quitar esta restricción podemos considerar que las fichas se pueden mover no importando si estan adyacentes al espacio o no.
Aquí, para llegar a la meta las 6 fichas se podrían mover.
}
\only<4>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-04.pdf}
\end{center}
}
\note<4>{
Por ejemplo.
La ficha 4 debe moverse una casilla hacia abajo para llegar a su posición deseada en la configuración final.
}
\only<5>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-05.pdf}
\end{center}
}
\note<5>{
La heurística entonces se define como el número de movimientos \emph{sin restricción} necesarios para alcanzar la meta.
}
\only<6>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-06.pdf}
\end{center}
}
\note<6>{
Para la ficha 4 es un movimiento.
}
\only<7>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-07.pdf}
\end{center}
}
\note<7>{
Para la ficha 1, también es un movimiento.
Acumulamos, los movimientos de todas las fichas para calcular una distancia del estado inicial al final.
Esta distancia que considera movimientos únicamente horizontales y verticales, pero no diagonales se conoce como distancia de \emph{Manhattan}.
}
\only<8>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-08.pdf}
\end{center}
}
\note<8>{
En nuestro ejemplo la distancia es 6.
La distancia de Manhattan es una heurística que no sobreestima.
Adicionalmente cumple con el requerimiento de que es computacionalmente poco costosa de calcular.
}
\only<9>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-09.pdf}
\end{center}
}
\note<9>{
Sin embargo, es más costosa de calcular que simplemente contar las fichas fuera de lugar.
¿Nos conviene este extra costo?
}
\only<10>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-10.pdf}
\end{center}
}
\note<10>{
Denotemos como $h_1$ la heurística que cuenta el número de fichas fuera de lugar.
Y como $h_2$ la heurística que calcula la distancia de Manhattan a la meta.
}
\only<11>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-11.pdf}
\end{center}
}
\note<11>{
Para la configuración mostrada
el valor de $h_1$ es 5.
El valor de $h_2$ es 6
}
\only<12>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-12.pdf}
\end{center}
}
\note<12>{
Podemos ver que la diferencia radica en que la ficha 2 tiene que moverse dos veces para llegar a la configuración deseada.
Una a la derecha y otra hacia arriba.
Si las heurísticas dan valores diferentes para la misma configuración.
¿cuál es mejor?
Para responder a esta pregunta no solo hay que tomar en cuenta el costo de calcular la heurística, sino también que tan buena es la estimación de la función.
}
\only<13>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-13.pdf}
\end{center}
}
\note<13>{
Ambas heurísticas no sobreestiman, esto quiere decir que las estimaciones se mantienen por debajo del costo real.
La más cercana al costo real debe ser la que nos entregue un valor más grande.
En este caso la distancia de Manhattan nos da una mejor aproximación del costo estimado para llegar a la meta.
}
\only<14>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-14.pdf}
\end{center}
}
\note<14>{
Esto nos permite plantear una manera de incorporar varias heurísticas en una nueva heurística más informativa.
Si tenemos $n$ heurísticas distintas, todas ellas admisibles,
proponemos una heurística nueva que calcula el máximo de los valores resultantes de aplicar cada heurística a un estado.
}
\only<15>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-15.pdf}
\end{center}
}
\note<15>{
Pero hay que tener cuidado.
En este ejemplo es claro que la heurística $h_2$ siempre nos entregará un estimado mayor o igual al de la heurística $h_1$.
Por lo tanto, es infructuoso calcular ambas.
Nos quedamos con la distancia de Manhattan.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Heurísticas basadas en base de datos de patrones}
\only<1>{
\begin{center}
\includegraphics[scale=0.08]{rubik.png}
\end{center}
}
\note<1>{
A veces encontrar heurísticas basadas en distancias no es suficiente.
}
\only<2>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-01.pdf}
\end{center}
}
\note<2>{
Para el cubo de Rubik, es posible construir una heurística basada en una distancia de Manhattan en 3 dimensiones.
Sin embargo, esta heurística es poco informativa.
}
\only<3>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-02.pdf}
\end{center}
}
\note<3>{
Para observar la razón, veamos que sucede si aplicamos una acción al cubo ordenado.
Digamos que lo rotamos 90 grados.
