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Add FAIKR non-informed search
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src/fundamentals-of-ai-and-kr/img/_search_tree.pdf
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||||
\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
|
||||
\lstdefinestyle{mystyle}{
|
||||
commentstyle = \color{codegreen},
|
||||
keywordstyle = \color{magenta},
|
||||
numberstyle = \tiny\color{codegray},
|
||||
stringstyle = \color{codepurple},
|
||||
basicstyle = \footnotesize\ttfamily,
|
||||
breakatwhitespace = false,
|
||||
breaklines = true,
|
||||
captionpos = b,
|
||||
keepspaces = true,
|
||||
numbers = none,
|
||||
showspaces = false,
|
||||
showstringspaces = true,
|
||||
showtabs = false,
|
||||
tabsize = 3
|
||||
}
|
||||
\lstset{style=mystyle}
|
||||
\lstset{language=Python}
|
||||
|
||||
\NewDocumentEnvironment{descriptionlist}{}{%
|
||||
\begin{description}[labelindent=1em]
|
||||
}{
|
||||
@ -60,6 +85,7 @@
|
||||
\pagenumbering{arabic}
|
||||
|
||||
\input{sections/_intro.tex}
|
||||
\input{sections/_search.tex}
|
||||
|
||||
|
||||
\end{document}
|
||||
182
src/fundamentals-of-ai-and-kr/sections/_search.tex
Normal file
182
src/fundamentals-of-ai-and-kr/sections/_search.tex
Normal file
@ -0,0 +1,182 @@
|
||||
\chapter{Search problems}
|
||||
|
||||
|
||||
|
||||
\section{Search strategies}
|
||||
\begin{description}
|
||||
\item[Solution space] \marginnote{Solution space}
|
||||
Set of all the possible sequences of actions an agent may apply.
|
||||
Some of these lead to a solution.
|
||||
|
||||
\item[Search algorithm] \marginnote{Search algorithm}
|
||||
Takes a problem as input and returns a sequence of actions that solves the problem (if exists).
|
||||
\end{description}
|
||||
|
||||
|
||||
\subsection{Search tree}
|
||||
\begin{description}
|
||||
\item[Expansion] \marginnote{Expansion}
|
||||
Starting from a state, apply a successor function and generate a new state.
|
||||
|
||||
\item[Search strategy] \marginnote{Search strategy}
|
||||
Choose which state to expand.
|
||||
Usually is implemented using a fringe that decides which is the next node to expand.
|
||||
|
||||
\item[Search tree] \marginnote{Search tree}
|
||||
Tree structure to represent the expansion of all states starting from a root
|
||||
(i.e. the representation of the solution space).
|
||||
|
||||
Nodes are states and branches are actions.
|
||||
A leaf can be a state to expand, a solution or a dead-end.
|
||||
\Cref{alg:search_tree_search} describes a generic tree search algorithm.
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.25\textwidth]{img/_search_tree.pdf}
|
||||
\caption{Search tree}
|
||||
\end{figure}
|
||||
|
||||
Each node contains:
|
||||
\begin{itemize}
|
||||
\item The state
|
||||
\item The parent node
|
||||
\item The action that led to this node
|
||||
\item The depth of the node
|
||||
\item The cost of the path from the root to this node
|
||||
\end{itemize}
|
||||
\end{description}
|
||||
|
||||
\begin{algorithm}
|
||||
\caption{Tree search algorithm} \label{alg:search_tree_search}
|
||||
\begin{lstlisting}
|
||||
def treeSearch(problem, fringe):
|
||||
fringe.push(problem.initial_state)
|
||||
# Get a node in the fringe and expand it if it is not a solution
|
||||
while fringe.notEmpty():
|
||||
node = fringe.pop()
|
||||
if problem.isGoal(node.state):
|
||||
return node.solution
|
||||
fringe.pushAll(expand(node, problem))
|
||||
return FAILURE
|
||||
|
||||
def expand(node, problem):
|
||||
successors = set()
|
||||
# List all neighboring nodes
|
||||
for action, result in problem.successor(node.state):
|
||||
s = new Node(
|
||||
parent=node, action=action, state=result, depth=node.dept+1,
|
||||
cost=node.cost + problem.pathCost(node, s, action)
|
||||
)
|
||||
successors.add(s)
|
||||
return successors
|
||||
\end{lstlisting}
|
||||
\end{algorithm}
|
||||
|
||||
|
||||
\subsection{Strategies}
|
||||
\begin{description}
|
||||
\item[Non-informed strategy] \marginnote{Non-informed strategy}
|
||||
Domain knowledge not available. Usually does an exhaustive search.
