Informed Search Strategies

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Informed Search Strategies
Modified 07/08/02
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Outline

• Best-First
• A
• Heuristics
• Hill-climbing
• Simulated Annealing

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Best-First

• Evaluation function
• estimate of desirability
• Expand most desirable unexpanded node
• QUEUINGFN inserts successors in decreasing order
  of desirability

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Example Tourist
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Heuristic

• Heuristic evaluation function h(n)
• e.g. hSLD (n) straight line distance from n to
  Bucharest

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Example
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Properties of Best-first

• Complete ?
• Can get stuck in loops
• Complete in finite space with repeat checking
• Time ?
• O(bm), but good heuristic improves performance
• Space ?
• O(bm), keeps all nodes in memory
• Optimal ? - No

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A

• Evaluation function
• f(n) g(n) h(n)
• g(n)- cost so far to reach n
• h(n)- estimated cost to goal from n
• f(n)- estimated cost of path through n to goal

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A cont.

• admissible heuristic
• h(n) lt h(n), where h(n) is true cost from n
• hSLD (n) never over estimates the actual road
  distance

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Example
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Optimality of A

• Assuming we have a suboptimal goal state G2
• a node n on the path of optimal goal G1
• f(G2 ) g( G2 ), since h( G2 ) 0
• gt g ( G1 ) since G2 is suboptimal
• gt f(n) since h is admissible
• Since f(G2 ) gt f(n) n will be selected before G2

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Properties of A

• Complete ?
• Yes unless infinite nodes with f lt f(G)
• Time ?
• Exponential in relative error in h length of
  solution
• Space ?
• Keeps all nodes in memory
• Optimal ?
• Yes

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Admissible Heuristics

• exact solution costs of relaxed problems
• e.g. 8s puzzle
• number of tiles out of place
• manhattan distance

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Dominance

• If h2(n) gt h1(n) for all n
• then h2 dominates h1 and is better for search

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Memory Bounded Search

• Iterative deepening A
• extension of IDS
• uses an f-cost limit not a depth limit
• Expands nodes of cost less than current f-cost

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Properties of IDA

• Complete ?
• Yes
• Time ?
• Depends on number of f-cost values
• Space ?
• Depth first, so store longest path, bm
• Optimal ?
• Yes

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Simplified Memory bound A

• SMA
• uses available memory
• avoids repeated expansions
• drops node with high f-cost
• remembers f-cost values of dropped subtrees

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Properties of SMA

• Complete ?
• Yes, if enough memory
• Time ?
• Depends on problem space
• Space ?
• Up to size of memory
• Optimal ?
• Yes, if enough memory

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Iterative improvement

• Optimisation problems
• path is a solution, improve the cost
• e.g
• Travelling salesman, find shortest path
• n-queens, find configuration satisfying
  constraints
• iterative improvement
• single state, constant space requirements

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Hill-climbing
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Simulated Annealing

• The probability of changing to a lower state
  depends on a temperature value
• p(x) alpha exp( deltaE(x) / kT)
• As T decreases, the probability of changing to a
  lower energy state goes to zero
• Can escape from local minima and find optimal
  state