En esta figura vemos del lado derecho dos configuraciones posibles si rotamos el cubo una vez.
Hemos aplanado las caras para poder verlas simultáneamente. Hay que imaginar que el cubo se obtiene doblando 90 grados en cada unión de las caras.
Observamos que se desacomodan 8 subcubos.
Si tomaramos de manera simple el número de subcubos fuera de lugar, esto resultaría en una heurística que sobreestima el valor real. En este caso solo se realizó un movimiento. Es decir tenemos un costo de real de 1.
}
\only<4>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-03.pdf}
\end{center}
}
\note<4>{
Para hacer la distancia de Manhattan en tres dimensiones una heurística admisible se tendría que dividir el valor entre 8.
}
\only<5>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-04.pdf}
\end{center}
}
\note<5>{
Con ayuda de las supercomputadoras de Google Tomas Rokicki demostró en 2010 que la distancia máxima a la que pueden estar dos configuraciones del cubo es 20 cuando se consideran como acciones rotaciones de las caras de 90 y 180 grados.
Si tenemos un total de 26 subcubos, de los cuales los seis cubos centrales de cada cara no pueden moverse. Podemos ver que 20 entre 8 nos daría una distancia máxima de 2.5.
Esta heurística es muy mala, pues esta muy alejada de el valor máximo esperado que es 20.
Korf propone tomar solo algunos subcubos por ejemplo los de las esquinas o los de las orillas en las cruces.
Tomando los de las orillas la distancia Manhattan se divide entre 4 y el valor esperado de distancia es de 5.5. Esto sigue siendo malo para guiar a los algoritmos informados en un espacio de más de 43 trillones de configuraciones.
}
\only<6>{
\begin{center}
\includegraphics[scale=0.7]{rubik-heuristica-05.pdf}
\end{center}
}
\note<6>{
Korf propone el uso de bases de datos de patrones, una idea desarrollada por Culberson y Schaeffer en 1996 para el rompecabezas del 15.
La idea es simple, partiendo de la configuración meta. Hay que realizar una búsqueda tipo BFS y observar cada configuración descubierta y poner atención solo a un subconjuntos de los subcubos.
Por ejemplo, aquí ponemos atención solo a los subcubos de las esquinas.
Guardamos en una base de datos el patron descubierto junto con la profundidad mínima a la que se encuentra dicho patrón.
Como vemos en la figura el patrón con los subcubos azules en las esquinas captura todas los estados en los que esto es posible.
Las configuraciones mostradas todas tienen el mismo patrón de esquinas.
La configuración a la que se encontró el patrón de esquinas azules, sirve como heurística para todos los demás estados.
}
\only<7>{
\begin{center}
\includegraphics[scale=0.7]{rubik-heuristica-06.pdf}
\end{center}
}
\note<7>{
Aquí mostramos un segundo patrón.
Ahora nos fijamos en los cubos de las orillas,
los que forman la cruz.
Al descubrirse este patrón de orillas azules, el algoritmo tipo BFS guardará el patrón junto con su profundidad.
La profundidad servirá para todo estado que exhiba el patrón, un conjunto muy grande.
Por construcción esta heurística es admisible.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Conclusión}
\begin{itemize}
\item Típicamente podemos construir una función heurística relajando las restricciones del problema original y planteando una distancia entre configuraciones.
\note<1>{
Sumarizando:
podemos relajar las restricciones del problema y proponer una heurística basada en una distancia entre estados.
}
\item Podemos combinar varias heurísticas en una sola, siempre que nos den información distinta.
\note<2>{
Se pueden combinar más de una heurística admisibles utilizando la función máximo sobre los valores calculados con cada una de ellas.
}
\item Hay que poder evaluar las heurísticas de manera eficiente.
\note<3>{
Las heurísticas deben poder calcularse de manera rápida, de otra forma minarán el desempeño de los
algoritmos pues son invocadas con cada expansión de estados.
}
\item Podemos generar estimaciones de costos mínimos de un conjuntos de estados descrito por un patrón al estado meta y almacenarlos en una base de datos.
\note<4>{
Con el uso de bases de datos de patrones se pueden generar heurísticas fuera de línea y ser guardadas en bases de datos.
}
\item Los agentes pueden incorporar tecnicas de aprendizaje máquina para aprender las heurísticas (Arfaee et al. 2011).
