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CityDeploy-Bench: Benchmarking Physics-Grounded Spatial Set Planning for Multi-Transmitter Network Deployment

Chenyang Yuan, Xiaoyuan Cheng

arXiv:2610.11065v1cs.LG

TL;DR

City-scale wireless deployment must account for urban propagation and interference, so individually strong transmitter sites may not form a good network. CityDeploy-Bench evaluates coordinated transmitter sets with a shared ray-tracing verifier and separates utility representation from planning dynamics. Its findings show that as physical coupling grows, deployment quality depends increasingly on representing collective interactions, and stronger search alone cannot compensate for missing relational structure.

  • Problem

    Urban geometry, propagation, and interference make city-scale wireless deployment a coordination problem over transmitter sets rather than independent site choices.

    Source: §1 · p. 2

  • Method

    CityDeploy-Bench combines ray-tracing-based service evaluation with learned set-level utility models and diverse planners, separating utility representation from planning dynamics.

    Source: §1 · pp. 2–3

  • Results

    As physical coupling grows, useful relational structure becomes more important, but its order is not universally maximal and stronger search cannot fully compensate for missing interactions.

    Source: §1 · p. 3

  • Takeaways & Limitations

    Multi-transmitter deployment is a coordination problem over physically interacting sets, and evaluation should distinguish peak quality, reliable service attainment, and infrastructure cost.

    Source: §4.2 · p. 8, §5 · p. 9

    Scene-level separation is not evidence of unseen-city generalization unless the complete target city is excluded from base training.

    Source: §4.2 · p. 9

Abstract

from arXiv · show

Automating city-scale wireless deployment remains challenging under complex urban propagation and network-wide interference. We introduce \textbf{CityDeploy-Bench}, a benchmark that reframes multi-transmitter deployment as \emph{physics-grounded spatial set planning} under a unified ray-tracing verifier. The benchmark separates utility representation from planning dynamics, enabling controlled comparison between direct scalar rewards, relational models, and higher-order interaction structures across diverse planners. Our experiments reveal a clear transition in planning behavior as physical coupling grows. Deployment quality becomes increasingly dependent on whether the learned utility captures collective transmitter interactions, whereas stronger search alone cannot compensate for missing relational structure. This establishes multi-transmitter deployment as a coordination problem over physically interacting sets rather than a collection of independent spatial decisions. We release CityDeploy-Data and the benchmark framework as a reproducible testbed for research linking decision learning with physically grounded wireless network design.

1 INTRODUCTION

CityDeploy-Bench frames city-scale wireless deployment as planning coordinated transmitter sets under physical verification, and separates utility representation from planning dynamics. Its findings connect deployment difficulty to physical coupling and show that representation, search, reliability, and infrastructure efficiency must be considered together.

Unified formulation

  • CityDeploy-Bench formulates deployment as physics-grounded spatial set planning, where each transmitter’s utility depends on the complete set through reassignment, redundancy, and interference.The benchmark uses a common ray-tracing-based service utility and executable road-constrained action space.Source: §1 · pp. 2–3

Motivation

  • Existing automatic wireless-planning studies vary in environments, physical verification, objectives, and metrics, making it difficult to isolate whether gains come from planners, rewards, settings, or protocols.Urban geometry and network-wide interference make coordinated deployment costly to design through expert iteration and repeated ray-tracing validation.Source: §1 · p. 2

Benchmark design

  • The benchmark separates learned utility representation from planning dynamics to compare how relational structure and inference interact under common physical verification.It includes pooled, pairwise, latent-relational, and higher-order hypergraph utilities, alongside nine planners spanning score-based search, Monte Carlo inference, and derivative-free optimization.Source: §1 · pp. 2–3

Mechanistic findings on multi-TX planning

  • Deployment difficulty depends on physical coupling rather than transmitter count alone, and relational order, search compatibility, and peak quality each have distinct limits.Densification can shift scenes from coverage-limited to interference-limited; high peak coverage does not guarantee target attainment or infrastructure efficiency.Source: §1 · p. 3

Evaluation

  • The benchmark evaluates simulator-verified joint and marginal service, planning and infrastructure efficiency, seed stability, and geographic transfer or adaptation under consistent constraints.This supports comparison beyond a single scene, objective, or optimization paradigm.Source: §1 · p. 3

2 PROBLEM FORMULATION

The formulation treats deployment as choosing feasible unordered transmitter sets and scoring their joint service through ray tracing. Learned utility surrogates and planners share a common interface, while their relational structure and search dynamics remain separately testable.

