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Co-Layout: LLM-driven Co-optimization for Interior Layout

🕒 Published (v1): 2025-11-16 06:20 UTC · Source: Arxiv · Venue: AAAI 2026 · link

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TL;DR

Co-Layout combines an LLM multi-agent workflow with grid-based integer programming to jointly optimize room layout and furniture placement from a single text prompt. A coarse-to-fine strategy reduces the combinatorial search space by solving a downsampled problem first and using that solution to warm-start the full-resolution IP. The joint co-optimization eliminates the spatial inconsistencies endemic to sequential two-stage pipelines.

Problem

Existing automated interior design systems decouple room layout and furniture placement into sequential stages. This ignores cross-level interdependencies: furniture size constrains viable room shapes, and room topology determines which furniture arrangements are reachable. Sequential pipelines produce designs with inaccessible rooms, corridor violations, and physically overlapping objects.

Method

Phase 1 — LLM Preprocessor: A multi-agent LLM workflow parses a free-text prompt and outputs a structured JSON scene graph containing room lists \(R = \{r_k\}\), furniture lists \(S = \{s_{k,l}\}\), adjacency requirements, orientation constraints, and target dimensions. LLMs also infer which rooms are "open" (corridor-equivalent).

Phase 2 — Grid-based Integer Programming: The floor is discretized into a 2D grid \(G\) (cell size = one "Modulor" unit). Binary variables \(x^k_{i,j}\), \(p_{i,j}\), \(f^{k,l}_{i,j}\) assign each cell to a room, corridor, or furniture item. Key constraint families: - Non-overlap: \(p_{i,j} + \sum_k x^k_{i,j} = 1\) - Corridor connectivity: flow-conservation on corridor/open-room cells with the entrance as a flow source - Room accessibility: binary access-point variables \(\alpha^k_{i,j}\) ensure each room borders the corridor with at least one furniture-free cell - Furniture shape/containment: bounding-box + area equality enforce rectangular furniture footprints inside their parent room

The weighted objective \(E = \sum_s \omega_s E_s\) combines room rectangularity, perimeter compactness, area targets, aspect ratio, relative furniture positioning, and centroid balance.

Coarse-to-Fine: A downsampled grid (e.g., \(12\times10 \to 6\times5\)) solves a room-only subproblem, reducing variables by 75%. The coarse assignment is mapped back cell-wise and used as a warm-start for the full joint IP, with a penalty term \(E_\text{ref} = \sum_{(i,j)} (1 - x^{\pi(i,j)}_{i,j}) \cdot z_{i,j}\) that encourages fine-grid consistency with the coarse solution.

Key Contributions

  • Joint co-optimization framework that simultaneously solves room layout and furniture placement as a single IP
  • Grid-based constraint formulation (flow-based corridor connectivity, accessibility with furniture-free access points, bounding-box room shape) that captures design requirements ignored by prior work
  • Coarse-to-fine warm-start strategy reducing variable count before full-resolution solve

Results

Evaluated on 5 diverse prompts against Holodeck and AnyHome (both two-stage baselines):

  • OOR (object overlap rate, ↓): Holodeck 0.82 → AnyHome 0.00 → Ours 0.00
  • OOB (out-of-boundary rate, ↓): Holodeck 2.33 → AnyHome 0.04 → Ours 0.00
  • IQA (image quality, ↑): Holodeck 4.03 → AnyHome 4.10 → Ours 4.17
  • IAA (image aesthetics, ↑): Holodeck 3.32 → AnyHome 3.32 → Ours 3.35
  • CLIP text-image alignment (↑): Holodeck 25.15 → AnyHome 25.75 → Ours 26.50
  • User study MRR (↑): Holodeck 0.59 → AnyHome 0.45 → Ours 0.80

Limitations

  • Benchmark is only 5 examples; statistical significance is not established
  • GUROBI is commercial; scalability to larger floor areas (higher grid resolution) is not characterized
  • Door and window placement is handled by post-processing rather than as optimization variables
  • Coarse warm-start initialization is not always feasible; infeasibility is handled by penalty relaxation rather than guaranteed recovery
  • LLM constraint extraction quality is not ablated—errors in the scene graph propagate silently to the IP

Relevance to Harnesses / Meta-Harnesses

Co-Layout is a concrete instance of the LLM-as-preprocessor harness pattern: the LLM multi-agent workflow acts as a structured constraint extractor, translating unstructured natural language into a JSON scene graph that feeds a deterministic downstream solver. This two-component architecture—where the LLM's role is bounded to producing a well-typed intermediate representation rather than generating the final artifact—is a canonical harness design that avoids hallucinated coordinates while retaining language-interface flexibility. The coarse-to-fine strategy further demonstrates how a harness can pipeline heterogeneous solvers (coarse IP → fine IP) sharing a common representation, an architectural pattern directly transferable to other harness systems that chain LLM calls with formal verifiers or planners.