\note<5>{
Existe investigación reciente sobre cómo un agente podría usar aprendizaje máquina para proponer heurísticas de manera automática.
Por ejemplo Arfaee, Zilles y Holte, aplican técnicas de aprendizaje máquina en el cubo de Rubik para mejorar las heurísticas de Korf basadas en bases de datos de patrones.
}
\end{itemize}
\end{frame}
\end{document}
\ No newline at end of file
curso-search/heuristicas-diseño.tex.bak 0 → 100644
\documentclass[xcolor=dvipsnames]{beamer}
\documentclass[xcolor=dvipsnames]{beamer}
\usepackage[spanish]{babel}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{pgfpages}
\usepackage[makeroom]{cancel}
% descomentar para generar handouts con notas
\setbeameroption{show notes on second screen=right}
\usepackage{tikz}
\tikzstyle{every picture}+=[remember picture]
\usefonttheme[onlymath]{serif}
\usepackage{verbatim}
\usepackage{pifont}
\usetheme{Antibes}
\usecolortheme{lily}
\usepackage{graphicx}
\usepackage{hyperref}
\newcommand{\I}[1]{\mathit{#1}}
\newcommand{\cierto}{\I{cierto}}
\newcommand{\falso}{\I{falso}}
\DeclareMathOperator*{\argmax}{argmax}
\spanishdecimal{.}
\title{Diseño de Funciones Heurísticas}
\author{Stalin Muñoz Gutiérrez}
\institute{
Centro de Ciencias de la Complejidad\\
Universidad Nacional Aut\'onoma de Mexico (UNAM)}
\date{}
\begin{document}
\parindent 2em
\frame
{
\titlepage
\note<1>{
Las funciones heurísticas son la base de operación de los algoritmos de búsqueda informada. Su diseño y características tiene un impacto sobre la optimalidad de la solución y el desempeño en tiempo y memoria de los algoritmos.
}
}
\begin{frame}
\frametitle{¿De dónde vienen las heurísticas?}
\begin{block}{Quitando restricciones del problema original}
Una manera común de proponer funciones heurísticas es quitar restricciones al problema original. Esto es, estimar el costo a la meta imaginando que el agente puede realizar acciones que el problema original no permite.
\end{block}
\note{
En muchas ocasiones se puede proponer funciones heurísticas relajando las restricciones del problema original.
}
\end{frame}
\begin{frame}
\frametitle{Distancia euclideana en mapas}
\begin{center}
\includegraphics[scale=0.22]{cdmx-colima-heuristica.pdf}
\end{center}
\note{
En el ejemplo de encontrar rutas en un mapa.
Consideramos la distancia en línea recta como una buena heurística.
En este mapa vemos que la restricción para un vehículo es moverse sobre el sistema carretero.
Esa ruta esta alejada de la línea recta.
Si quitamos esta restricción, estamos considerando que el agente puede viajar en línea recta. A pesar de que esto no es cierto en la realidad,esta heurística es una buena aproximación respecto del costo a la meta.
Cumple además con el criterio de que es facilmente computable.
Como en el mejor de los casos la carretera es una recta entre los puntos de interés, en un espacio Euclideano esta heurística es consistente y admisible.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Distancia de Manhattan en el juego del 8}
\only<1>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-01.pdf}
\end{center}
}
\note<1>{
Otro ejemplo donde podemos proponer una función heurística a partir de relajar las restricciones del problema es el rompecabezas del 8.
}
\only<2>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-02.pdf}
\end{center}
}
\note<2>{
La restricción del juego solo permite el movimiento de las fichas adyacentes al espacio libre.
En esta configuración las fichas 7 y 8.
}
\only<3>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-03.pdf}
\end{center}
}
\note<3>{
Al quitar esta restricción podemos considerar que las fichas se pueden mover no importando si estan adyacentes al espacio o no.
Aquí, para llegar a la meta las 6 fichas se podrían mover.
}
\only<4>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-04.pdf}
\end{center}
}
\note<4>{
Por ejemplo.
La ficha 4 debe moverse una casilla hacia abajo para llegar a su posición deseada en la configuración final.
}
\only<5>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-05.pdf}
\end{center}
}
\note<5>{
La heurística entonces se define como el número de movimientos \emph{sin restricción} necesarios para alcanzar la meta.
