Heuristics for backtracking algorithms - PowerPoint PPT Presentation

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Heuristics for backtracking algorithms

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Heuristics for backtracking algorithms. Variable ordering (important) what ... static ordering example: Suppose x1, x2, x3, x4 with domain sizes 2, 4, 8, 16. ... – PowerPoint PPT presentation

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Title: Heuristics for backtracking algorithms


1
Heuristics for backtracking algorithms
  • Variable ordering (important)
  • what variable to branch on next
  • Value ordering (not yet so important)
  • given a choice of variable, what order to try
    values
  • Constraint ordering (not so important)
  • what order to propagate constraints
  • most likely to fail or cheapest propagated first

2
Variable ordering
  • Domain dependent heuristics
  • Domain independent heuristics
  • Static variable ordering
  • fixed before search starts
  • Dynamic variable ordering
  • chosen during search

3
Variable ordering Possible goals
  • Minimize the underlying search space
  • static ordering example Suppose x1, x2, x3, x4
    with domain sizes 2, 4, 8, 16. Compare static
    ordering x1, x2, x3, x4 vs x4, x3, x2, x1
  • Minimize expected depth of any branch
  • Minimize expected number of branches
  • Minimize size of search space explored by
    backtracking algorithm
  • intractable to find best variable

4
Basic idea
  • Assign a heuristic value to a variable that
    estimates how difficult it is to find a
    satisfying value for that variable
  • Principle most likely to fail first
  • or dont postpone the hard part

5
Some variable ordering heuristics
  • minimum domain size (dom)
  • maximum degree (deg)
  • most constraining
  • plus combining tie break strategies
  • e.g., dom deg, dom / deg

6
Open questions
  • Dynamic variable ordering heuristics for
    non-binary CSPs

7
Value ordering
  • All solutions
  • value ordering not so important
  • One solution
  • if a solution exists, there exists a perfect
    value ordering

8
Value ordering Intuition
  • Goal minimize size of search space explored
  • Principle
  • given that we have already chosen the next
    variable to instantiate, choose first the values
    that are most likely to succeed
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