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\subsection{附加任务 5,6 实现} + \subsubsection{附加任务 5,6 实现} \textbf{AI 独立线程} @@ -391,8 +391,10 @@ \caption{联机对局界面演示} \end{figure} - 由于在判断落子成立时禁止了棋手自杀，因此对局结束的条件只有超时和认输两种。 - + 虽然我方在判断落子成立时禁止了自杀，但是对方仍然具有自杀的可能，因此对局结束的条件有自杀、超时和认输 $3$ 种。 + + 当一方自杀后，胜方发送 \verb|SUICIDE_OP|，负方在收到该信息后回复同样的 \verb|SUICIDE_OP|，表示确认以“一方自杀”为理由结束对局。此时联机对战结束，棋盘不能被操作。 + 当一方认输，即点击 Resign 按钮后，认输方发送 \verb|GIVEUP_OP|，胜方在收到该信息后回复 \verb|GIVEUP_END_OP| 表示请求以“一方认输”为理由结束对局。认输方收到 \verb|GIVEUP_END_OP| 回复同样的信息以确认。此时联机对战结束，棋盘不能被操作。 当一方超时，胜方的计时器会调用 \verb|GameWidget::playerTimeout_OL()| 槽函数，发送 \verb|TIMEOUT_END_OP| 表示请求以“一方超时”为理由结束对局，负方回复同样的信息以确认。此时联机对战结束，棋盘不能被操作。 @@ -402,10 +404,12 @@ \section{AI 算法设计} - 由于助教在 \verb|/guidance| 中建议不要卷 AI 的强度，所以本项目 AI 采用推荐的 Minimax 搜索算法。 + 由于助教在 \verb|/guidance| 中建议不要卷 AI 的强度，所以本项目 AI 采用推荐的 Minimax 搜索算法，为 SA + Minimax。 同时，对于用 MCTS 爆杀本项目 AI 的隔壁队伍表示强烈的谴责。 + 同时，对于很多队伍都用 MCTS 欺负老实人的行为表示发自内心的强烈的谴责。 + \subsection{Minimax 搜索和 Alpha-Beta 剪枝} Minimax 算法又叫极小化极大算法，是一种找出失败的最大可能性中的最小值的算法。 @@ -421,8 +425,8 @@ // minimax 搜索 double Bot::alphaBeta(double a, double b, int depth) { - time_t curTime = clock(); - if((curTime - searchStartTime) / (BOT_TIMEOUT * 1000) > 0.9) + qint64 curTime = QDateTime::currentMSecsSinceEpoch(); + if(curTime - searchStartTime > BOT_TIMEOUT * 900) return depth & 1 ? b : a; // 判断超时 if(depth == Max_Dep) return judgeBoard(); // 叶子节点返回估价 @@ -489,32 +493,35 @@ 一开始估价函数以 $e$ 为底数，而大量测试表明，趋近于 $\frac 12$ 而不是 $\frac 1e$ 会更为理想。 - \subsection{参数调整} + \subsection{SA 参数调整} 在 Alpha-Beta 剪枝的过程中，需要传入 $\alpha, \beta$ 的初值。对于理想的 AI 对局来说，$\alpha, \beta$ 都应该趋近于 $\frac 12$。 - 同样在大量的对局测试和 AI 自迭代优化后，笔者取 $\alpha = 0.39,\beta = 0.61$。 + 同样在大量的对局测试（尤其是和隔壁队伍的 MCTS）和 AI 四次自迭代优化后，笔者取 $\alpha = 0.31,\beta = 0.61$，这是一个反常识但是非常高效的参数，原因是因为我们的估价函数 $>0.5$ 不一定会赢，$<0.5$ 也不一定会输，甚至可能负相关\sout{，惊不惊喜意不意外}。 - 此外，笔者对于 Alpha-Beta 剪枝的操作空间做出了一定的优化。AI 对于每一次落子后的估价函数进行模拟退火，若估价函数小于 $\frac 12$，对 $\alpha, \beta$ 带来 $\varepsilon$ 的扰动，$\varepsilon$ 随次数增多而逐渐趋于 $0$。 + 此外，笔者对于 Alpha-Beta 剪枝的操作空间做出了一定的优化。AI 对于每一次落子后的估价函数进行模拟退火，若估价函数波动较大，有 $e^{-\varepsilon/\varepsilon_0}$ 的概率对 $\alpha, \beta$ 带来 $\varepsilon$ 的扰动，$\varepsilon$ 随操作次数增多而逐渐趋于 $0$。 - 实际测试表明，对于较弱的对手，没有必要进行扰动。代码实现如下： + 代码实现如下： \begin{lstlisting} /* --- bot.h --- */ -double eps = 0.03, alpha = 0.39, beta = 0.61; -const double delta = 0.93; +double eps = 0.03, alpha = 0.31, beta = 0.61; +const double delta = 0.97; -alphaBeta(alpha, beta, 0); // 得到最终落子 (finalx, finaly) -judge->PlaceAPiece(finalx, finaly); // 更新落子 -/* 若为联机模式，更新对局 */ double curRatio = judgeBoard(); -if(curRatio < 0.5) +if(curRatio < 0.45 && (rand() % 100 + 1) * 0.01 < exp(-eps / 0.03)) { // 对面太强了，退火一下 - alpha += (0.5 - alpha) * eps; + alpha -= (0.5 - alpha) * eps; beta -= (beta - 0.5) * eps; - eps *= delta; } +if(curRatio > 0.55 && (rand() % 100 + 1) * 0.01 < exp(-eps / 0.03)) +{ + // 对面太菜了，退火一下 + alpha += (0.5 - alpha) * eps; + beta += (beta - 0.5) * eps; +} +eps *= delta; // 降温 \end{lstlisting} \subsection{AI 对战强度} @@ -533,9 +540,11 @@ \caption{测试过程} \end{figure} - 同时由于 Minimax 搜索算法本身就不够优秀，所以与隔壁组的 MCTS 对战结果是打不过，合情合理。 + 同时由于 Minimax 搜索算法本身对搜索时间的利用就不够优秀（非常浪费），所以与隔壁组的 MCTS 对战胜率仅有 $15\%$，合情合理。 对于固定策略的 AI，对战结果可能与先后手相关性较强，该测试样本量较小，所以具体情况尚不明。理论上是因为固定策略会让估价函数有较大幅度的波动，对于调参造成了一定困难。 + + 参数仅对 Minimax 和 MCTS 有较强针对性，对于更多的贪心和随机算法对战结果未知。 \section{感谢} @@ -557,4 +566,57 @@ 感谢雀魂麻将牌谱的设计参考。 + \section{附录} + + 本项目仓库：\href{https://github.com/sheriyuo/Qt-NoGo/}{https://github.com/sheriyuo/Qt-NoGo/} + + 两个 MCTS 打出来的逆天棋局： + + \begin{figure}[!htb] + + \centering + \includegraphics[width=8cm]{img/ps1.jpg} + + \counterwithin{figure}{section} + \caption{采用隔壁队伍的 MCTS 测试} + \end{figure} + + 对参数的评价： + + \begin{figure}[!htb] + + \centering + \includegraphics[width=8cm]{img/ps2.png} + + \counterwithin{figure}{section} + \caption{感谢 pusheen.com 提供的表情} + \end{figure} + + \newpage + 未尝败绩的终结： + + \begin{figure}[!htb] + + \centering + \includegraphics[width=8cm]{img/ps3.png} + + \counterwithin{figure}{section} + \caption{感谢助教提供的支持} + \end{figure} + + 某一个修了一晚上才发现的 RE bug： + + 你直接复制一个 \verb|vector>| 不爆 \verb|heap| 谁爆啊.jpg + + 但是为什么与 \verb|judge| 耦合较低的存档功能会让棋盘主程序 RE 呢？我们不得而知。 + + \begin{figure}[!htb] + + \centering + \includegraphics[width=8cm]{img/ps4.png} + + \counterwithin{figure}{section} + \caption{感谢赵培宇同学请吃的饭} + \end{figure} + \end{document} \ No newline at end of file diff --git a/report/report.toc b/report/report.toc index bee6c0b..b1f871d 100644 --- a/report/report.toc +++ b/report/report.toc @@ -11,17 +11,18 @@ \contentsline {subsection}{\numberline {2.7}信息窗口}{7}{subsection.2.7}% \contentsline {subsection}{\numberline {2.8}更多功能}{7}{subsection.2.8}% \contentsline {subsubsection}{\numberline {2.8.1}附加任务 1,2 实现}{7}{subsubsection.2.8.1}% -\contentsline {subsection}{\numberline {2.9}附加任务 5,6 实现}{9}{subsection.2.9}% -\contentsline {subsubsection}{\numberline {2.9.1}其他功能}{9}{subsubsection.2.9.1}% +\contentsline {subsubsection}{\numberline {2.8.2}附加任务 5,6 实现}{9}{subsubsection.2.8.2}% +\contentsline {subsubsection}{\numberline {2.8.3}其他功能}{9}{subsubsection.2.8.3}% \contentsline {section}{\numberline {3}联机对战设计}{9}{section.3}% \contentsline {subsection}{\numberline {3.1}通信协议}{9}{subsection.3.1}% \contentsline {subsection}{\numberline {3.2}联机对战逻辑}{10}{subsection.3.2}% \contentsline {subsubsection}{\numberline {3.2.1}双方建立连接}{10}{subsubsection.3.2.1}% \contentsline {subsubsection}{\numberline {3.2.2}一方发起对局，另一方确认对局}{10}{subsubsection.3.2.2}% \contentsline {subsubsection}{\numberline {3.2.3}完成对局并确认胜负}{10}{subsubsection.3.2.3}% -\contentsline {section}{\numberline {4}AI 算法设计}{11}{section.4}% +\contentsline {section}{\numberline {4}AI 算法设计}{12}{section.4}% \contentsline {subsection}{\numberline {4.1}Minimax 搜索和 Alpha-Beta 剪枝}{12}{subsection.4.1}% \contentsline {subsection}{\numberline {4.2}估价函数}{13}{subsection.4.2}% -\contentsline {subsection}{\numberline {4.3}参数调整}{13}{subsection.4.3}% +\contentsline {subsection}{\numberline {4.3}SA 参数调整}{14}{subsection.4.3}% \contentsline {subsection}{\numberline {4.4}AI 对战强度}{14}{subsection.4.4}% \contentsline {section}{\numberline {5}感谢}{15}{section.5}% +\contentsline {section}{\numberline {6}附录}{15}{section.6}%