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A Machine Learning Based Splitting Heuristic for Divide-and-Conquer Solvers

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Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

In this paper, we present a machine learning based splitting heuristic for divide-and-conquer parallel Boolean SAT solvers. Splitting heuristics, whether they are look-ahead or look-back, are designed using proxy metrics, which when optimized, approximate the true metric of minimizing solver runtime on sub-formulas resulting from a split. The rationale for such metrics is that they have been empirically shown to be excellent proxies for runtime of solvers, in addition to being cheap to compute in an online fashion. However, the design of traditional splitting methods are often ad-hoc and do not leverage the copious amounts of data that solvers generate.

To address the above-mentioned issues, we propose a machine learning based splitting heuristic that leverages the features of input formulas and data generated during the run of a divide-and-conquer (DC) parallel solver. More precisely, we reformulate the splitting problem as a ranking problem and develop two machine learning models for pairwise ranking and computing the minimum ranked variable. Our model can compare variables according to their splitting quality, which is based on a set of features extracted from structural properties of the input formula, as well as dynamic probing statistics, collected during the solver’s run. We derive the true labels through offline collection of runtimes of a parallel DC solver on sample formulas and variables within them. At each splitting point, we generate a predicted ranking (pairwise or minimum rank) of candidate variables and split the formula on the top variable. We implemented our heuristic in the Painless parallel SAT framework and evaluated our solver on a set of cryptographic instances encoding the SHA-1 preimage as well as SAT competition 2018 and 2019 benchmarks. We solve significantly more instances compared to the baseline Painless solver and outperform top divide-and-conquer solvers from recent SAT competitions, such as Treengeling. Furthermore, we are much faster than these top solvers on cryptographic benchmarks.

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Notes

  1. 1.

    Runtime of a solver here refers to the wallclock time of solving a formula.

  2. 2.

    We only compare our MaplePainless-DC solver against the state-of-the-art DC solvers because it is well-known that the most notable portfolio solvers often outperform the DC solvers on application benchmarks.

  3. 3.

    PAR-k is the Penalized Average Runtime, counting each timeout as k times the wallclock timeout.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    Saeed Nejati & Vijay Ganesh

  2. LRDE, EPITA, Le Kremlin-Bicêtre, France

    Ludovic Le Frioux

Authors
  1. Saeed Nejati
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  2. Ludovic Le Frioux
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  3. Vijay Ganesh
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Correspondence to Saeed Nejati .

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  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Nejati, S., Le Frioux, L., Ganesh, V. (2020). A Machine Learning Based Splitting Heuristic for Divide-and-Conquer Solvers. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_52

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_52

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