Discrete facility layout design involves placing physical entities to minimize handling costs while adhering to strict safety and spatial constraints. This combinatorial problem is typically addressed using Mixed Integer Linear Programming (MILP) or Constraint Programming (CP), though these methods often face scalability challenges as constraint density increases. This study systematically evaluates the potential of Conflict-Driven Clause Learning (CDCL) with VSIDS heuristics as an alternative computational engine for discrete layout problems. Using a unified benchmarking harness, we conducted a controlled comparison of CDCL, CP-SAT, and MILP across varying grid sizes and constraint densities. Experimental results reveal a distinct performance dichotomy: while CDCL struggles with optimization objectives due to cost-blind branching, it demonstrates unrivaled dominance in feasibility detection, solving highly constrained instances orders of magnitude faster than competing paradigms. Leveraging this finding, we developed a novel "Warm-Start" hybrid architecture that utilizes CDCL to rapidly generate valid feasibility hints, which are then injected into a CP-SAT optimizer. Our results confirm that this layered approach successfully accelerates exact optimization, using SAT-driven pruning to bridge the gap between rapid satisfiability and proven optimality.

翻译：离散设施布局设计涉及在满足严格安全与空间约束的前提下放置物理实体，以最小化搬运成本。这一组合优化问题通常采用混合整数线性规划（MILP）或约束规划（CP）方法求解，然而随着约束密度增加，这些方法常面临可扩展性挑战。本研究系统评估了结合VSIDS启发式的冲突驱动子句学习（CDCL）作为离散布局问题替代计算引擎的潜力。通过统一的基准测试框架，我们在不同网格规模和约束密度下对CDCL、CP-SAT与MILP进行了受控比较。实验结果表明存在明显的性能二分现象：尽管CDCL因成本无感知的分支策略而在优化目标求解中表现不佳，但其在可行性检测方面展现出无可匹敌的优势，能够以数量级更快的速度求解高约束密度实例。基于这一发现，我们开发了一种新颖的"热启动"混合架构，利用CDCL快速生成有效可行性提示，并将其注入CP-SAT优化器。实验结果证实，这种分层方法通过SAT驱动的剪枝技术，成功加速了精确优化过程，弥合了快速可满足性验证与可证明最优性之间的鸿沟。