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CANDO: Cooperative Agentic Network for Layout Design Optimization

Athanasios Masouris, Zheng Jing, Benjamin Sam Chandler, Hadi Jamali-Rad

arXiv:2610.10044v1cs.MA

TL;DR

Existing layout benchmarks often use simpler domains and distributional metrics, leaving real-world facility layouts and their interacting constraints inadequately represented. The paper introduces ALPS-Bench and CANDO, a training-free cooperative framework that refines layouts through verification. CANDO reports strong results across PubLayNet, RICO, and PKU-PosterLayout.

  • Problem

    Many layout benchmarks target simpler placements and use distributional metrics that reward dataset-prior conformity, while real-world facilities require reasoning over irregular boundaries, orientations, access, and routing.

    Source: §1 · p. 1

  • Method

    The paper introduces ALPS-Bench with 1,000 annotated facility layouts and a design-manual scoring protocol, plus CANDO, a training-free cooperative agentic framework using tool-grounded verification.

    Source: §1 · p. 2

  • Results

    CANDO achieves state-of-the-art mIoU and alignment on PubLayNet and RICO, and lowest overlap on all five PKU-PosterLayout tasks with highest strict-underlay in four of five.

    Source: §7 · p. 10

  • Takeaways & Limitations

    The results support cooperative agentic design as a broadly effective recipe for constraint-aware layout synthesis.

    Source: §7 · p. 10

    ALPS-Bench covers outdoor service facilities, transfer to a new domain requires a corresponding design manual and possibly an ICL development corpus, and parallel branching incurs more LLM calls than single-agent baselines.

    Source: §7 · p. 10

Abstract

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Layout generation for real-world facilities is a challenging problem, requiring reasoning over irregular site boundaries, heterogeneous orientations, access-aware placements, and motion-planning feasibility. Yet, most existing layout benchmarks in the generative AI space target simpler placements over rectangular domains and rely on distributional metrics such as FID and IoU that reward conformity to dataset priors, thus discounting design innovation. Motivated by these gaps, we introduce ALPS-Bench, a benchmark of $1,000$ professionally annotated real-world facility layouts paired with an instance-specific scoring protocol grounded in a structured design manual. As a strong baseline for ALPS-Bench, we propose CANDO, a training-free multi-agent framework in which specialized agents iteratively refine layouts through a verification-grounded loop, concentrating reasoning on strategic spatial decisions. We demonstrate that CANDO surpasses state-of-the-art trained and LLM-based baselines on the widely adopted PubLayNet, RICO, and PKU-PosterLayout benchmarks, establishing cooperative agentic design as a broadly effective recipe for constraint-aware layout synthesis.

1 Introduction

Existing layout benchmarks emphasize simpler domains and distributional similarity, leaving real-world facility design’s interacting spatial and operational constraints underserved. The paper introduces ALPS-Bench and CANDO to address this gap, reporting strong results across established layout benchmarks.

1 Introduction

  • Prior benchmarks favor simpler indoor or rectangular layouts and distributional metrics that can penalize valid but atypical designs.The introduction argues that such protocols can reduce evaluation to matching dataset priors and may not transfer to compositional, orientation-aware settings.Source: §1 · p. 1
  • Real-world facility layouts require reasoning over irregular boundaries, heterogeneous orientations, designated access, and motion-planning feasibility across vehicle scenarios.A placement can avoid overlap yet obstruct routing, while clean clustering can still violate access-aware constraints.Source: §1 · p. 1
  • ALPS-Bench pairs 1,000 professionally annotated real-asset layouts with a structured design manual and compliance scoring on a held-out test set.The protocol evaluates diverse spatial constraints for standardized evaluation.Source: §1 · p. 2
  • CANDO is a cooperative agentic framework for constraint-aware synthesis, combining structured agent cooperation, tool-grounded verification, and motion planning.The paper motivates an explicitly decomposed, verification-grounded architecture for spatial arithmetic, multi-constraint reasoning, and long-horizon planning.Source: §1 · p. 2
  • CANDO achieves leading overlap and strict-underlay performance on PKU-PosterLayout, alongside alignment on PubLayNet and RICO.The introduction also reports state-of-the-art mIoU and alignment on PubLayNet and RICO.Source: §1 · p. 2

2 Related Work

Prior layout-generation work spans trained generative models and training-free LLM approaches, but common benchmarks and distributional metrics leave a gap in evaluating complex constraint-aware design. CANDO builds on agentic systems by combining specialized cooperation and verification with layout-specific planning.

