From 1e29668ef3342e5c7d856a1772bb501a5b0275e4 Mon Sep 17 00:00:00 2001 From: siulkilulki Date: Sun, 25 Mar 2018 17:48:44 +0200 Subject: [PATCH] =?UTF-8?q?Doko=C5=84czono=20algorytmy=20genetyczne.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- baza_danych.png | Bin 73087 -> 0 bytes beeminder.txt | 198 ++++++++++++++++++++++++++++++---------- czesc_dziecka.png | Bin 192517 -> 0 bytes czesc_opiekuna.png | Bin 302319 -> 0 bytes diagram_komponentow.png | Bin 377353 -> 0 bytes diagram_wdrozeniowy.png | Bin 238080 -> 0 bytes directory_structure.png | Bin 96098 -> 0 bytes google_trends.png | Bin 45001 -> 0 bytes master.tex | 5 + model.png | Bin 76509 -> 0 bytes model_schema.png | Bin 35082 -> 0 bytes pakiety.tex | 1 + rozdzial_1.tex | 175 ++++++++++++++++++++++++++++------- uam_logo.jpg | Bin 10894 -> 0 bytes wymagania_projektu.png | Bin 53961 -> 0 bytes zakres_projektu.png | Bin 43439 -> 0 bytes 16 files changed, 296 insertions(+), 83 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Algorytm odzierciedla zjawisko ewolucji biologicznej. -W procesie naturalnej selekcji najlepsze osobniki wezmą udział w reprodukcji -dając początek nowej lepiej przystosowanej generacji. +W procesie naturalnej selekcji najlepsze osobniki biorą udział w reprodukcji, +dając początek nowej, lepiej przystosowanej generacji. +% przecinek Naturalna selekcja zaczyna się od doboru najdoskonalszych osobników z populacji. Biorą one udział w reprodukcji przekazując część swoich genów potomkom. Nowa -generacja powinna być lepiej przystosowana niż rodzice ponieważ, jest -połączeniem genów, które zapewniły przeżycie rodzicom. Nawet gdyby wśród nowego -potomstwa znalazły się słabe +generacja powinna być lepiej przystosowana niż rodzice, ponieważ jest +połączeniem genów, które zapewniły przeżycie rodzicom. W przypadku gdy wśród nowego +potomstwa znalazłyby się słabe organizmy, to nie ma obawy, że ich geny przejdą do następnego pokolenia, ponieważ najprawdobniej nie dożyją one okresu rozrodczego. W ten sposób każde kolejne pokolenie jest lepsze niż poprzednie. -Ta wiedzę przyrodnicza została przełożona na algorytm genetyczny. - +Powyższa wiedza, wynikająca z obserwacji praw natury, została przełożona na grut +matemtyki i informatyki tworząc algorytm genetyczny. +% przecinek +\newpage +\enlargethispage{12\baselineskip} Na algorytm genetyczny składają się: -\begin{itemize} -\item inicjalizacji populacji, -\item funkcja przystosowania, +\vspace*{-1mm} +\begin{itemize}[noitemsep] +% \setlength\itemsep{0.005em} +\item inicjalizacja populacji, +\item funkcja przystosowania (stosowana przy ewaluacji i selekcji), \item selekcja, \item krzyżowanie, \item mutacja. \end{itemize} -\subsection{Inicjalizacja populacji} -Algorytm zaczyna się od utworzenia zbioru osobników, zwanych populacją. Każdy z -osobników jest rozwiązaniem problemu obliczeniowego. Osobnik reprezentowany jest -poprzez zbiór genów (parametrów), nazywanych chromosem. +\vspace*{-8mm} + +\begin{figure}[h!] +\centering +\includegraphics[width=0.9\hsize]{overview_GA.png} +\caption{Schemat działania algorytmu genetycznego.} +\label{overview_ga_pic} +\end{figure} + +\newpage +\subsection{Inicjalizacja populacji} +Algorytm zaczyna się od utworzenia zbioru osobników zwanych populacją. Każdy z +osobników jest rozwiązaniem problemu obliczeniowego. Osobnik reprezentowany jest +poprzez zbiór genów (parametrów) nazywanych chromosem. +Chromosom \newline jest najczęściej kodowany za pomocą: +\begin{itemize} +\item wektora genów, z których każdy reprezentowany jest przez liczbę całkowitą, + a czasem nawet liczbę rzeczywistą, +\item drzewiastych struktur danych. +\end{itemize} + + +\begin{example} +\end{example} +\begin{figure}[tbh] +\centering +\includegraphics[width=0.7\hsize]{kodowanie.png} +\caption{Przykład osobników zakodowanych binarnie.} +\label{kodowanie_pic} +\end{figure} -\textbf{Przykład} \subsection{Funkcja przystosowania} Funkcja przystosowania określa jak bardzo przystosowany jest osobnik (miara -jakości osobnika). +jakości osobnika). Im bardziej będzie przystosowany dany osobnik tym bardziej będzie +faworyzowany w procesie selekcji. Funkcja przystosowania dobierana jest w +zależności od modelu rozwiązywanego problemu, zwykle algorytm genetyczny dąży \newline do +jej minializacji lub maksymalizacji. +\begin{example} +Dla problemu +komiwojażera algorytm genetyczny będzie premiował te rozwiązania (w tym wypadku cykle Hamiltona), których suma +wag krawędzi jest najbliższa minimalnej sumie wag krawędzi w cyklu Hamiltona. +\end{example} + \subsection{Selekcja} -Z każdej generacji wybierany jest