CANDO: Cooperative Agentic Network for Layout Design Optimization

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

cs.MAOct 7, 2026

CANDO: Cooperative Agentic Network for Layout Design Optimization

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

Organizations: Shell Information Technology International · Shell China Limited · Delft University of Technology (TU Delft)

Abstract

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.

Figures & tables

Figure 1: Left : Sample from ALPS-Bench . Right : Voronoi-based motion planning.

Figure 2: The interplay and cooperation among the agents in CANDO . Upon an ICL Initialization, Verifier, Historian, Planner and Generator communicate in a structured manner within a loop.

Figure 3: Mean CS Score vs. $T$ for Table 1

Method	Summary Statistics			$T$	Avg. Iterations to Comply	Time Complexity	Compliance (%)
Method	AGG $\uparrow$	CS $\uparrow$	RE $\uparrow$	$T$	Avg. Iterations to Comply	Time Complexity	Compliance (%)
$\blacktriangle$ Qwen-LoRA-ALPS †	$0.07_{\pm 0.12}$	$0.01_{\pm 0.08}$	$0.13_{\pm 0.22}$	$1$	–	$\tau$	–
$\blacklozenge$ LayoutDM † [ 19 ]	$0.13_{\pm 0.13}$	$0.01_{\pm 0.03}$	$0.24_{\pm 0.25}$	–	–	–	–
$\blacktriangle$ LayoutPrompter (GPT-5.2) [ 32 ]	$0.17_{\pm 0.11}$	$0.01_{\pm 0.06}$	$0.33_{\pm 0.21}$	$1$	–	$\tau$	–
$\blacktriangle$ LayoutCoT (GPT-5.2) [ 44 ]	$0.19_{\pm 0.20}$	$0.13_{\pm 0.24}$	$0.25_{\pm 0.24}$	$4$	–	$4\tau$	–
$\bullet$ Single-Agent (GPT-5.2)	$0.40_{\pm 0.27}$	$0.47_{\pm 0.37}$	$0.32_{\pm 0.22}$	$200$	$80.6$	$80.6\tau$	$22.4$

Table 1: Quantitative results of layout generation models evaluated on the ALPS-Bench test set (

\mathcal{D}^{\textup{test}}

). † denotes methods trained or fine-tuned on ALPS-Bench; all other methods are training-free with respect to ALPS-Bench. Symbols indicate the generation paradigm:

\blacklozenge

diffusion-based,

\blacktriangle

single-LLM/MLLM, and

\bullet

agentic.

		RICO [ 7 ]				PubLayNet [ 59 ]
Task	Method	mIoU $\uparrow$	FID $\downarrow$	Align $\downarrow$	Over $\downarrow$	mIoU $\uparrow$	FID $\downarrow$	Align $\downarrow$	Over $\downarrow$
Gen-T	LayoutGAN++ [ 25 ]	0.298	5.954	0.261	0.620	0.297	14.875	0.124	0.148
	BLT [ 26 ]	0.216	25.633	0.150	0.983	0.140	38.684	0.036	0.196
	LayoutFormer++ [ 22 ]	0.432	1.096	0.230	0.530	0.348	8.411	0.020	0.008
	LayoutPrompter [ 32 ]	0.604	2.134	0.002	0.029	0.619	1.648	0.001	0.004
	LayoutCoT [ 44 ]	0.719	2.189	0.001	0.022	0.772	1.227	0.000	0.002

Table 2: Quantitative results on PubLayNet and RICO datasets. Extended version in Appendix E.4 .

Task	Method	Occ $\downarrow$	Rea $\downarrow$	Und S $\uparrow$	Ove $\downarrow$	FID $\downarrow$
Gen-T	RALF [ 16 ]	0.136	0.0127	0.890	0.0091	2.36
	UniLayDiff [ 33 ]	0.122	0.0129	0.963	0.0018	3.09
	CANDO (ours)	0.144	0.0196	1.000	0.0009	9.83
Gen-TS	RALF [ 16 ]	0.138	0.0123	0.876	0.0113	0.61
	UniLayDiff [ 33 ]	0.128	0.0132	0.918	0.0046	0.66
	CANDO (ours)	0.145	0.0197	0.990	0.0000	4.47

Table 3: Quantitative results on PKU-PosterLayout dataset. Additional tasks are reported in Appendix E.5 .

