CS621 : Artificial Intelligence

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CS621 Artificial Intelligence

• Pushpak BhattacharyyaCSE Dept., IIT Bombay
• Lecture 3 - Search

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Common Dimensions in Search Methods

• How does a solution correspond to a search tree?
• Solutions can be any nodes
• Solutions must be terminal nodes
• Solutions are paths through the tree
• When does a search method stop?
• Satisficing when its finds one solution
• Exhaustive when it has considered all possible
  solutions
• Optimizing when it has found the best solution
• Resource limited when it has exhausted its
  computational resources
• Due process when it has searched with a method
  that has proven adequate for most cases

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Common Dimensions in Search Methods (contd.)

• How is the search directed?
• Blind systematic search through possibilities
• Directed heuristics used to guide the search
• Hierarchical abstract solutions used to organize
  the search
• How thorough is the search
• Complete If there is a solution in the search
  space, the system will find it
• Incomplete the system may miss some solutions

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AI search is always backed up by knowledge

• Ontological knowledge a hierarchy of concepts

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The Hierarchical Assembly in an automobile system
Motor System
Breaking System
Transmission System
Engine System
Electrical System
Cooling System
Cooling hose
Radiator
Charging System
Starter System
Voltage Regulator
Battery
Solenoid
Starter Motor
Ignition System
Generator
Spark Plugs
Coil
Motor System
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Informed Search

• Avoid useless subtrees
• Important for Web

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Intelligent Search on Web

• Give Shakespeare's Hamlet.
• No point going to Economics subtree.
• Document clustering and classification needed.

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Two Cardinal Theorems for A

• Admissibility
• A always terminates finding the optimal path.
• Informedness
• More informed heuristic is better, i.e., a less
  informed heuristic will expand at least as many
  times as a more informed one.

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Proof of Admissibility
Start Node
S
N1
N2
N is the node on optimal path on open list, All
its ancestors are in closed list
Ni N
G
Goal Node
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Proof of Admissibility (contd.)

• If A does not terminate f values of nodes on
  open list become unbounded.
• f(N) g(N) h(N)
• and g(N)gt e .Sarcs
• eleast cost on the arcs (ve).

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Proof of Admissibility (cont.)

• N is on optimal path.
• Ns ancestors are all in CL
• g(N) g(N) optimal path to N found
• h(N) lt h(N), by defn of A
• Hence,
• f(N) lt f(N) f(S)
• Since for each N on optimal path f values are
  equal and equal to the cost of the optimal path
  from S to G.

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Proof of Admissibility (cont.)

• Fact 1 If A does not terminate f values of
  nodes on OL become unbounded.
• Fact 2 Any time before A terminates there
  exists on OL a node N with f(N) lt f(S)
• These two can be reconciled iff A terminates

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Intuition of Termination

• A keeps wavering and straying. But is brought
  back to the correct path.