|
||||
|
||||
\item[Informed strategy] \marginnote{Informed strategy}
|
||||
Use domain knowledge by using heuristics.
|
||||
\end{description}
|
||||
|
||||
|
||||
\subsection{Evaluation}
|
||||
\begin{description}
|
||||
\item[Completeness] \marginnote{Completeness}
|
||||
if the strategy is guaranteed to find a solution (when exists).
|
||||
|
||||
\item[Time complexity] \marginnote{Time complexity}
|
||||
time needed to complete the search.
|
||||
|
||||
\item[Space complexity] \marginnote{Space complexity}
|
||||
memory needed to complete the search.
|
||||
|
||||
\item[Optimality] \marginnote{Optimality}
|
||||
if the strategy finds the best solution (when more solutions are possible).
|
||||
\end{description}
|
||||
|
||||
|
||||
|
||||
\section{Non-informed search}
|
||||
|
||||
\subsection{Breadth-first search (BFS)}
|
||||
\marginnote{Breadth-first search}
|
||||
Always expands the less deep node. The fringe is implemented as a queue (FIFO).
|
||||
|
||||
\begin{center}
|
||||
\def\arraystretch{1.2}
|
||||
\begin{tabular}{c | m{10cm}}
|
||||
\hline
|
||||
\textbf{Completeness} & Yes \\
|
||||
\hline
|
||||
\textbf{Optimality} & Only if cost is uniform (i.e. all edges have same cost) \\
|
||||
\hline
|
||||
\textbf{\makecell{Time and space\\complexity}}
|
||||
& $O(b^d)$, where the depth is $d$ and the branching factor is $b$ (i.e. each non-leaf node has $b$ children) \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
The exponential space complexity makes BFS impractical for large problems.
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.40\textwidth]{img/_bfs.pdf}
|
||||
\caption{BFS visit order}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Uniform-cost search}
|
||||
\marginnote{Uniform-cost search}
|
||||
Same as BFS, but always expands the node with the lowest cumulative cost.
|
||||
|
||||
\begin{center}
|
||||
\def\arraystretch{1.2}
|
||||
\begin{tabular}{c | m{10cm}}
|
||||
\hline
|
||||
\textbf{Completeness} & Yes \\
|
||||
\hline
|
||||
\textbf{Optimality} & Yes \\
|
||||
\hline
|
||||
\textbf{\makecell{Time and space\\complexity}}
|
||||
& $O(b^d)$, with depth $d$ and branching factor $b$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.60\textwidth]{img/_ucs.pdf}
|
||||
\caption{Uniform-cost search visit order. $(n)$ is the cumulative cost}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\subsection{Depth-first search}
|
||||
\marginnote{Depth-first search}
|
||||
Always expands the deepest node. The fringe is implemented as a stack (LIFO).
|
||||
|
||||
\begin{center}
|
||||
\def\arraystretch{1.2}
|
||||
\begin{tabular}{c | m{10cm}}
|
||||
\hline
|
||||
\textbf{Completeness} & No \\
|
||||
\hline
|
||||
\textbf{Optimality} & No \\
|
||||
\hline
|
||||
\textbf{Time complexity}
|
||||
& $O(b^d)$, with depth $d$ and branching factor $b$ \\
|
||||
\hline
|
||||
\textbf{Space complexity}
|
||||
& $O(b \cdot d)$, with depth $d$ and branching factor $b$ \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\end{center}
|
||||
|
||||
\begin{figure}[h]
|
||||
\centering
|
||||
\includegraphics[width=0.40\textwidth]{img/_dfs.pdf}
|
||||
\caption{DFS visit order}
|
||||
\end{figure}
|
||||
Reference in New Issue
Block a user