Variant	AGG $\uparrow$	CS $\uparrow$	RE $\uparrow$	Verifier-Compliant Layouts	Mean Iterations	Regression Rate
CANDO (full)	$0.62_{\pm 0.19}$	$0.83_{\pm 0.25}$	$0.41_{\pm 0.16}$	74%	13.28	7.0%
w/o CoDe	$0.35_{\pm 0.30}$	$0.38_{\pm 0.45}$	$0.32_{\pm 0.23}$	44%	16.75	6.3%
w/o Historian	$0.61_{\pm 0.23}$	$0.80_{\pm 0.34}$	$0.42_{\pm 0.16}$	59%	13.35	6.7%
w/o ICL	$0.57_{\pm 0.26}$	$0.75_{\pm 0.37}$	$0.40_{\pm 0.19}$	53%	14.39	5.8%
w/o Planner	$0.62_{\pm 0.22}$	$0.82_{\pm 0.32}$	$0.43_{\pm 0.15}$	51%	14.63	6.7%
w/o Strategies	$0.61_{\pm 0.23}$	$0.80_{\pm 0.32}$	$0.42_{\pm 0.16}$	53%	14.60	18.4%

Table 4: Component ablation of CANDO . Regression rate denotes the percentage of refinement iterations for which the verification score decreases after applying the proposed changes.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description
Layout domain (Section 3 )
$\mathcal{C}$	Vocabulary of semantic element classes.
$E$	Number of elements to be placed.
$\mathcal{A}$	Set of designated entrance and exit access regions.
$\mathcal{E}=\{(c_{i},\,G_{i})\}_{i=1}^{E}$	Full element specification (fixed input).
$G_{i}\subset\mathbb{R}^{2}$	Canonical (fixed) shape of element $i$ , centered at the origin.

Appendix

Table 5: Summary of mathematical notation used throughout the paper.

Panel of Figure 4 — Figure 4: Complexity statistics for ALPS-Bench . Left : Distribution of the surface complexity score. Right : Its two components, surface-annotation count and surface utilization; dotted lines mark their medians. Darker shades indicate greater complexity in both panels.

Figure 5: Class distribution in ALPS-Bench . Left : Fraction of layouts containing each class. Right : Mean number of instances among layouts in which the class is present. The premise record is omitted.

Vehicle type	Intermediate Waypoint Sequence
Car	Car Service Area
	Car Service Area $\rightarrow$ Car Parking
	Car Service Area $\rightarrow$ Priority Parking
	Car Parking
	EV Service Area
Bike	Bike Service Area

Appendix

Table 6: Evaluated routing sequences per vehicle type. All routes implicitly begin at any Entrance and terminate at any Exit .

Constraint Type	Rule Specification
Compositionality
Rectangular Blocks / Single Line	car service area (group size 4, distance tolerance up to 3.0 m), bike service area (group size 2, distance tolerance up to 3.0 m), and underground service facility (group size 2, distance tolerance up to 1.0 m). Odd counts format to primary lines; even counts format to dense multi-axis grids (for example, 2 by 2, or 2 by 3 blocks).
Strict Single Line	car parking (group size 3, tolerance up to 0.5 m), bike parking (size 4, tolerance up to 0.5 m), hgv service area (size 2, tolerance up to 10.0 m), priority parking (size 2, tolerance up to 1.0 m), ev service area (any size).
Proximity and Clearances
Boundary Stacking	underground access point (longer edge), bike parking , hgv parking , and shop (longer edge) are ideally stacked against or placed proximally adjacent to the layout polygon .
Element Stacking	car parking (shorter edge) and priority parking must uniformly stack against the shop . priority parking must also remain placed closest to the entrance .