Layout Design and Its Benchmarks

  • Most prior methods are evaluated on PubLayNet and RICO using distributional metrics, leaving complex constraint-aware layout design underrepresented.The related-work discussion links this gap to the motivation for ALPS-Bench and CANDO.Source: §2 · p. 2
  • Layout generation progressed from GANs and VAEs to transformers, diffusion models, and LLM-based approaches, including training-free in-context generation and fine-tuned structured-code methods.Examples include LayoutTransformer, LayoutFormer++, LayoutDM, LayoutFlow, DiffuScene, LayoutPrompter, LayoutGPT, LayoutNUWA, and PosterLlama.Source: §2 · p. 2

Cooperative Agentic AI

  • CANDO combines tool-grounded verification, episodic feedback memory, role-specialized cooperation, and block-wise BoN into a training-free framework.The paper situates this design among work on verification, environment-grounded actions, external tools, and multi-agent orchestration.Source: §2 · p. 2

3 Problem Formulation

The formulation treats layout synthesis as constrained optimization of element positions and orientations within a premise. It separates hard validity requirements from soft design criteria, then seeks a valid configuration with the highest weighted compliance score.

3 Problem Formulation

  • Layout synthesis optimizes rigid-body placements in a 2D plane to satisfy geometric feasibility and minimize design-constraint violations.The premise is an outer polygon with access points on its edges, which designate vehicle entry and exit regions.Source: §3 · p. 3
  • Element shapes, sizes, semantic classes, and counts are fixed inputs; optimization changes only their spatial placement.Each element is specified by a semantic class and canonical shape, while the input also includes the premise, access points, and constraint partition.Source: §3 · p. 3
  • Each placed element is represented by a centroid and orientation, which translate and rotate its canonical shape into the layout.The configuration q bundles these position-orientation tuples as the optimization variables.Source: §3 · p. 3
  • Hard constraints require containment, non-overlap, and collision-free routes for every specified routing scenario.Routes are ordered sequences of intermediate points, and feasibility requires a path through free space for each scenario.Source: §3 · p. 3
  • Soft constraints score compositionality, orientation, and proximity, and the objective maximizes their weighted score over valid configurations.Each score ranges from 0 to 1; a configuration is compliant when it satisfies all hard constraints and reaches J(q) = 1.Source: §3 · p. 3

4 Asset Layout Planning and Synthesis (ALPS) Benchmark

ALPS-Bench addresses the limited coverage of real-world facility design in existing layout benchmarks with annotated layouts from operational sites. Its instance-specific evaluation scores design-manual compliance and routing efficiency against withheld ground-truth layouts.

4 Asset Layout Planning and Synthesis (ALPS) Benchmark

  • ALPS-Bench contains 1,000 professionally annotated layouts from operational sites, with variable premises, instance-specific element compositions, and a shared design manual.Polygon annotations were produced from original CAD drawings; the 1,000 instances are split into 900 development layouts and 100 held-out test layouts.Source: §4 · pp. 3–4