}
\only<6>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-06.pdf}
\end{center}
}
\note<6>{
Para la ficha 4 es un movimiento.
}
\only<7>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-07.pdf}
\end{center}
}
\note<7>{
Para la ficha 1, también es un movimiento.
Acumulamos, los movimientos de todas las fichas para calcular una distancia del estado inicial al final.
Esta distancia que considera movimientos únicamente horizontales y verticales, pero no diagonales se conoce como distancia de \emph{Manhattan}.
}
\only<8>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-08.pdf}
\end{center}
}
\note<8>{
En nuestro ejemplo la distancia es 6.
La distancia de Manhattan es una heurística que no sobreestima.
Adicionalmente cumple con el requerimiento de que es computacionalmente poco costosa de calcular.
}
\only<9>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-09.pdf}
\end{center}
}
\note<9>{
Sin embargo, es más costosa de calcular que simplemente contar las fichas fuera de lugar.
¿Nos conviene este extra costo?
}
\only<10>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-10.pdf}
\end{center}
}
\note<10>{
Denotemos como $h_1$ la heurística que cuenta el número de fichas fuera de lugar.
Y como $h_2$ la heurística que calcula la distancia de Manhattan a la meta.
}
\only<11>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-11.pdf}
\end{center}
}
\note<11>{
Para la configuración mostrada
el valor de $h_1$ es 5.
El valor de $h_2$ es 6
}
\only<12>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-12.pdf}
\end{center}
}
\note<12>{
Podemos ver que la diferencia radica en que la ficha 2 tiene que moverse dos veces para llegar a la configuración deseada.
Una a la derecha y otra hacia arriba.
Si las heurísticas dan valores diferentes para la misma configuración.
¿cuál es mejor?
Para responder a esta pregunta no solo hay que tomar en cuenta el costo de calcular la heurística, sino también que tan buena es la estimación de la función.
}
\only<13>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-13.pdf}
\end{center}
}
\note<13>{
Ambas heurísticas no sobreestiman, esto quiere decir que las estimaciones se mantienen por debajo del costo real.
La más cercana al costo real debe ser la que nos entregue un valor más grande.
En este caso la distancia de Manhattan nos da una mejor aproximación del costo estimado para llegar a la meta.
}
\only<14>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-14.pdf}
\end{center}
}
\note<14>{
Esto nos permite plantear una manera de incorporar varias heurísticas en una nueva heurística más informativa.
Si tenemos $n$ heurísticas distintas, todas ellas admisibles,
proponemos una heurística nueva que calcula el máximo de los valores resultantes de aplicar cada heurística a un estado.
}
\only<15>{
\begin{center}
\includegraphics[scale=0.6]{8-puzzle-heuristica-15.pdf}
\end{center}
}
\note<15>{
Pero hay que tener cuidado.
En este ejemplo es claro que la heurística $h_2$ siempre nos entregará un estimado mayor o igual al de la heurística $h_1$.
Por lo tanto, es infructuoso calcular ambas.
Nos quedamos con la distancia de Manhattan.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Heurísticas basadas en base de datos de patrones}
\only<1>{
\begin{center}
\includegraphics[scale=0.08]{rubik.png}
\end{center}
}
\note<1>{
A veces encontrar heurísticas basadas en distancias no es suficiente.
}
\only<2>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-01.pdf}
\end{center}
}
\note<2>{
Para el cubo de Rubik, es posible construir una heurística basada en una distancia de Manhattan en 3 dimensiones.
Sin embargo, esta heurística es poco informativa.
}
\only<3>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-02.pdf}
\end{center}
}
\note<3>{
Para observar la razón, veamos que sucede si aplicamos una acción al cubo ordenado.
Digamos que lo rotamos 90 grados.
En esta figura vemos del lado derecho dos configuraciones posibles si rotamos el cubo una vez.
Hemos aplanado las caras para poder verlas simultáneamente. Hay que imaginar que el cubo se obtiene doblando 90 grados en cada unión de las caras.
Observamos que se desacomodan 8 subcubos.
Si tomaramos de manera simple el número de subcubos fuera de lugar, esto resultaría en una heurística que sobreestima el valor real. En este caso solo se realizó un movimiento. Es decir tenemos un costo de real de 1.
