From 7e10be8bbfa93243a110b6ed1c01511fcafb5192 Mon Sep 17 00:00:00 2001 From: kssilveira Date: Wed, 2 Jun 2010 14:17:33 -0300 Subject: [PATCH] =?utf8?q?fazendo=20tabelas=20de=20resultados=20das=20exec?= =?utf8?q?u=C3=A7=C3=B5es=20do=20algoritmo=20gen=C3=A9tico=20no=20relat?= =?utf8?q?=C3=B3rio?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit --- MinimaxEnemy.cpp | 6 ++-- relatorio/final.pdf | Bin 38396 -> 71156 bytes relatorio/final.tex | 77 ++++++++++++++++++++++++++++++++++++++++++++++++++-- 3 files changed, 77 insertions(+), 6 deletions(-) rewrite relatorio/final.pdf (88%) diff --git a/MinimaxEnemy.cpp b/MinimaxEnemy.cpp index 6423ca2..8263611 100644 --- a/MinimaxEnemy.cpp +++ b/MinimaxEnemy.cpp @@ -355,13 +355,13 @@ HeuType MinimaxEnemy::masscenter(Board &board, bool player, bool plastmove) if(player == plastmove) { cmx = board.cmx[player]; cmy = board.cmy[player]; - res = SQU(cmx) + SQU(cmy); + res = SQU(cmx - 3.5) + SQU(cmy - 3.5); board.masscenter[player] = res; resb = board.masscenter[!player]; } else { cmx = board.cmx[!player]; cmy = board.cmy[!player]; - resb = SQU(cmx) + SQU(cmy); + resb = SQU(cmx - 3.5) + SQU(cmy - 3.5); board.masscenter[!player] = resb; res = board.masscenter[player]; } @@ -379,7 +379,7 @@ HeuType MinimaxEnemy::masscenter(Board &board, bool player, bool plastmove) //HeuType resb = SQU(cmx) + SQU(cmy); //printf(": %f %f\n", res, resb); - return (res - resb) / 52.5; + return (res - resb) / 24.5; } HeuType MinimaxEnemy::quads(Board &board, bool player, bool plastmove) diff --git a/relatorio/final.pdf b/relatorio/final.pdf dissimilarity index 88% index d8e1a71e3a75514e49437fcb93d95484ea4a46ba..ca73b2b87b763acbd3170b4840ac9883bbeebb7b 100644 GIT binary patch literal 71156 zcwV%-1z254wy=%6yGw9)IJmn*2=4A~!3pjb2<{f#-916@AExjl2| z|KKV1+EukztyT3_opp80nFxIz*ahs2PE$ukTh}6EVx?@I2 zTl+R#Qz~9AD?o1DAsbI-4~&H%xC-^=zSMX~k^v5RQ~NBeeyfwsx89# zda=niNT9Grw1+a}`~5TovVAQIAYypX$<4!UMIU)Tzcup`no&9mkcV=Uc{3~!CuK4i 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Cada uma delas calcula o valor correspondente a cada um dos jogadores e retorna a diferença entre estes valores. Algumas utilizam o valor do centro de massa, calculado como: +Foram implementadas 7 funções heurísticas, inspiradas em \cite{tese}. Cada uma delas calcula o valor correspondente a cada um dos jogadores e retorna a diferença (normalizada entre 0 e 1) entre estes valores. -$$ \frac{|P(p)|}{\sum_{(i, j) \in P(p)}(i, j)} $$ +Algumas utilizam o valor do centro de massa, calculado como a média das coordenadas das peças do jogador em questão. + +%$$ \frac{|P(p)|}{\sum_{(i, j) \in P(p)}(i, j)} $$ \subsubsection{Distância para o centro} É o inverso da média das distâncias euclidianas das peças para o centro. Objetiva recompensar configurações em que temos várias peças no centro, pois é necessário passar pelo centro para reunir as peças, e se for possível reuní-las no centro é melhor ainda. @@ -120,6 +122,7 @@ $$ \frac{|P(p)|}{\sum_{(i, j) \in P(p)}(i, j)} $$ É a média da qualidade das posições das peças, segundo a seguinte tabela de pesos: \begin{table}[htbp] +\centering \begin{tabular}{cccccccc} -80 & -25 & -20 & -20 & -20 & -20 & -25 & -80 \\ -25 & 10 & 10 & 10 & 10 & 10 & 10 & -25 \\ @@ -136,12 +139,80 @@ $$ \frac{|P(p)|}{\sum_{(i, j) \in P(p)}(i, j)} $$ O objetivo é penalizar peças na borda do tabuleiro (que são facilmente bloqueáveis pelo inimigo e que têm mais chance de estar longe do grupo principal) e recompensar as peças que estão mais perto do centro. -\subsection{Pesos} +\subsubsection{Centro de Massa} + + É a distância euclidiana do centro de massa para o centro do tabuleiro. Se o centro de massa está no centro do tabuleiro, as peças podem estar arbitrariamente longe (como no início do jogo, por exemplo). Quanto mais longe do centro do tabuleiro estiver o centro de massa, mais próximas as peças têm que estar. + +\subsubsection{Quadrados} + + É a quantidade de quadrados de lado 2 com pelo menos três peças do jogador em questão e a no máximo duas casas de distância do centro de massa. A vantagem de se ter estruturas