4.1 Evaluation and Benchmarking

  • The instance-specific scorer evaluates design-manual satisfaction and routing efficiency against withheld ground-truth configurations rather than similarity to dataset priors.The authors note that metrics such as IoU or FID can penalize design innovation by promoting prior matching.Source: §4.1 · p. 4
  • Hard-constraint scoring checks required elements and sizing, containment, non-overlap, and routing feasibility across predefined scenarios.Routing uses inflated obstacles and Voronoi medial axes to identify paths with maximum clearance; geometric validity and routing feasibility are weighted 0.2 and 0.8.Source: §4.1 · pp. 4–5
  • Soft-constraint scoring combines proximity, spatial compositionality, and within-group orientation alignment.The respective weights are 0.6, 0.3, and 0.1.Source: §4.1 · p. 5
  • Ground-truth routing metrics compare generated layouts with withheld configurations on path length, maneuverability, and path clearance.The three measures are normalized to [0, 1], with 0.5 indicating equivalence to ground truth; invalid scenarios score zero.Source: §4.1 · p. 5
  • The aggregate score averages constraint satisfaction and routing efficiency, capping constraint satisfaction at 0.5 when hard constraints are violated.Scores are computed per layout and then averaged over the relevant split.Source: §4.1 · p. 5

5 Methodology

CANDO uses an in-context initializer and four specialized agents to iteratively refine layouts, grounding decisions in deterministic verification and layout history. Parallel branches explore refinements before a blockwise best-of-N step selects which branch continues.

5 Methodology

  • CANDO combines in-context initialization with Verifier, Historian, Planner, and Generator agents in a parallel-branching refinement loop.Deterministic tools handle low-level geometric computations, which language models struggle with.Source: §5 · pp. 5–6
  • The initializer retrieves structurally similar development layouts, conditions an LLM on their input-output examples, and selects the candidate with the best geometric hard-constraint proxy.Retrieval features cover class counts and area, access points, element sizes, and layout descriptors; the proxy ranks containment and non-overlap.Source: §5 · p. 6
  • The Verifier scores candidate layouts against ground-truth-free design-manual checks, while the Historian records recent feedback changes and their spatial causes for the Planner.Ground-truth routing measures are reserved for benchmark evaluation and are not optimization signals.Source: §5 · p. 6
  • The Planner reconciles diagnostic feedback, history, coordinates, and a plotted layout into a remediation plan, which the Generator applies through varied candidate edits.Candidates range from conservative local repairs to single-category priorities and larger layout-wide modifications.Source: §5 · pp. 6–7
  • Each refinement block runs sequential planning-generation-verification steps on independent branches, then carries the highest-scoring branch and its history into the next block.Blockwise best-of-N selection allows structurally different refinements to be explored without committing prematurely to one branch.Source: §5 · p. 7

6 Experiments

Experiments evaluate CANDO on ALPS-Bench and three public benchmarks, with component ablations on ALPS-Bench. CANDO outperforms considered ALPS-Bench baselines and shows strong constraint-related results across public layout tasks.

Results on ALPS-Bench

  • Both CANDO variants significantly outperform all considered ALPS-Bench baselines on AGG, CS, and RE, while remaining statistically comparable to each other.The comparison covers 100 held-out instances; all baseline comparisons have pHolm ≤0.0059, while the two CANDO variants have pHolm=1.000.Source: Table 1 · p. 8, §6 · p. 8
  • CANDO’s overall complexity is half or less than the Single-Agent baseline’s, despite accounting for four sequential agent calls per iteration.The comparison uses average iterations to compliance on samples that achieve compliance.Source: §6 · p. 8

Results on PubLayNet and RICO

  • CANDO achieves the highest mIoU and perfect alignment on both PubLayNet and RICO for Gen-T and Gen-TS tasks.Across RICO’s five tasks, it also improves overlap over LayoutCoT in four cases, with Gen-TS as the exception.Source: Table 2 · p. 9, §6 · p. 9
  • CANDO’s FID performance is inconsistent because geometrically precise layouts that satisfy requirements can still be penalized for departing from the training-data distribution.The paper notes that distribution-trained methods can minimize FID even when their spatial accuracy is lower.Source: §6 · p. 9

Results on PKU-PosterLayout

  • On PKU-PosterLayout, CANDO attains Strict Underlay scores of 1.000 and 0.990 and overlap of 0.0009 and 0.0 across Gen-T and Gen-TS.It does not consistently improve occurrence or readability and obtains higher FID scores.Source: Table 3 · p. 9, §6 · p. 9