2.1 MULTI-TX DEPLOYMENT AND SERVICE UTILITY

  • For a scene, a deployment is an unordered set of N transmitter locations on deployable roads, with at least 20 m separation between sites.Feasible sets are constrained to the scene’s road domain.Source: §2.1 · p. 3
  • The ray-tracing operator evaluates the complete feasible transmitter set, combining strongest-power serving association with full-frequency-reuse interference to define joint-metric coverage over road cells.Coverage is assessed against fixed service thresholds; because association and interference depend on the set, utility need not improve monotonically with transmitter count.Source: §2.1 · p. 3
  • Figure 2 summarizes the pipeline from urban scenes and feasible transmitter sets through full-set ray-tracing evaluation to constrained planning for joint service coverage.The figure identifies Sionna RT as the evaluator accounting for propagation, serving association, and interference.Source: Figure 2 · p. 4

2.2 LEARNED UTILITY REPRESENTATIONS

  • The learned utility predictor is permutation-invariant, taking a rasterized scene representation and normalized transmitter coordinates as inputs.Direct utility evaluation is expensive because each query requires ray tracing.Source: §2.2 · p. 4
  • Four utility models span increasing relational structure: pooled independent features, pairwise message passing, learned latent relations, and higher-order subset potentials.The hypergraph model’s learned potentials are a predictive decomposition, not an assumed one-to-one mapping to physical interaction energies.Source: §2.2 · p. 4

2.3 REWARD-GUIDED PLANNING

  • All planners use a shared penalized utility score and a common selection-and-repair operator before final simulator verification.Ray-tracing outputs are not used to rerank candidates during search; planners include annealed score-based, Monte Carlo, and derivative-free methods.Source: §2.3 · pp. 4–5
  • Figure 3 describes dataset composition through representative urban morphologies, building and deployable-road fractions across 60 scenes and three scales, and deployment counts by active transmitter number.The caption reports 54,193 unique deployments.Source: Figure 3 · p. 5

3 BENCHMARKS

CityDeploy-Bench pairs geographically diverse urban scenes with constrained set-valued planning and a common physical verifier. CityDeploy-Data supplies dense deployment responses, while benchmark tasks assess fixed-budget service, target attainment, and transfer or adaptation.

3 BENCHMARKS

  • CityDeploy-Bench combines realistic urban geometry, jointly simulated wireless interactions, scene-specific constraints, set-valued objectives, and a common physical verifier.Figure 2 summarizes the benchmark pipeline.Source: §3 · p. 5

3.1 CITYDEPLOY-DATA

  • CityDeploy-Data contains 54,193 deployments across 60 scenes in six cities at 128, 256, and 512 m scales, with aligned geometry, semantic and radio-material maps, roads, and receiver grids.Deployments span multiple transmitter cardinalities and are evaluated through the common ray-tracing pipeline.Source: §3.1 · p. 5
  • Each deployment has dense path-loss, SS-RSRP, SINR, and effective-throughput responses and service labels recomputed for the complete active transmitter set.Geographically overlapping regions are grouped before partitioning to prevent spatial leakage.Source: §3.1 · p. 5

3.2 BENCHMARK TASKS

  • Fixed-cardinality planning measures simulator-verified joint-metric coverage, marginal service coverages, and planning cost for a prescribed transmitter count.The task measures use of a fixed infrastructure budget.Source: §3.2 · pp. 5–6
  • Target-coverage planning searches transmitter counts in ascending order and stops at the first simulator-verified success, reporting success rate, count, peak coverage, and cumulative cost.Because each cardinality search is approximate, the returned count is the first successful tested count, not a claimed global minimum.Source: §3.2 · p. 6
  • Transfer evaluation tests zero-shot utility models and few-shot or full-pool adaptation on new geographic scenes, keeping adaptation and evaluation deployments disjoint.City-level generalization is claimed only when the complete target city is excluded from base training.Source: §3.2 · p. 6

4 EXPERIMENTS

The experiments separate utility representation from search strategy and evaluate final deployments with the physical simulator. They find that planning quality depends on matching relational utility structure to physical coupling, while service quality, target reliability, cost, and transfer remain distinct considerations.

4 EXPERIMENTS

  • The benchmark varies utility structure and planning algorithms separately, reports simulator-verified service and planning costs, and aggregates independent random seeds unless stated otherwise.It evaluates pooled, pairwise, latent-relational, and hypergraph utilities with nine search algorithms.Source: §4 · p. 6, §4.1 · p. 6

4.2 FINDINGS

  • 42.44% of 9,320 nested deployment pairs had lower JM coverage after adding a transmitter, despite possible gains in path-loss coverage.The count describes the observed held-out pairs, not a probability over arbitrary deployments.Source: Figure 4 · p. 7, §4.2 · p. 7
  • As physical coupling grows, higher-order utility structure becomes more valuable; generic model capacity alone does not reliably improve utility prediction.Increasing represented interaction order improves verified planning quality at matched inference budgets.Source: §4.2 · pp. 7–8
  • Utility representation and search provide complementary gains: planner responses vary by reward landscape, and greater inference budgets do not erase higher-order advantages.The results identify relational structure and search effort as addressing different bottlenecks.Source: §4.2 · p. 8
  • Planning methods occupy different quality, cost, and seed-sensitivity trade-offs, and several stochastic planners combine high JM coverage with low variation.The quality–efficiency frontier changes with deployment scale; results summarize variation over five seeds.Source: §4.2 · p. 8, Figure 5 · p. 8
  • At the 70% JM target, Diffusion succeeded in all 15 trials with 2.20 ± 0.45 TXs at first success, while TuRBO succeeded in 66.67% despite comparable peak coverage.WS-L reached 93.33% success with the lowest cumulative planning time among high-success methods.Source: §4.2 · p. 8
  • In the 12-TX Paris setting, adaptation improves simulator-verified service, while the 4th-order model stays above pooled and pairwise alternatives across adaptation regimes.Its JM coverage rises from 39.42 ± 2.68% zero-shot to 43.18 ± 2.14% few-shot and 44.72 ± 1.73% with full-pool supervision; these experiments do not establish unseen-city generalization.Source: Table 2 · p. 9, §4.2 · p. 9

