VIGOR: Verifiable Industrial Geometry Optimization and Repair in Scene Programs

Large language models (LLMs) increasingly generate structured layouts and executable scene programs from natural-language instructions. However, executability does not imply engineering feasibility: an industrial scene program may execute successfully while its final state still violates coupled boundary, collision, clearance, aisle, or structural constraints. We identify this mismatch as the executability-engineering-feasibility gap, where locally plausible placements can remain globally infeasible because corrections to one device may introduce violations elsewhere. To make this gap measurable in a controlled setting, we construct an execution-grounded industrial scene-program dataset with 1,749 constructible scenarios, complete executable programs, and 94 final-state geometric checks per scenario. We further propose VIGOR, which combines supervised scene-program generation with execution-grounded verification and staged geometric refinement. Supervised fine-tuning establishes complete program generation, local projection resolves independently correctable violations, and joint conflict-graph repair coordinates residual multi-object conflicts while preserving structural relations. Experiments show that VIGOR achieves 96.86% Complete Feasibility and an Overall score of 91.20, outperforming the strongest evaluated baseline by 10.42 points in Overall. These results show that, under controlled industrial layout conditions, reliable scene-program generation requires not only executable programs, but also explicit verification and coordinated resolution of coupled engineering constraints.