Component Ablation

  • Replacing CoDe with a single refinement trajectory reduces AGG from 0.62 to 0.35 and CS from 0.83 to 0.38; removing deterministic verification yields only 0.27 AGG and 0.28 CS.Without deterministic tools, the LLM verifier declares 95% of layouts compliant, while the independent evaluation reports the lower scores.Source: §6 · pp. 9–10, Table 4 · p. 10
  • Removing strategy diversification raises regression rate from 7.0% to 18.4%, while removing ICL or the Planner reduces compliance from 74% to 53% or 51%, respectively.Removing ICL also reduces AGG from 0.62 to 0.57 and CS from 0.83 to 0.75; removing the Planner leaves mean AGG nearly unchanged at 0.62.Source: §6 · p. 10

7 Concluding Remarks

The paper introduces ALPS-Bench and CANDO, then reports strong results across layout benchmarks while identifying domain, cost, and distributional-evaluation limitations. It frames CANDO as decision support and calls for qualified engineering review before deployment.

7 Concluding Remarks

  • CANDO achieves state-of-the-art mIoU and alignment on PubLayNet and RICO, and the lowest overlap on all five PKU-PosterLayout tasks with the highest strict-underlay score on four.The authors conclude that cooperative agentic design is a broadly effective recipe for constraint-aware layout synthesis.Source: §7 · p. 10
  • ALPS-Bench contains 1,000 professionally annotated facility layouts with instance-specific scoring, while CANDO is a training-free cooperative framework that refines layouts through verification.The broader-impact discussion describes the dataset as anonymized site geometries without identifying information about operators or locations.Source: §7 · p. 10, A Broader Impact · p. 16
  • The authors report that CANDO does not optimize for distributional similarity, yielding strong mIoU but weaker FID on PubLayNet, RICO, and PKU.They also identify domain transfer and parallel-branching cost as limitations.Source: §7 · p. 10

A Broader Impact

  • CANDO is intended as decision support, but the authors say final layouts should be reviewed by a qualified engineer before deployment.Its routing checks use inflated obstacle margins and strict no-backtracking rules.Source: A Broader Impact · p. 16

B Limitations

The limitations concern domain transfer, computational cost, and distributional evaluation. The appendices describe notation, annotation provenance, and the stored layout format.

B Limitations

  • Transferring CANDO beyond outdoor automotive service facilities requires a corresponding design manual and, when ICL initialization is used, a development corpus of annotated examples.The benchmark’s design manual, routing scenarios, and 14-class vocabulary are specific to this setting.Source: B Limitations · p. 16
  • CANDO’s parallel-branching strategy uses more LLM calls per layout than Single-Agent or LayoutPrompter, and its highest-scoring configuration is also the most expensive.Resource-constrained deployment may require reducing N, B, or K at some cost to layout quality.Source: B Limitations · p. 16
  • Because CANDO does not optimize distributional similarity, its FID rankings are inconsistent even where mIoU and alignment performance is state of the art on PubLayNet and RICO.The authors advise caution when an evaluation protocol weights FID heavily.Source: B Limitations · p. 16

C Notation

  • The notation table groups mathematical symbols by the section in which they are introduced, including routing scores, constraint metrics, and CANDO’s search-state variables.Examples include path-clearance and path-length sub-scores, branch count N, and candidate count K.Source: C Notation · pp. 17–18

D.1 Data Provenance and Annotation Process

  • ALPS-Bench derives from industrial operational assets, with approximately 20 professional annotators working over five weeks and domain experts reviewing the annotations in multiple rounds.Only anonymized site geometries are released.Source: §D.1 · p. 19

D.2 Annotation Format

  • Each layout is stored as a JSON Lines record containing an identifier and element records, whose polygons are ordered coordinate pairs measured in meters.The site premise is stored as an element of its own class.Source: §D.2 · p. 19

D.3 Dataset Statistics

The appendix characterizes ALPS-Bench’s layout statistics and design constraints, then details vehicle-routing scenarios and Voronoi-based motion planning. It also describes adaptations of trained ALPS-Bench baselines.