Appendix

Table 7: Comprehensive breakdown of

\mathcal{SC}

Vehicle	Length (m)	Width (m)
Car	4.5	1.8
Bike	2.0	0.75
HGV	16.5	2.55

Appendix

Table 8: Average vehicle dimensions.

Figure 6: Step-by-step illustration of CANDO ’s motion planning tool.

Hyperparameter	PubLayNet	RICO	PKU-PosterLayout
Retrieved exemplars	$8$	$8$	$8$
Initial layouts	$10$	$10$	$10$
Branches $N$	$4$	$4$	$2$
Steps per branch $B$	$5$	$5$	$5$
Candidates per step $K$	$8$	$8$	$8$
Maximum iterations $T$	$10$	$10$	$10$

Appendix

Table 9: Refinement configuration of simplified CANDO on public benchmarks.

Method	Compute	Mean trial latency	Median	Batch wall time	Effective time/layout
Single-Agent (GPT-5.2)	Cloud API	$10.49\pm 5.83$ h	$12.42$ h	$20.20$ h	$\sim$ 12 min 07 s
CANDO (BoN/GPT-5.2)	Cloud API	$47.12\pm 39.34$ min	$33.51$ min	$2.50$ h	$\sim$ 1 min 30 s
CANDO (CoDe/GPT-5.2)	Cloud API	$42.75\pm 36.34$ min	$29.42$ min	$2.39$ h	$\sim$ 1 min 26 s
CANDO (CoDe/Qwen)	8 $\times$ H100 (80 GB)	$2.86\pm 1.73$ h	$2.67$ h	$16.7$ h	$\sim$ 10 min 02 s

Appendix

Table 10: Compute resources and latency for final ALPS-Bench test-set evaluations. Mean trial latency is reported as mean

\pm

standard deviation. Effective time per layout measures throughput, whereas trial latency measures the end-to-end duration of an individual trial under concurrent load.

Task	PubLayNet	RICO	PKU
Gen-T	104.8 s	66.8 s	46.8 s
Gen-TS	125.7 s	137.4 s	111.4 s
Gen-R	166.1 s	74.7 s	102.9 s
Completion	65.4 s	31.1 s	18.0 s
Refinement	71.8 s	54.1 s	39.3 s

Appendix

Table 11: Median per-sample response time of CANDO on the PubLayNet, RICO, and PKU-PosterLayout public benchmarks. Results were measured in isolated runs (single-sample inference, diagnostics disabled) and do not include graph loading overhead.

		RICO				PubLayNet
Task	Method	mIoU $\uparrow$	FID $\downarrow$	Align $\downarrow$	Over $\downarrow$	mIoU $\uparrow$	FID $\downarrow$	Align $\downarrow$	Over $\downarrow$
Gen-T	LayoutGAN++ [ 25 ]	0.298	5.954	0.261	0.620	0.297	14.875	0.124	0.148
	BLT [ 26 ]	0.216	25.633	0.150	0.983	0.140	38.684	0.036	0.196
	LayoutFormer++ [ 22 ]	0.432	1.096	0.230	0.530	0.348	8.411	0.020	0.008
	LayoutPrompter [ 32 ]	0.604	2.134	0.002	0.029	0.619	1.648	0.001	0.004
	LayoutCoT [ 44 ]	0.719	2.189	0.001	0.022	0.772	1.227	0.000	0.002

Appendix

Table 12: Quantitative results on the PubLayNet and RICO datasets for Type Generation, Type-Size Generation, Relationship Generation (Gen-R), Completion (Comp.), and Refinement (Refine) tasks.

