From Requirements and Drawings to Optimized Warehouse Floorplans: LLM-Driven Formulation and Solver-Based Design

Warehouse layout design must translate natural-language requirements into feasible spatial decisions while accounting for operational performance. We present FLOWS (Formulation-Led Optimization of Warehouses with Solvers), a neuro-symbolic framework that connects language-based modeling with symbolic optimization through an explicit integer-programming formulation. A formulation agent grounds decision variables, objectives, and constraints in a graph representation of warehouse geometry and a finite rack catalog. A separate strategy agent selects admissible solution procedures without changing the underlying problem. Candidate layouts undergo static validation and simulation-based acceptance; diagnostic feedback supports formulation revision while preserving the original requirements. This separation makes the model, solution procedure, and acceptance decision independently inspectable. With replayed formulations and a fixed constructive portfolio, FLOWS produces verified layouts on all 42 warehouse plans and improves mean operating performance over two adapted planners. Small component ablations identify declaration-repair gains but do not establish an advantage for adaptive strategy selection or operational feedback.