D.3 Dataset Statistics

  • The 1,000 canonical layouts have premise areas of 390.33–19,358.82 m2 and contain 7–101 polygon annotations, excluding the premise.Mean and median premise areas are 3,228.40 and 2,705.12 m2; annotation counts average 22.75 with a median of 21.Source: §D.3 · p. 19
  • Surface complexity combines equally weighted ranks for annotation count and covered premise area; median utilization is 17.5% and median complexity is 48.7.Figure 4 shows the score distribution and its two components, with dotted median lines and darker shades denoting greater complexity.Source: §D.3 · p. 19, Figure 4 · p. 19
  • UNDERGROUND SERVICE FACILITY, ENTRANCE, and EXIT appear in every layout, while specialized classes such as BIKE SERVICE AREA occur in only 8.6%.Figure 5 distinguishes class coverage from mean within-layout multiplicity conditional on presence.Source: §D.3 · p. 19, Figure 5 · p. 20

D.4.1 Hard Constraints

  • Hard constraints require containment within the premise, no overlap, specified element quantities, and routing feasibility.The manual separates hard constraints from soft constraints.Source: §D.4.1 · p. 20, §D.4 · p. 20

D.4.2 Soft Constraints

  • Soft constraints evaluate compositionality, proximity, and orientation, including coherent clusters, functional clearances, and angular agreement among grouped elements.Compositionality favors compact grids for even-sized groups and linear arrangements for odd-sized groups; orientation tolerance is 5°.Source: §D.4.2 · pp. 20–21

D.5 Routing Scenarios

  • Routing scenarios cover Cars, Bikes, and HGVs, requiring each vehicle to travel from an ENTRANCE through specified waypoints to an EXIT with vehicle-specific minimum clearance.The evaluated routes are listed by vehicle type.Source: §D.5 · p. 21

D.6 Voronoi-Based Motion Planning Evaluation

  • The motion planner inflates obstacles by a vehicle-dependent margin, samples their boundaries, builds a Voronoi medial-axis graph, and searches it for a shortest route.Underground facilities are excluded from surface obstacles, and critical service areas generally prohibit reversing out.Source: §D.6 · pp. 21–22, Figure 6 · p. 23

E.1 Trained ALPS-Bench Baselines

  • LayoutDM is adapted from axis-aligned page boxes to oriented bounding boxes in the site frame, while Qwen-LoRA-ALPS is fine-tuned to generate all element polygons in one response.LayoutDM’s FID pathway remains based on (x, y, w, h) and does not evaluate orientation; its box approximation can still permit boundary crossings or overlaps.Source: §E.1 · p. 24

E.2 Simplified CANDO for Public Benchmarks

The simplified CANDO pipeline adapts its agents, branching settings, and evaluation protocol to PubLayNet, RICO, and PKU-PosterLayout. PKU adds multimodal content checks, while the protocols report benchmark-specific metrics.

E.2 Simplified CANDO for Public Benchmarks

  • All public-benchmark agent roles use Qwen3.6-35B-A3B-FP8 without task-specific fine-tuning, and the ICL initializer retrieves eight exemplars and samples ten initial layouts.Valid initial layouts are ranked using alignment, overlap, and dissimilarity weights of 0.2, 0.2, and 0.6.Source: §E.2 · p. 24
  • PubLayNet and RICO use four parallel branches, five steps per branch, up to ten iterations, and eight candidate action sequences per refinement step.The simplified pipeline retains Verifier, Planner, Generator, and Historian agents, with benchmark-specific checks replacing ALPS-specific routing and compositionality workers.Source: §E.2 · p. 24
  • PKU-PosterLayout uses two branches and adds multimodal content-Verifier and content-Planner agents that inspect layouts overlaid on the in-painted poster and saliency map.The original composed poster is excluded to prevent target-layout leakage; termination requires a content score of at least 0.8.Source: §E.2 · p. 24
  • PubLayNet and RICO are evaluated on their complete test splits using mIoU, alignment, overlap, and LayoutNet FID, while PKU uses 1,000 test samples and the RALF metrics.PKU metrics include occlusion, unreadability, strict underlay effectiveness, non-underlay overlay, and FIDNetV3 FID.Source: §E.2 · pp. 24–25