Task	Method	Occ $\downarrow$	Rea $\downarrow$	Und S $\uparrow$	Ove $\downarrow$	FID $\downarrow$
Gen-T	RALF	0.136	0.0127	0.890	0.0091	2.36
	UniLayDiff	0.122	0.0129	0.963	0.0018	3.09
	CANDO (ours)	0.144	0.0196	1.000	0.0009	9.83
Gen-TS	RALF	0.138	0.0123	0.876	0.0113	0.61
	UniLayDiff	0.128	0.0132	0.918	0.0046	0.66
	CANDO (ours)	0.145	0.0197	0.990	0.0000	4.47

Appendix

Table 13: Quantitative results on the PKU-PosterLayout dataset for Type Generation (Gen-T), Type-Size Generation (Gen-TS), Relationship Generation (Gen-R), Completion (Comp.), and Refinement (Refine) tasks.

Strategy	# Times Won	Win Percentage
Conservative	930	17.6%
Proximity-focused	875	16.6%
Surgical	724	13.7%
Aggressive	629	11.9%
Macro-spatial	610	11.5%
Compositionality-focused	548	10.4%

Appendix

Table 14: Distribution of winning refinement strategies across CANDO refinement steps. A strategy is considered the winner when its candidate achieves the highest verification score among the strategies explored at that step.

Hyperparameter				Evaluation Metric
$N$	$B$	$K$	$W$	CS $\uparrow$	RE $\uparrow$	AGG $\uparrow$
4	10	6	6	0.76	0.42	0.59
4	5	8	6	0.71	0.37	0.54
2	5	4	6	0.68	0.37	0.52
4	5	8	3	0.67	0.37	0.52
2	10	8	9	0.63	0.38	0.51

Appendix

Table 15: Impact of

N

B

K

, and

W

, for

T{=}10

Block Size ( $B$ )	CS $\uparrow$	Compliance Rate $\uparrow$	Mean Iters to Comply $\downarrow$
1	$0.702_{\pm 0.274}$	30.6%	7.0
5	$\mathbf{0.750}_{\pm 0.264}$	38.0%	6.9
8	$0.730_{\pm 0.271}$	40.0%	6.1
10	$0.742_{\pm 0.277}$	36.4%	5.8
20	$0.740_{\pm 0.270}$	42.4%	8.3

Appendix

Table 16: Effect of block size

B

on best layout score, constraint compliance rate, and mean number of iterations to comply. Fixed hyperparameters:

N{=}4

K{=}8

W{=}6

T_{\max}{=}20

	AGG			CS			RE
Comparison	$\bm{\Delta}$	95% CI	$\bm{p_{\mathrm{Holm}}}$	$\bm{\Delta}$	95% CI	$\bm{p_{\mathrm{Holm}}}$	$\bm{\Delta}$	95% CI	$\bm{p_{\mathrm{Holm}}}$
CANDO-Qwen vs. Qwen-LoRA-ALPS	0.543	[0.497, 0.585]	$<0.001$	0.816	[0.762, 0.864]	$<0.001$	0.281	[0.228, 0.332]	$<0.001$
CANDO-GPT vs. Qwen-LoRA-ALPS	0.527	[0.473, 0.578]	$<0.001$	0.768	[0.697, 0.835]	$<0.001$	0.289	[0.237, 0.341]	$<0.001$
CANDO-Qwen vs. LayoutDM	0.491	[0.451, 0.529]	$<0.001$	0.822	[0.770, 0.870]	$<0.001$	0.170	[0.120, 0.220]	$<0.001$
CANDO-GPT vs. LayoutDM	0.475	[0.429, 0.522]	$<0.001$	0.774	[0.704, 0.839]	$<0.001$	0.178	[0.127, 0.229]	$<0.001$
CANDO-Qwen vs. LayoutPrompter	0.451	[0.416, 0.484]	$<0.001$	0.824	[0.772, 0.872]	$<0.001$	0.088	[0.050, 0.127]	$0.0005$

Appendix

Table 17: Paired significance tests on ALPS-Bench

\mathcal{D}^{\text{test}}

(

N{=}100

) using two-sided Wilcoxon signed-rank tests with Holm correction and paired-bootstrap

95\%

confidence intervals.

\Delta

denotes the mean paired difference (first method minus second).

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