{"type":"ScholarlyArticle","title":"Towards Cardinality-Aware Local Search for SAT with Cardinality Constraints","authors":[{"name":"Shuli Hu","slug":"shuli-hu","given":"Shuli","family":"Hu","affiliation":""},{"name":"Dian Ling","slug":"dian-ling","given":"Dian","family":"Ling","affiliation":""},{"name":"Jiaqi Li","slug":"jiaqi-li","given":"Jiaqi","family":"Li","affiliation":""},{"name":"Minghao Yin","slug":"minghao-yin","given":"Minghao","family":"Yin","affiliation":""}],"abstract":"Satisfiability (SAT) with cardinality constraints arises naturally in many practical applications,  where high-level counting requirements coexist with standard Conjunctive Normal Form (CNF) clauses. Translating these constraints into CNF can destroy structural information, limiting the effectiveness of search-based heuristics. In this paper, we propose a cardinality-aware local search framework to solve this problem, denoted as CardSAT-LS. CardSAT-LS integrates a preprocessing phase based on the generalized unit propagation and resolution, a cardinality-sensitive scoring function combining the make-break mechanism and cardinality violation, and an initialization based on fake-backbone variables. Furthermore, CardSAT-LS employs a unified framework that adaptively alternates between flip and swap operators when the search gets trapped in local optima. Finally, we conduct experiments on five public benchmarks from real-world applications as well as the MaxSAT and SAT competitions. Compared with ten state-of-the-art competitors, including SAT, MaxSAT, and PB solvers, CardSAT-LS solves the most instances with the lowest PAR-2 score. Additionally, we integrate CardSAT-LS into exact solvers for phase selection, which leads to significant speedups.","doi":"10.24963/ijcai.2026/251","url":"https://ijcai.org/proceedings/2026/251","pdf":"https://ijcai.org/proceedings/2026/0251.pdf","markdown":"https://ijcai.org/proceedings/2026/251.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/251","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"Constraint Satisfaction and Optimization","track":"Main Track","number":251,"pages":{"first":2256,"last":2264},"keywords":["Search: Combinatorial search and optimisation","Constraint Satisfaction and Optimization: Satisfiabilty","Search: Local search"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}