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Expand Up @@ -314,7 +314,7 @@
\caption{对局重现}
\end{figure}

\subsection{附加任务 5,6 实现}
\subsubsection{附加任务 5,6 实现}

\textbf{AI 独立线程}

Expand Down Expand Up @@ -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。
Expand All @@ -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。
Expand All @@ -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
Expand Down Expand Up @@ -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}
Expand All @@ -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}

Expand All @@ -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<pair<int,int>>| 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}
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\contentsline {section}{\numberline {3}联机对战设计}{9}{section.3}%
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\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}%

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