}
\only<4>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-03.pdf}
\end{center}
}
\note<4>{
Para hacer la distancia de Manhattan en tres dimensiones una heurística admisible se tendría que dividir el valor entre 8.
}
\only<5>{
\begin{center}
\includegraphics[scale=0.6]{rubik-heuristica-04.pdf}
\end{center}
}
\note<5>{
Con ayuda de las supercomputadoras de Google Tomas Rokicki demostró en 2010 que la distancia máxima a la que pueden estar dos configuraciones del cubo es 20 cuando se consideran como acciones rotaciones de las caras de 90 y 180 grados.
Si tenemos un total de 26 subcubos, de los cuales los seis cubos centrales de cada cara no pueden moverse. Podemos ver que 20 entre 8 nos daría una distancia máxima de 2.5.
Esta heurística es muy mala, pues esta muy alejada de el valor máximo esperado que es 20.
Korf propone tomar solo algunos subcubos por ejemplo los de las esquinas o los de las orillas en las cruces.
Tomando los de las orillas la distancia Manhattan se divide entre 4 y el valor esperado de distancia es de 5.5. Esto sigue siendo malo para guiar a los algoritmos informados en un espacio de más de 43 trillones de configuraciones.
}
\only<6>{
\begin{center}
\includegraphics[scale=0.7]{rubik-heuristica-05.pdf}
\end{center}
}
\note<6>{
Korf propone el uso de bases de datos de patrones, una idea desarrollada por Culberson y Schaeffer en 1996 para el rompecabezas del 15.
La idea es simple, partiendo de la configuración meta. Hay que realizar una búsqueda tipo BFS y observar cada configuración descubierta y poner atención solo a un subconjuntos de los subcubos.
Por ejemplo, aquí ponemos atención solo a los subcubos de las esquinas.
Guardamos en una base de datos el patron descubierto junto con la profundidad mínima a la que se encuentra dicho patrón.
Como vemos en la figura el patrón con los subcubos azules en las esquinas captura todas los estados en los que esto es posible.
Las configuraciones mostradas todas tienen el mismo patrón de esquinas.
La configuración a la que se encontró el patrón de esquinas azules, sirve como heurística para todos los demás estados.
}
\only<7>{
\begin{center}
\includegraphics[scale=0.7]{rubik-heuristica-06.pdf}
\end{center}
}
\note<7>{
Aquí mostramos un segundo patrón.
Ahora nos fijamos en los cubos de las orillas,
los que forman la cruz.
Al descubrirse este patrón de orillas azules, el algoritmo tipo BFS guardará el patrón junto con su profundidad.
La profundidad servirá para todo estado que exhiba el patrón, un conjunto muy grande.
Por construcción esta heurística es admisible.
}
\end{frame}
\begin{frame}[<+->]
\frametitle{Conclusión}
\begin{itemize}
\item Típicamente podemos construir una función heurística relajando las restricciones del problema original y planteando una distancia entre configuraciones.
\note<1>{
Sumarizando:
podemos relajar las restricciones del problema y proponer una heurística basada en una distancia entre estados.
}
\item Podemos combinar varias heurísticas en una sola, siempre que nos den información distinta.
\note<2>{
Se pueden combinar más de una heurística admisibles utilizando la función máximo sobre los valores calculados con cada una de ellas.
}
\item Hay que poder evaluar las heurísticas de manera eficiente.
\note<3>{
Las heurísticas deben poder calcularse de manera rápida, de otra forma minarán el desempeño de los
algoritmos pues son invocadas con cada expansión de estados.
}
\item Podemos generar estimaciones de costos mínimos de un conjuntos de estados descrito por un patrón al estado meta y almacenarlos en una base de datos.
\note<4>{
Con el uso de bases de datos de patrones se pueden generar heurísticas fuera de línea y ser guardadas en bases de datos.
}
\item Los agentes pueden incorporar tecnicas de aprendizaje máquina para aprender las heurísticas (Arfaee et al. 2011).
\note<5>{
Existe investigación reciente sobre cómo un agente podría usar aprendizaje máquina para proponer heurísticas de manera automática.
Por ejemplo Arfaee, Zilles y Holte,
}
\end{itemize}
\end{frame}
\end{document}
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