Auto-Walksat: A Self-Tuning Implementation of Walksat

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Auto-Walksat A Self-Tuning Implementation of
Walksat

• JIN Xiaolong

(Based on 1 )
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Background

• Trade-off random decisions heuristic
  decisions
• Noise 0-100
• Optimal noise setting

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Walksat-SKC

• Randomly choose an unsatisfied clause c
• If there is a literal in c whose value can be
  changed without causing any new clauses to become
  unsatisfied, let v be this literal. Otherwise,
• With probability N choose v in c randomly
• With probability 1-N choose v such that when its
  value is changed, the smallest number of
  satisfied clauses become unsatisfied
• Change the truth assignment of v.

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Invariant ratio

• objective function value
• mean objective function value (mo)
• standard deviation of the objective function
  (stdo)
• invariant ratio mo / stdo
• McAllesters observation
• the optimal performance of several stochastic
  algorithms occurs when the noise level is
  approximately ten percent above that which
  minimizes the invariant ratio.

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Auto-Walksat (based on Walksat-SKC)

• The first step (preprocessing)
• Find noise level n that minimizes the invariant
  ratio
• Golden Section Search
• Parabolic interpolation
• The second step
• Adjust n and run walksat-SKC

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Auto-Walksat (Cont.)
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Results
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Results (Cont.)
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Exceptions
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An example
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Thoughts

• Auto-Walksat
• Noise level
• Preprocessing
• MASSAT
• Probabilities of strategies
• Strategies (combinations, new strategy)
• Real-time tuning

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Reference

• 1. Donald J. Patterson and Henry Kautz,
  Auto-Walksat a Self-Tuning Implementation of
  Walksat, Electronic Notes in Discrete Mathematics
  (ENDM), 9, 2001, Elsevier. Presented at the LICS
  2001 Workshop on Theory and Applications of
  Satisfiability Testing, June 14-15, 2001, Boston
  University, MA.