deste tipo é que são necessário pelo menos dois movimentos para desconectá-las. A razão para exigir uma distância mínima do centro de massa é evitar que se formem grupos isolados. + +\subsubsection{Concectividade} + + É o número médio de peças aliadas adjacentes das peças do jogador em questão. Objetiva recompensar aglomerações de peças em oposição a formação em linha, em que uma peça só está conectada com outras duas, as quais são mais fáceis de destruir. + +\subsubsection{Uniformidade} + É o inverso da área do menor quadrado de lados paralelos aos lados do tabuleiro que engloba todas as peças do jogador em questão. Objetiva recompensar configurações com peças em linhas e colunas próximas. + +\subsection{Algoritmo Genético} \begin{itemize} \item Algoritmo Genético \item ... \end{itemize} + O valor final da função de avaliação foi definido como sendo uma média ponderada das heurísticas. Para determinar a melhor tupla de valores de pesos, utilizamos um algoritmo genético, detalhado a seguir. + +\subsubsection{Representação do Problema} + + A representação escolhida foi uma tupla com os pesos (entre 0 e 1) dados para cada função heurística. + +\subsubsection{Geração da População Inicial} + + A população inicial (parâmetro) é gerada sorteando-se valores de pesos aleatórios para cada heurística de cada indivíduo. + + \subsubsection{Avaliação da População} + + A avaliação é feita simulando partidos de todos contra-todos em dois turnos (alternando quem faz a jogada inicial) e somando-se a quantidade de vitórias obtidas. + +\subsubsection{Seleção, Recombinação e Mutação} + + Após feita a avaliação de uma geração, um certa porcentagem (parâmetro) dos indivíduos mais adaptados é escolhida para permanecer (clonagem). Então os indivíduos restantes da população são fruto da recombinação destes. Essa recombinação se dá primeiro escolhendo aleatoriamente dois indivíduos diferentes para serem combinados, e então aleatoriamente de qual destes indivíduos cada peso é herdado. Ainda há uma certa porcentagem de chance (parâmetro) de um destes pesos ser sortiado aleatoriamente novamente, caracterizando uma mutação. + +\subsubsection{Critério de Parada} + O algoritmo para após uma certa quantidade de iterações (parâmetro). + +\subsubsection{Fator Aleatório na Função Heurística} + Para evitar que houvessem empates por repetição de jogadas, foi incluído um fator aleatório na heurística, variando entre 0 e 1, cujo peso também foi incluído na composição dos indivíduos. + +\subsubsection{Parâmetros Utilizados} + + O algoritmo foi executado com uma população de 10 indivíduos, uma porcentagem de seleção de 50% e de mutação de 10%, durante 100 iterações, com profundidade 3 no negamax. O resultado encontra-se na tabela \ref{tab:pesos1}. + +0.00763 0.38113 0.63358 0.89597 0.03325 0.41463 0.78261 0.01670 + + Pode-se verificar que o peso do fator aleatório ficou quase 0, como era de se esperar. Além disso, outras duas funções heurísticas ficaram com peso bem baixo (NOMES AQUI). Dada a complexidade do cálculo destes funções, decidimos eliminá-las da heurística para poder atingir uma profundidade maior. Executamos o algoritmo genético com os mesmos parâmetros, porém eliminando estas funções heurísticas (\ref{tab:pesos2}). + +0.00616 0.87480 0.07819 0.66735 0.41734 0.32783 + + Desta vez obtivemos um peso baixo para a função heurística NOME AQUI. Pelas mesmas razões citadas anteriormente, executamos novamente o algoritmo removendo mais esta função (\ref{tab:pesos3}). Finalmente atingimos pesos satisfatórios, ou seja, todas as heurísticas têm uma contribuição significativa para a avaliação final. + +0.00251 0.82723 0.97915 0.96032 0.96950 + +\begin{table}[htbp] + \begin{tabular}{lc} + Fator Aleatório & \\ + Distância para o centro & \\ + Concentração & \\ + Centralização & \\ + Centro de Massa & \\ + Quadrados & \\ + Conectividade & \\ + Uniformidade & \\ + \end{tabular} + \caption{Resultado da Execução do Algoritmo Genético} + \label{tab:pesos} +\end{table} + \subsection{Resultados} \begin{itemize} \item Profundidade -- 2.11.4.GIT