Portfolio Selection for SAT Instances

SAT problems are fundamental in representing and solving combinatorial applications. Over the past years, many sophisticated SAT solvers have been proposed. Due to the topic’s relevance, a SAT competition is scheduled yearly to promote solving hard SAT instances. There is no unique solver to tackle all SAT problems efficiently. Indeed, some solvers work best for some SAT instances but perform poorly for others. This limitation has been addressed, in the literature, by identifying a pool of solvers that complement each other for efficiently tackling a given set of SAT instances. This pool of solvers is called a portfolio. Several studies have been conducted to find the optimal portfolio maximizing the number of solved SAT instances, minimizing the overall running time, or a trade-off between both. In this context, we present a new approach that first finds the suitable portfolio meeting each of these objectives. Then, the approach predicts the best solver for any new SAT instance. Our approach is based on Greedy search techniques, clustering, and deep learning. More precisely, we investigate two different scenarios. In the first one, our goal is to find the best portfolio capable of solving the largest number of instances within a given time limit. Both the Greedy-based method and clustering are used in this case. The second scenario aims to find the optimal portfolio to minimize the penalized average running time. The latter objective captures a good trade-off between the objective in the first scenario and the overall average running time. In addition to Greedy search and clustering, we consider a variant of the Beam-search technique to address this scenario. To assess the performance of our approach regarding the two scenarios, we conduct multiple experiments on the SAT2021 competition datasets that include SAT instances together with participants’ solvers’ results for each instance. The outcomes from the conducted experiments are encouraging and promising.