Learn to relax: Integrating 0-1 integer linear programming with pseudo-Boolean conflict-driven search

Conflict-driven pseudo-Boolean solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though have potential to be exponentially more efficient than CDCL in theory, practice they can sometimes get hopelessly stuck even when programming (LP) relaxation is infeasible over reals. Inspired mixed (MIP), we address this problem interleaving incremental LP solving with cut generation within search. This hybrid approach, which for first time combines MIP techniques full-blown conflict analysis operating directly on inequalities using cutting planes method, significantly improves performance a wide range of benchmarks, approaching “best-of-both-worlds” scenario between SAT-style search and MIP-style branch-and-cut.