Exact Approaches for the Diverse Satisfiability Problem
Résumé
Given a Conjunctive Normal Form (CNF) formula ϕ and a positive integer k, the problem of Diversity Satisfiability (Diverse SAT) consists in finding k assignments satisfying ϕ while maximizing the sum of pairwise distances among them. Previous related works mainly focus on the design of heuristic algorithms, while this paper focuses on introducing exact methods. A quadratic integer programming (QIP) model is first proposed. Then, based on two novel weight functions, namely the direct weight (DW) and the incremental weight (IW), we reformulate the QIP models into two integer linear programming (ILP) models, which can also be adapted to Maximum Satisfiability (MaxSAT) instances. Extensive experiments were conducted to evaluate the efficiency of the proposed methods, showing that the proposed approaches are able to compute optimal solutions for the studied instances with linear models achieving superior performance.
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Est identique à hal-05305175 Objet présenté à une conférence Zhifei Zheng, Sami Cherif, Rui Sá Shibasaki, Chu-Min Li, Jialu Zhang. Exact Approaches for the Diverse Satisfiability Problem. JELIA:European Conference on Logics in Artificial Intelligence, Sep 2025, Kutaisi, Georgia, France. pp.207-224, ⟨10.1007/978-3-032-04590-4_15⟩. ⟨hal-05305175⟩