podzbiór populacji, który będzie brał udział w -rozmnażaniu, w tworzeniu nowej generacji. Pojedyńcze osobniki wybierane są na +\enlargethispage{6\baselineskip} +Z każdej generacji wybierany jest podzbiór populacji, który będzie brał udział +\newline w +rozmnażaniu, czyli w tworzeniu nowej generacji. Pojedyńcze osobniki wybierane +\newline są na podstawie funkcji przystosowania. Im lepiej przystosowany dany osobnik tym większe będzie miał szanse na wzięcie udziału w reprodukcji. -\subsection{Krzyżowanie} -Metoda używana do tworzenia nowych osobników. Każdy nowy osobnik tworzony jest -z pary rodziców. Krzyżowanie polega na łączeniu dwóch -genotypów w jeden. Potomek rodziców ma zespół cech które są kombinacją genotypów rodziców. -\subsection{Mutacja} -Operator genetyczny gwarantujący różnorodność osobników. Mutacja wprowadza do -genotypu losowe zmiany. - - -Proces generacji trwa aż do osiągnięcia kryterium stopu. Popularne kryteria to: +\noindent Wśród metod selekcji chromosomów wyróżniamy między innymi: +\vspace*{-3mm} \begin{itemize} -\item ustalona z góry liczba iteracji -\item osobnik (rozwiązanie), która spełnia minimalne kryterium % ??? -\item wykorzystanie określonej liczby zasobów np. czasu pracy procesora lub pieniędzy -\item kolejne iteracje nie tworzą lepszych rozwiązań -\item osiągnięcie najlepszego rozwiązania +\setlength\itemsep{0.005em} +\item metodę ruletki, +\item metodę rankingową, +\item metodę turniejową. \end{itemize} + +\begin{example} +\textbf{Metoda ruletki.} \newline +Niech $f(o_i)$ będzie przystosowaniem osobnika $o_i$ z populacji $P$, wtedy +prawdopodbieństwo wyboru $o_i$ wynosi: +\begin{equation*} + p_i = \frac{f(o_i)}{\sum_{j=1}^N f(o_i)}, +\end{equation*} +gdzie $N$ to rozmiar populacji $P$. +\end{example} +\vspace*{-3mm} +\begin{figure}[h!] +\centering +\includegraphics[width=0.7\hsize]{selekcja.png} +\caption{Przykład selekcji metodą ruletki. Losowana jest liczba $r$ z zakresu + $(0,F)$. \newline W +tym wypadku wybrany został osobnik $o_4$.} +\label{selekcja_pic} +\end{figure} + +\subsection{Krzyżowanie} +Krzyżowanie jest to metoda używana do tworzenia nowych osobników. Każdy nowy osobnik tworzony jest +z pary rodziców. Krzyżowanie polega na łączeniu dwóch +genotypów w jeden. Potomek rodziców ma zespół cech, które są kombinacją genotypów +rodziców. +\enlargethispage{4\baselineskip} + +\begin{example} +\end{example} +\begin{figure}[h!] +\centering +\includegraphics[width=1\hsize]{krzyzowanie.png} +\caption{Przykładowe krzyżowanie osobników zakodowanych binarnie.} +\label{krzyzowanie_pic} +\end{figure} + +\subsection{Mutacja} +Mutacja jest to operator genetyczny gwarantujący różnorodność osobników. Mutacja wprowadza do +genotypu losowe zmiany. Zazwyczaj mutacja zachodzi z bardzo niskim +prawdopodbieństwem - najczęściej około 1\%. Wyższe prawdopodbieństwo mogłoby +spowodobać, że rozwiązania psułyby się zamiast delikatnie zmieniały. + +W zależności od kodowania mutację można przeprowadzić przykładowo na następujące sposoby: +\begin{itemize} +\item w przypadku kodowania binarnego można zanegować losowy bit, +\item w przypadku kodowania liczbami całkowitymi (rzeczywistymi) można losowy + gen zamienić liczbą wylosowaną z ustalonego ręcznie zakresu liczb całkowitych (rzeczywistych). +\end{itemize} + +\newpage +\begin{example} +\end{example} +\begin{figure}[th] +\centering +\includegraphics[width=0.3\hsize]{mutacja.png} +\caption{Mutacja poprzez zanegowanie losowego bitu.} +\label{mutacja_pic} +\end{figure} + +\subsection{Kryterium stopu} +Proces generowania coraz to nowyszych pokoleń trwa aż do osiągnięcia kryterium stopu. Popularne kryteria to: +\begin{itemize} +\item z góry ustalona liczba iteracji, +\item znalezienie osobnika (rozwiązania), dla którego funkcja przystosowania + \newline da + wystarczająco dobry wynik, +\item wykorzystanie określonej liczby zasobów np. czasu pracy procesora lub pieniędzy, +\item przerwanie procesu, gdy kolejne iteracje nie tworzą lepszych rozwiązań, +\item osiągnięcie najlepszego rozwiązania. +\end{itemize} + +\newpage +\section{Sieci neuronowe} diff --git a/uam_logo.jpg b/uam_logo.jpg deleted file mode 100644 index 8639d61333efed464f6322e2a4417922805cf299..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 10894 zcmbVyXH-*Bux{v0L8=r(M@T3tO?qz$(n6D}G=)IuL5g&#N(%u5q!S=iX`u)xNJpum z1_UVrp@~#M^l|T6Z{2&}`}N+OwPu}}v(N0k&pLbd%s2br+`kpTEvODe2S7qX0?@m@ z0RR31m^FP}9Q<9Jd0)8syYlKn42=H~0Ga>_GIDZqGKyGKY)~xgp85oUoQX%0FaQAT~Fb^h=h`gnv{Zuob39s#w`E| z85tQV895adDLK`3Gm`6j3Q9%*6%*eBYG!p7eiH{8Rsl($$TT($m}68?_iZUbO;cYX 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