E.3 Compute Resources and Latency

The section describes compute setups and latency reporting for ALPS-Bench and public-benchmark evaluations, distinguishing concurrent-load trial latency from evaluation throughput. It also notes that broader ablation work is excluded from the final test-evaluation totals.

E.3 Compute Resources and Latency

  • ALPS-Bench Qwen runs used eight H100 GPUs and 24 concurrent workers; GPT-5.2 runs used Azure OpenAI, with 100 workers for Single-Agent and CANDO CoDe and 50 for CANDO BoN.The final test evaluations covered 100 layouts; LayoutPrompter used the same API infrastructure as the other GPT-5.2 experiments.Source: §E.3 · p. 25, Table 10 · p. 25
  • Trial latency measures one layout’s elapsed time under concurrent load, whereas effective time per layout represents amortized throughput across the parallel evaluation.For local experiments, GPU-hours are batch wall time multiplied by allocated GPUs; overlapping trial durations should not be summed.Source: §E.3 · p. 25, Table 10 · p. 25
  • The final ALPS-Bench test-evaluation totals exclude an estimated 2,500 H100 GPU-hours spent on component and hyperparameter ablations.Source: §E.3 · p. 25, Table 10 · p. 25
  • Public-benchmark latency covers generation, candidate evaluation, verification, and refinement, but no matched competitor latency is reported.Measurements used isolated single-sample runs on a randomly selected subset of 50 samples per task, with diagnostics disabled and graph-loading overhead excluded.Source: §E.3 · pp. 25–26, Table 11 · p. 25

E.4 Additional Results on PubLayNet and RICO

The additional results extend the public-benchmark evaluation with task-specific results for PubLayNet, RICO, and PKU-PosterLayout. The supplied passages identify the tasks covered by each table but do not state outcome values.

E.4 Additional Results on PubLayNet and RICO

  • Table 12 reports PubLayNet and RICO results for relationship generation, completion, and refinement.Source: §E.4 · p. 26, Table 12 · p. 26
  • Across the two additional-results tables, coverage spans relationship generation, completion, and refinement, with generation tasks also reported for PKU-PosterLayout.Source: §E.4 · p. 26, §E.5 · p. 26

E.5 Additional Results on PKU-PosterLayout

  • Table 13 reports PKU-PosterLayout results for type generation, type-size generation, relationship generation, completion, and refinement.Source: §E.5 · p. 26

E.6 Component Ablation Analysis

The component ablation examines strategy diversification during refinement. Removing diversification leaves average AGG and CS relatively stable but substantially raises the rate of regressive refinement steps.

Strategy Diversification

  • Removing strategy diversification raises the regression rate from 7.0% to 18.4%, while average AGG and CS remain relatively stable.Regression rate is the percentage of refinement iterations in which verification score decreases after proposed changes.Source: §E.6 · p. 26
  • Conservative strategies account for 17.6% of winning candidates, Proximity-focused for 16.6%, and Hard-constraint-focused for 8.3%.A strategy wins when its candidate achieves the highest verification score among the strategies explored at that step.Source: §E.6 · p. 27, Table 14 · p. 27
  • The distribution of winning strategies supports exploring multiple specialized refinement strategies rather than relying on one fixed instruction.The authors report that different constraint configurations require qualitatively different repair behaviors.Source: §E.6 · p. 27

E.7 Hyperparameter Tuning

The ALPS-Bench significance tests find both CANDO variants outperforming the considered baselines across AGG, CS, and RE, while the two backbones are statistically comparable. Hyperparameter analyses identify a best tested joint setting and show that block size has non-monotonic effects.

