Conflict-Driven Clause Learning with VSIDS Heuristics for Discrete Facility Layout

This paper studies the use of Conflict-Driven Clause Learning (CDCL) with VSIDS heuristics as a computational engine for discrete facility layout problems. The facility layout problem is modeled as a combinatorial assignment problem with dense logical structure arising from adjacency, separation, and slot-availability constraints. We develop a CNF-based formulation for layout feasibility and compare CDCL-based SAT solving against CP-SAT and MILP formulations under a unified benchmarking framework. Empirical results show that CDCL exhibits near-constant runtime behavior for feasibility detection across increasing problem sizes and constraint densities, while CP-SAT and MILP display polynomial and exponential scaling respectively. To address the limitation of CDCL in objective optimization, we introduce two hybrid architectures that combine CDCL-based feasibility search with CP-SAT optimization. The first architecture rapidly enumerates feasible layouts to trade optimality for speed, while the second uses CDCL to generate warm-start solutions that accelerate exact optimization. The results demonstrate that hybrid approaches can significantly reduce time-to-solution while preserving correctness guarantees, clarifying the algorithmic trade-offs between clause-learning search and exact optimization methods in large-scale discrete layout problems.