AutoWalksat A SelfTuning Implementation of Walksat JIN Xiaolong

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

Background Trade-off: random decisions & heuristic decisions; Noise: 0%-100%; Optimal noise setting; 10/19/2021 2

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. 10/19/2021 3

Invariant ratio objective function value; mean objective function value (mo); standard deviation of the objective function (stdo); invariant ratio = mo / stdo ; Mc. Allester’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. 10/19/2021 4

Auto-Walksat (based on Walksat-SKC) The first step (preprocessing): Find noise level n that minimizes the invariant ratio: n n Golden Section Search; Parabolic interpolation; The second step: Adjust n and run walksat-SKC; 10/19/2021 5

Auto-Walksat (Cont. ) 10/19/2021 6

Results 10/19/2021 7

Results (Cont. ) 10/19/2021 8

Exceptions 10/19/2021 9

An example 10/19/2021 10

Thoughts Auto-Walksat: n n Noise level; Preprocessing; MASSAT: n n n Probabilities of strategies; Strategies (combinations, new strategy); Real-time tuning; 10/19/2021 11

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. 10/19/2021 12