E.7 Hyperparameter Tuning

  • The best tested joint setting is N=4, B=10, K=6, and W=6, achieving 0.76 CS, 0.42 RE, and 0.59 AGG.This setting is used with a final evaluation budget of T=20 in the reported ALPS-Bench experiments.Source: §E.7 · p. 27, Table 15 · p. 28
  • For matched N, B, and K, increasing history window W from 3 to 6 improves AGG from 0.52 to 0.54.The authors interpret this as highlighting the Planner’s use of historical trajectories to avoid cyclic edits.Source: §E.7 · p. 27
  • With other hyperparameters fixed, block size B=5 peaks at mean score 0.750, while B=20 yields a 42.4% constraint compliance rate but a slightly lower best score.The one-factor analysis fixes K=8, so it does not determine the final joint configuration selected in Table 15.Source: §E.7 · pp. 27–28, Table 16 · p. 28

E.8 Statistical Significance on ALPS-Bench

  • The significance analysis uses two-sided Wilcoxon signed-rank tests with Holm correction and paired-bootstrap 95% confidence intervals over the same 100 held-out instances.Table 17 reports mean paired differences, confidence intervals, and adjusted p-values for AGG, CS, and RE.Source: §E.8 · p. 28, Table 17 · p. 28
  • Both CANDO variants significantly outperform every considered baseline across AGG, CS, and RE after Holm correction (pHolm ≤0.0059), while CANDO-Qwen and CANDO-GPT show no significant difference.All baseline-comparison paired-bootstrap confidence intervals exclude zero; the backbone-comparison intervals contain zero, with pHolm=1.000 for all three metrics.Source: §E.8 · pp. 28–29, Table 17 · p. 28

F Methodology Details

This appendix details CANDO’s retrieval, repair, planning, supervision, and generation workflows, including the prompts and constraints used to refine layouts through verification and visual evidence. It also documents the datasets, models, implementations, and licensing terms used.

F.1 ICL Initializer: Feature Extraction and Scoring

  • The ICL retrieval vector combines per-class counts and occupancy, access roles and positions, per-class dimension statistics, and premise geometry descriptors.Premise descriptors include boundary area, perimeter, aspect ratio, and compactness.Source: §F.1 · p. 30
  • After standardizing features, retrieval weights compositional and access-point similarity above boundary geometry, while infeasible top candidates receive sparse repairs that preserve compliant elements.The repair loop proposes translations or rotations to restore containment and non-overlap, stopping early upon feasibility or after a fixed number of steps.Source: §F.1 · p. 30

F.2 Generator: Strategy Library

  • The Generator cycles through eight configurations, mixing cautious or surgical plan-following and constraint-focused strategies with unguided exploratory branches to escape poor local optima.Unguided branches receive no Planner output, and strategies are assigned randomly within each round.Source: §F.2 · p. 30

F.3 Planner and Generator Prompts

  • At runtime, the Generator base prompt is combined with a strategy-specific extension, while the deterministic full CANDO Verifier has no LLM system prompt.Prompts for the ICL Initializer, initial-layout repair, Historian, specialized Planner-workers, strategy extensions, and no-tool Verifier are available in the released codebase.Source: §F.3 · p. 30

