Year: 2025
Type: conference-paper
Abstract: Optimization Modulo Nonlinear Real Arithmetic, abbreviated as OMT(NRA), generally focuses on optimizing a given objective subject to quantifier-free Boolean combinations of primitive constraints, including Boolean variables, polynomial equations, and inequalities. It is widely applicable in areas like program verification, analysis, planning, and so on. The existing solver, OptiMathSAT, officially supporting OMT(NRA), employs an incomplete algorithm. We present a sound and complete algorithm, Optimization Cylindrical Algebraic Covering (OCAC), integrated within the Conflict-Driven Clause Learning (CDCL) framework, specifically tailored for OMT(NRA) problems. We establish the correctness and termination of CDCL(OCAC) and explore alternative approaches using cylindrical algebraic decomposition (CAD) and first-order formulations. Our work includes the development of the first complete OMT solver for NRA, demonstrating significant performance improvements. In benchmarks generated from SMT-LIB instances, our algorithm finds the optimum value in about 150% more instances compared to the current leading solver, OptiMathSAT.
Authors: Fuqi Jia, Yuhang Dong, Rui Han, Pei Huang, Minghao Liu, Feifei Ma, Jian Zhang
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: 高维SMT公式的求解与解空间大小计算, G8267205545
OpenAlex ID: W4409365671