A Study of Parallel Continuous Local Search

• URL: http://arxiv.org/abs/2606.06656v2
• Date: Mon, 08 Jun 2026 15:19:28 GMT
• Title: A Study of Parallel Continuous Local Search
• Abstract summary: Continuous Local Search is a solution approach for satisfiability problems with symmetric pseudo-Boolean constraints.<n>We show that CLS shows promise as a sub-solver in hybridised settings, quickly completing partial assignments.<n>Our findings inform practical uses of CLS for SAT on modern accelerator hardware.
• Score: 0.6353525052246608
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints. Here, the $n$-variable PB-satisfiability problem is relaxed to a continuous optimisation problem with a differentiable objective function on an $n$-dimensional hypercube. For satisfiable instances, the global minimisers of this optimisation problem correspond to satisfying assignments of the SAT problem at hand. We present several novel findings via empirical experiments: (i) redundant constraints can inhibit rather than accelerate convergence; (ii) CLS shows promise as a sub-solver in hybridised settings, quickly completing partial assignments; and (iii) local search rapidly converges to a stable distribution of solution quality (i.e., degree of satisfaction), due to saddle-dense objectives where additional solver steps yield diminishing returns. Our findings inform practical uses of CLS for SAT on modern accelerator hardware.

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