F.3.1 Supervisor Planner System Prompt

  • Tier 1 anchors are prioritized for placement in iterations 0–3, then stabilized from iteration 4 onward so other elements are generally moved around them.During stabilization, boundary violations still require moving Tier 1 anchors inside the layout; overlap and proximity fixes should generally move other elements.Source: §F.3.1 · p. 31
  • The supervisor treats narrow, category-specific worker plans as local suggestions, validating or overriding them using the full layout, verification results, and history.Workers lack awareness of violations outside their category and may propose actions without knowing whether the target position is occupied.Source: §F.3.1 · p. 32
  • The final plan consolidates repeated compatible steps into group actions and preserves any supplied target_edge_index instead of replacing it with a cardinal side label.For example, multiple elements stacked against the same side of the same target become one stack_group operation.Source: §F.3.1 · pp. 33, 36
  • The supervisor treats geometry-tool verification feedback as ground truth, prioritizing hard_constraints and flow before proximity, orientation, and assembly once validity is achieved.Category scores help determine urgency, and plans should target listed violations rather than introduce unnecessary steps for compliant categories.Source: §F.3.1 · p. 34
  • Hard-constraint or flow violations cap the overall score at 0.5, while compliance across all five workers yields 1.0.The score is overall_score = valid * 0.5 + 0.5 * soft_score, with soft_score = 0.6 * proximity.score + 0.1 * orientation.score + 0.3 * assembly.score.Source: §F.3.1 · p. 34
  • Before placing an element at a target position, the supervisor checks for blockers and plans their relocation first, including moves needed to create rotation clearance.This precondition planning applies across categories so the main corrective action can be executed rather than obstructed.Source: §F.3.1 · p. 34
  • The supervisor analyzes the layout image for stacking edges, orientation, cluster coherence, empty space, and corridor viability, overriding worker plans that conflict with global spatial context.Visual observations can also reveal problems no worker addressed and justify corrective steps grounded in the layout data.Source: §F.3.1 · pp. 34–35
  • Conflicting proposals are resolved using category weights and minimal changes, with visual quality guiding ties and the planner emitting refined actions by category.The planner preserves useful geometric references and exact worker-supplied distances when producing concrete steps.Source: §F.3.1 · pp. 36, 38
  • The planner checks worker steps against verified violations, visual observations, anchor rules, occupancy, and cross-category conflicts before adopting, modifying, replacing, or discarding them.It adds relocation preconditions when target zones are occupied and grounds emitted steps in verification findings.Source: §F.3.1 · pp. 37–38

F.3.2 Generator Base System Prompt

  • The generator treats the strategy as highest priority, addresses hard-constraint violations first, and produces an independently executable action sequence.Without planner guidance, it reasons from layout data; with guidance, it resolves category conflicts while following the strategy.Source: §F.3.2 · p. 39
  • Hard-constraint violations take priority, and conflicting suggestions must yield one move or rotation per element to avoid sequential errors.The prompt also says to modify or skip actions that would create new violations or geometric impossibilities.Source: §F.3.2 · p. 40
  • Sequences address hard constraints first, then proceed through major repositioning, grouping, alignment, and fine-tuning while respecting dependencies and minimizing interference.The prompt identifies overlaps, out-of-bounds placements, and spacing violations as mandatory first-phase issues.Source: §F.3.2 · p. 40
  • Actions must specify executable geometric parameters, while group moves preserve relative positions and group rotations distinguish individual pivots from rigid-body rotation.For stacking, the prompt specifies target edges or sides, source-edge orientation, distance, and placement location.Source: §F.3.2 · pp. 41–42
  • The prompt directs the generator to prioritize hard constraints, weight other categories, follow the supplied strategy, explain expected improvements, and consolidate equivalent individual actions into group operations.High-weight categories should dominate planning, while compatible stack or move actions can be combined into stack_group or move_group actions.Source: §F.3.2 · p. 42
  • Compatible moves, rotations, and alignments are consolidated into group actions only when their shared parameters match; otherwise, elements retain individual actions.Grouped alignments carry over a shared target edge, and omit the target element when there is no shared target.Source: §F.3.2 · pp. 42–43
  • The prompt requires concrete, nonduplicate actions, omits no-op rotations, and specifies a JSON ActionSequence with actions, a rationale, and an impact priority.An action array can be empty but should usually contain 1–10 actions; the output must be a single JSON object.Source: §F.3.2 · p. 43
  • Each element may appear in at most one move action and at most one rotate action in a sequence.The prompt also requires the output to contain only the JSON object, without markdown or commentary.Source: §F.3.2 · p. 43

G Licenses

  • The text reports using Qwen3.6, GPT-5.2 via Azure OpenAI, and the official LayoutDM and LayoutCoT [44] implementations; LayoutCoT’s repository specified no explicit software license at access time.Source: G Licenses · p. 44

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