# A Study of Parallel Continuous Local Search

arXiv: https://arxiv.org/abs/2606.06656 · HTML: https://mlsanity.com/paper/2606.06656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [The SCIP Optimization Suite 9.0](https://mlsanity.com/paper/2402.17702/) (2024)
- [Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs](https://mlsanity.com/paper/2308.15020/) (2023)

## Abstract (arXiv)

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.