CS 170 Artificial Intelligence

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CS 170 Artificial Intelligence

• Prof. Rao Vemuri
• Search 1
• Problem Solving by Searching

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Searching

• Search is needed when a solution requires a
  sequence of choices
• The history of the choices considered forms a
  tree.
• Each node represents a choice.
• Each path represents a set of choices that build
  on each other.
• Note Search tree nodes may be different from
  problem nodes.

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Example Problems

• The Monkeys Bananas
• The Missionaries Cannibals
• Wolf, Goat and Cabbage
• The Towers of Hanoi
• Route Finding
• Water Jugs Problem
• Time Table Problem

• The 8-Puzzle
• The 8 Queens Problem
• Tic-Tac-Toe Game
• Checkers
• Chess
• Bridge

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Canonical Problem Formulation

• State What the world is doing at this time?
• State Space A collection of possible states
• Initial State Where the search starts
• Goal State Where the search ends
• Path A sequence of operators leading from one
  state to another
• Path Cost Sum of the costs of operators along
  the path

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Example1 Route Finding

• Find Route From Here to There
• State Current location on a map
• Initial State Starting City, say City A
• Goal State Destination City, say City Z
• Operators Move along a road to another city
• Path Costs Sum of lengths from here to there
• Solution Path from here to there
• Issues
• What is the Cost of Finding the Route?
• What is the Cost of Traversing the Route?

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Example2 Timetable

• Find Lecture Timetable by Incrementally Modifying
  a Draft to Eliminate Conflicts
• State A version of a time table
• Initial state A draft version of a timetable
• Goal State A timetable with no conflicts
• Operators exchange a pair of assigned time slots
  
• Costs Time taken to make the exchange and verify
  conflicts
• Solution A timetable with no time conflicts
  (Here the path is irrelevant)

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Search Trees Terminology

• Search is equivalent to building a search tree
• Node, Branch, Path, Root node, Leaf node
• Parent, Ancestor Child, Descendent
• Expanding Determining the children
• Open Node is open until expanded, then it
  becomes closed
• Nodes are data structures Nodes have parents,
  children, depth (d), etc.
• Fringe is a collection of nodes waiting to be
  expanded
• A Queue is one way to organize the fringe.

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Search Trees Terminology

• Branching Factor b of a Node The number of
  children of a node.
• Branching Factor of a Tree If every node has the
  same branching factor, then it has a branching
  factor b.
• The total number of paths in a tree of depth d
  with a branching factor b is bd.
• Number of paths explode exponentially with d.
• State Where am I now? What choices do I have?
• Strategy The choice of which state to expand
  next.

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Search Space

• Three kinds of nodes in search space
• Visited nodes seen, processed, and expanded
• May be remembered
• Fringe nodes seen but not processed or expanded.
  Waiting to be expanded
• Must be remembered
• Unvisited nodes not seen yet (implicit)

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Basic Search Algorithm

• Repeat
• Take some nodes off the fringe
• Expand them (find their neighbors)
• Add neighbors to the fringe
• Until solution is found

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General Search Algorithm

• Repeat
• Initialize parameters of search.
• Repeat
• Take some nodes off the fringe
• Decide whether to stop (1)
• Expand them (find their neighbors)
• Add neighbors to the fringe
• Evaluate neighbors
• Add to fringe and reorder fringe
• Prune fringe
• Decide whether to stop (2)
• Until done
• Until done

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Expanding Nodes

• (constructing neighbors)
• Lots of flexibility
• add step onto end of plan.
• add step onto beginning of plan
• add step into middle of plan
• Even more flexibility
• combine parts of two poor solutions to make a new
  candidate
• e. g. timetables.
• (Genetic Algorithms)

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Adding to the Fringe

• (Queue discipline of Fringe)
• LIFO Depth First''
• FIFO Breadth first''
• BIFO Best/priority First''
• What counts as best?
• Heuristics to guide the search
• Constructing good heuristics are an important
  part of many AI systems.

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Managing the Fringe

• Queue Discipline of fringe
• LIFO, Depth First
• FIFO, Breadth First
• BIFO, Best/Priority First
• Keeping the entire fringe is too expensive
• Keep just the best node (Hill Climbing'')
• Keep just the best nodes (Beam Search'')
• Keep a random subset of the fringe
• Prune all but first duplicate
• Prune all but best duplicate (Dynamic
  Programming'')
• Prune whenever partial solution is already worse
  than the best solution found so far. (Branch
  and Bound'')
• What is best?
• Heuristics (The heart of AI)

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Radical Pruning

• Keeping the entire fringe is too expensive
• Keep just the best node (Hill Climbing'')
• Keep just the best nodes (Beam Search'')
• Keep a random subset of the fringe.

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Three Varieties of Search

• Blind Search
• Depth-first search
• Breadth first search
• Random search
• Heuristic Search
• Hill climbing DFS Quality measurements
• Beam search, expands severalpartial paths and
  purges the rest
• Best-first search, Expands the best partial path
• Optimal Search
• Branch and Bound, Expands least cost partial path
  
• Branch and Bound augmented by under-estimates
• A - BB plus under estimates plus dynamic
  programming