1. Local search characteristics of incomplete SAT procedures
Tang Yi
Based on [1]

2. Local search methods
Effective engineering methods for finding satisfying assignments
Incomplete and cannot prove if the solution exists
Systematic understanding remains elusive
Analysis largely empirical and hard to predict the effects of a minor change

3. Measuring local search performance (1)
Depth
how many clauses remain unsatisfied as search proceeds
by averaging depth over all search steps as an overall summary

4. Measuring local search performance(2)
Mobility
how rapidly a local search moves in search space (while it tries to simultaneously stay deep in the object)
by calculating the Hamming distance between variable assignments that are k steps apart and average this quantity over the entire sequence

5. Measuring local search performance(3)
Coverage
how many systematically the search explores the entire space
by computing the coverage rate to be (n – max gap) / search steps where max gap is the maximum Hamming distance between unexplored assignment and the nearest evaluated assignment

6. SDF: a new local search strategy
Two main different components
(1) steepest descent in more informative objective function
(2) multiplicative clauses re-weighting to move out of local minima and travel to promising new regions
Weighted-score function
h(x, w) =

7. SDF procedure
SDF
Flip the variable that leads to the greatest increase in weighted-score function
Re-weight
re-weight the unsatisfied clauses and re-normalize the clause weights so that the resulting largest difference is
flatten the weight profile of the satisfied clauses by shrinking of the distance towards their common mean

8. Discussion Systematically reduce the number of flips
Greater computational overhead per flip

9. Reference
[1]Schuurmans,D. and Southey,F.,Local search characteristics of incomplete SAT procedures, Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-2000),Austin,TX,July 2000.