Search Techniques

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Search Techniques

• MSc AI module

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Search

• In order to build a system to solve a problem we
  need to
• Define and analyse the problem
• Acquire the knowledge
• Represent the knowledge
• Choose the best problem solving technique
• This where SEARCH TECHNIQUES are important

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SEARCH

• Searches are used to search a problem space - not
  for a particular piece of data, but for a PATH
  that joins the initial problem description to the
  desired (or GOAL) state.
• The path represents the solution steps.
• Searching for a solution develops a SOLUTION
  SPACE.
• A problem space is procedurally developed as the
  search progresses (not pre-defined like a data
  structure)
• We are defining a problem as a STATE SPACE SEARCH
  this forms the basis of many AI problem-solving
  techniques.

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SEARCH

• For some problems were only interested in the
  solution. E.g. crosswords
• For others, were interested in the PATH i.e. how
  we arrived at the solution.
• e.g. finding the shortest distance between two
  places, or the Towers of Hanoi puzzle.
• Also interested in the optimal solution, i.e.
  final state and the cost

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Generate Test

• This is the simplest form of Search.
• List each possible candidate solution in turn and
  check to see if it satisfies constraints.
• Either stop at 1st solution or keep going for
  next.
• e.g. 3x3 magic square
• Want to make every row, column, diagonal add up
  to 15
• There are (9!) 362880 candidate solutions to this
  combinatorial explosion if we generate check
  them all.

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Generate Test (fig3.4 finlay dix)

• The idea of representing the approach to solving
  this as a tree, enables the elimination of
  branches beyond certain levels

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Generate Test - fig 3.5 finlay Dix

• Another useful representation technique is a
  graph. We can represent states and move between
  them on graphs. These can be translated into a
  tree notation to represent the search space.

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Towers of Hanoi Search Tree
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SEARCH

• Methods for pruning search trees are integral to
  many search algorithms.
• This enables unfruitful branches not to be
  expanded.
• More sophisticated methods include the idea of
  heuristics to select best branches.
• Often use a heuristic evaluation function a
  number calculated for each node/path that says
  how good/bad its likely to be.
• N.B. entire trees arent necessarily constructed
  in the computers memory.
• They represent the solution space i.e. the
  possible solutions.

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Depth First Search and Breadth First Search

• Simplest type
• Depth first
• 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
• Breadth first
• 1 2 8 11 3 5 9 12 14 4 6 7 10 13 15 16
• Depending on where the goal state is, one may
  reach a solution more quickly than the other.
• These are known as Blind Searches.

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Depth First Search and Breadth First Search

• Advantages of Depth First Search
• Requires less memory, only nodes on current path
  are stored (breadth first stores everything)
• May find a solution very quickly (e.g. if
  solution is at end of first branch).
• Advantages of Breadth First Search
• Will not get trapped exploring a blind alley
  (i.e. if first branch goes on forever)
• Guaranteed to find a solution, and if there are a
  few solutions, the minimal one will be found
  first.

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Branch Bound

• If searching for a solution want to find the
  best one based on cost (cost can be anything
  distance, time, etc.)
• some branches can be ignored below a certain
  level if the cost of expanding it beyond that
  level is greater than the cost of the already
  found solution.
• There are variants of this based on depth first
  breadth first.

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Branch Bound

• e.g. Looking for the shortest path between
  Gainesville Key West.

1
Jacksonville
Gainesville
2
5
4
3
Orlando
2
3
Ft. Pierce
Tampa
4
5
3
Miami
3
Key west
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Branch and Bound step by step development of a
search tree
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Branch and Bound Cont.
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Branch and Bound cont
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Heuristic Search

• Consider wanting to find the best route to
  Glasgow from Leicester.
• Search space too big to consider every
  possibility
• Construct a scoring function that provides
  estimates re which paths/nodes are most
  promising.
• Promising ones explored first i.e. try paths
  that seem to be getting nearer the goal state.
• Uses an evaluation function, such as as the crow
  flies distance between start town and target
  town.

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Hill Climbing

• Imagine were at the hospital, heading for the
  church

There is no through road from the park
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Hill Climbing

• Using as crow flies evaluation function as
  heuristic would opt for route to the shop rather
  than route to the park.
• The Hill Climbing algorithm is as follows
• Start with current-state initial-state
• Until current-state goal- state OR there is no
  change in current-state DO
• 1. get successors of current-state and use
  evaluation function to assign score to each
  successor
• 2. if one of successors has a better score than
  current-state then set the new curren- state to
  be the successor with the best score.

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Hill Climbing

• This terminates when there are no successor
  states that are better than the current state.
• Problem can reach a dead end (local maxima)
• If we were trying to get from the library to the
  university,

• using hill-climbing would take us from the
  library, to the hospital, to the park which
  is a dead end, no new state would bring us
  nearer, so it stops.

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Hill Climbing

• Also, see example below. If were aiming for the
  park from the library. We would go to the school,
  and then no new nodes improve it so the algorithm
  stops.

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Best First Search

• This is like Hill Climbing but is exhaustive and
  will eventually search all possible paths. This
  therefore avoids local maxima problem of hill
  climbing.
• To do this it keeps a list of all the nodes that
  are still to be explored.
• Start with agenda (i.e. list of nodes) initial
  state
• While agenda is not empty do
• Remove best node from agenda
• If it is a goal then return with success
  otherwise find successors
• Assign successor nodes a score using evaluation
  function and add the scored nodes to the agenda

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Best First Search

• Consider the above tree. The number at each node
  indicates the cost to solution estimates, (so
  lowest is best).
• Breadth first A B C D E F G
• Depth First - A B D E G
• Hill Climbing A C then gets stuck at local
  maxima
• Best First A C B E G (this needs a good
  evaluation function to get the best results from
  using it.)

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A Algorithm

• Best first uses estimated cost to goal, but
  doesnt use the cost so far when choosing the
  node to search next.
• A attempts to minimise the total cost of the
  solution path
• Evaluation function Cost (est to goal) Cost
  (from start)

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Comparison of A and Best First

• A guarantees to find the shortest path if the
  evaluation function is suitable
• It is important not to overestimate the
  cost-to-goal function.

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A

• Looking for the shortest path between Gainesville
  Key West.

Jacksonville
1
Gainesville
2
5
4
3
Underestimates Gainsevill 8 Jacksonville
9 Orlando 6 Tampa 4 Ft. Pierce 5 Miami
2 Key West - 0
Orlando
2
3
Tampa
Ft. Pierce
4
5
3
Miami
Key west
3
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A - Solution
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A - solution