Artificial Intelligence Expert Systems Advanced Search Techniques

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Artificial Intelligence / Expert SystemsAdvanced
Search Techniques

• Justin Gaudry
• May 24, 2007

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Constraint Satisfaction

• Find the goal state that satisfies all
  constraints
• 8-queens
• Brute-force (blind search)
• Branching factor is 60 (average)
• Depth is 8
• Constrained
• Branching factor is reduced by two each move
  8,6,4,2
• Depth is 8
• Forward checking
• Most / least constrained variable
• Sudoku

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8-Queens
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Sudoku

• 9 rows and 9 columns and 9 3x3 grids
• Each row, column, and grid contains the digits
  1-9
• No row, column, or grid repeats a digit
• Use these constraints to reduce the search space

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Heuristic Search

• Heuristic
• Rule or method providing guidance in decision
  making
• Rule of Thumb or sometimes Best Guess
• Tic-tac-toe

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Best-First Search

• Each node has heuristic value of how near it is
  to a goal state
• Value generated by an evaluation function
• Start with set of initial nodes and sort by their
  value
• Choose best, generate its children, add to the
  set, sort, and repeat
• No lookahead except as children are generated

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Heuristic Repair

• Generate a solution and fix its problems
• Find a problem state and change it to where it
  has the minimum amount of conflicts
• Go to those conflicts and change them
• Repeat

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Hill-Climbing

• Keeps track only of nodes with best values
  encountered so far
• Set n to initial node
• If value of n is greater than the value of its
  children, exit and return n
• Otherwise, set n to value of greatest child and
  repeat - greedy

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Local Minima and Maxima

• Local minimum
• All neighboring states have higher value
• Local maximum
• All neighboring states have lower value
• Global maximum
• State with highest value
• Huge problem for optimization

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Gradient Search

• Hill-climbing method from calculus
• Find x in R maximizing theta(x)
• Derivative is gradient d theta(x) / dx
• Repeat x x Beta(d theta(x) / dx)
• until d theta(x) / dx lies between an acceptable
  stopping point
• Beta is very small step rate
• Local maximum not global maximum where d theta

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Simulated Annealing

• Occasionally take large steps, not small ones
  indicated by the gradient
• Uses a temperature parameter that is adjusted
  during search
• If temperature is high (far away), take large
  step (random choice)
• If temperature is low (close), take small step
• Repeat until temperature 0
• Allows more potential for getting to global
  maximum

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Simulated Annealing

• Find the minimum energy for the system
• Make small change, if energy lower, choose
• If energy higher, use Boltzmann acceptance
  criterion to determine whether to keep
• e(-dE/T)
• T is temperature, dE is change in energy after
  small change to current state
• Generate 0.0,1.0, if lower, keep new state
• Scheduling and vehicle routing

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Genetic Algorithms

• Start with random set of chromosomes
• Split and recombine and compare values to
  originals
• Keep best two
• Repeat until have acceptable value