1. Auto-Walksat: A Self-Tuning Implementation of Walksat JIN Xiaolong (Based on [1] )

2. 6/20/20152 Background Trade-off: random decisions & heuristic decisions; Noise: 0%-100%; Optimal noise setting;

3. 6/20/20153 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.

4. 6/20/20154 Invariant ratio objective function value; mean objective function value (m o ); standard deviation of the objective function (std o ); invariant ratio = m o / std o ; McAllester’s observation: the optimal performance of several stochastic algorithms occurs when the noise level is approximately ten percent above that which minimizes the invariant ratio.

5. 6/20/20155 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;

6. 6/20/20156 Auto-Walksat (Cont.)

7. 6/20/20157 Results

8. 6/20/20158 Results (Cont.)

9. 6/20/20159 Exceptions

10. 6/20/201510 An example

11. 6/20/201511 Thoughts Auto-Walksat: Noise level; Preprocessing; MASSAT: Probabilities of strategies; Strategies (combinations, new strategy); Real-time tuning;

12. 6/20/201512 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.