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Heuristic Search

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					  Finish up the five “uninformed
         search” strategies
• Slides actually contained in s09
   Programming Assignment #1
• Posted online – I will reference this in class
  Programming Assignment #1
1111
1111
1111
1111

There are several “optimal” solutions
 2, 8, 9, 15 or 15, 9, 8, 2 or 2, 15, 9, 8 …
   Programming Assignment #1
• Your language must be “approved”
• Your deliverable must include a readme file
  about how to run your code in the
  WRT/ITTC labs.
• Your code must take an input String
  describing the board
  – All on would be “1111111111111111”
• Your final result should include the solution
  path, an indication of how many nodes were
  expanded (time) and how many nodes are
  still in memory (space)
  Chapter 3.5
Heuristic Search
           Learning Objectives
• Heuristic search strategies
   – Best-first search
   – A* algorithm


• Heuristic functions
           Heuristic Search
• Review: tree search
  a strategy is defined by picking the order of
  node expansion
           Heuristic Search
• Best-first search: use an evaluation function
  for each node
  – Estimate of “desirability”
  – Expand most desirable unexpanded node
  – Implementation: fringe is a queue sorted in
    decreasing order of desirability
  – Special cases:
     • Greedy search
     • A* search
          Heuristic Search
• Romania with step costs in km
           Heuristic Search
• Greedy search
  – Evaluation function h(n) (heuristic) =
       estimate of cost from n to closest goal
  – Example: hSLD(n) = straight-line distance from
    n to Bucharest
  – Greedy search expands the node that appears to
    be closest to goal
          Heuristic search
• Greedy search example
         Heuristic Search
• Greedy search example
         Heuristic Search
• Greedy search example
          Heuristic Search
• Properties of greedy search
  – Complete??
            Heuristic Search
• Complete?? No – can get stuck in loops, e.g., start
  in Iasi with Oradea as goal….




• Iasi  Neamt  Iasi  Neamt 
• Complete in finite space with repeated-state
  checking
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time??
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time?? O(bm), but a good heuristic can give
    dramatic improvement
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time?? O(bm), but a good heuristic can give
    dramatic improvement
  – Space??
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time?? O(bm), but a good heuristic can give
    dramatic improvement
  – Space?? O(bm) – keeps all nodes in memory
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time?? O(bm), but a good heuristic can give
    dramatic improvement
  – Space?? O(bm) – keeps all nodes in memory
  – Optimal??
            Heuristic Search
• Properties of greedy search
  – Complete?? No – can get stuck in loops, e.g.,
     Complete in finite space with repeated-state checking
  – Time?? O(bm), but a good heuristic can give
    dramatic improvement
  – Space?? O(bm) – keeps all nodes in memory
  – Optimal?? No

				
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