A Linear Weight Transfer Rule for Local Search
This work addresses the challenge of enhancing local search SAT-solving algorithms for combinatorial problems, representing an incremental improvement over the existing ddfw method.
The authors tackled the problem of improving the Divide and Distribute Fixed Weights (ddfw) algorithm for SAT-solving by proposing three modifications, including a linear weight transfer method, which resulted in boosted performance on benchmarks and solved hard combinatorial instances, such as refuting a conjecture on Van der Waerden numbers and addressing a decades-old graph-coloring instance.
The Divide and Distribute Fixed Weights algorithm (ddfw) is a dynamic local search SAT-solving algorithm that transfers weight from satisfied to falsified clauses in local minima. ddfw is remarkably effective on several hard combinatorial instances. Yet, despite its success, it has received little study since its debut in 2005. In this paper, we propose three modifications to the base algorithm: a linear weight transfer method that moves a dynamic amount of weight between clauses in local minima, an adjustment to how satisfied clauses are chosen in local minima to give weight, and a weighted-random method of selecting variables to flip. We implemented our modifications to ddfw on top of the solver yalsat. Our experiments show that our modifications boost the performance compared to the original ddfw algorithm on multiple benchmarks, including those from the past three years of SAT competitions. Moreover, our improved solver exclusively solves hard combinatorial instances that refute a conjecture on the lower bound of two Van der Waerden numbers set forth by Ahmed et al. (2014), and it performs well on a hard graph-coloring instance that has been open for over three decades.