5 CONCLUSION

CityDeploy-Bench concludes that multi-TX planning depends on physical coupling and interaction-aware utility, and presents CityDeploy-Data as a reproducible testbed. Its construction links urban scenes and feasible deployments to joint physical evaluation.

5 CONCLUSION

  • Densification shifts planning toward interference-aware coordination, and stronger search cannot fully compensate for missing interactions.The conclusion also reports that useful relational order varies with coupling, while peak coverage does not necessarily imply reliable target attainment or infrastructure efficiency.Source: §5 · p. 9

A CITYDEPLOY-DATA CONSTRUCTION

A.1 GEOGRAPHIC SOURCES AND SCENE CONSTRUCTION

  • Each of six cities contributes ten scenes, built from OpenStreetMap features projected into a local metric frame.Building heights follow available attributes, level counts, or a deterministic building-type prior; material assignments specify the simulation model, not measured composition.Source: §A.1 · p. 13

A.2 SPATIAL COORDINATES AND DEPLOYABLE REGIONS

  • Planning coordinates are normalized to [0, 1]^2, while separation constraints remain in meters and road cells define the deployment and service-evaluation domains.The three scene sizes are 128 × 128, 256 × 256, and 512 × 512 m^2; service evaluation uses the road mask.Source: §A.2 · p. 13

A.3 DEPLOYMENT SAMPLING AND SUBSET FAMILIES

  • Master deployments use uniform, maximin, and clustered sampling at 50%, 30%, and 20%, respectively, with a 20 m separation constraint.Related subsets preserve feasibility, and their service labels are recomputed jointly from the active TXs despite reusing per-TX propagation maps.Source: §A.3 · pp. 13–14

A.4 DATASET COMPOSITION AND GEOGRAPHIC SPLITS

The appendix documents dataset composition and geographic splits, then specifies the radio simulation and received-power calculations used to produce service labels.

A.4 DATASET COMPOSITION AND GEOGRAPHIC SPLITS

  • 54,193 unique scene–deployment records and 54,900 family memberships are retained, with duplicate physical deployments stored once and their family links preserved.The records span deployment cardinalities N = 1 through 9.Source: §A.4 · p. 14

A.5 SAMPLE SCHEMA AND DATA INTEGRITY

  • Geographic overlap groups are kept within a single split, so the partition tests held-out areas within included cities rather than whole-city transfer.The authors state that holding out an entire city requires a separate partition; records retain simulation provenance and service maps.Source: §A.4 · p. 14, §A.5 · p. 14

B WIRELESS SIMULATION AND SERVICE UTILITY

  • The forward operator recomputes received powers, serving association, interference, service maps, and coverage labels for the active TX set.The same definitions apply to dataset construction and simulator evaluation of planned deployments.Source: B WIRELESS SIMULATION AND SERVICE… · p. 15

B.1 RADIO AND PROPAGATION CONFIGURATION

  • Ray tracing uses a fixed radio profile, including 10 m TX height, 1.5 m receiver height, and shared carrier and bandwidth across active TXs.The setup uses Sionna RT with specified propagation mechanisms, scattering coefficients, and a recorded software version.Source: §B.1 · p. 15, Table 5 · p. 15

B.2 RECEIVED POWER AND SERVING ASSOCIATION

  • Each TX’s received power is its transmit power times propagation gain, and the serving TX is selected by maximum received power.Path loss and wideband received power are then calculated from the serving gain and power; the reference-signal label uses a reproducible subcarrier power conversion.Source: §B.2 · p. 15

B.3 INTERFERENCE AND SERVICE METRICS

The benchmark defines service through interference-aware radio metrics and joint coverage, then reviews planning and utility representations for multi-TX deployment. The related work progresses from search methods to interaction-aware models.

B.3 INTERFERENCE AND SERVICE METRICS

  • Every non-serving active TX contributes co-channel interference, and effective throughput is a capped Shannon-based proxy with a configured maximum of 39 Mbps.The proxy uses fixed efficiency and resource-share assumptions, not traffic-dependent scheduling or user load.Source: §B.3 · pp. 15–16

B.4 COVERAGE LABELS AND JOINT SERVICE UTILITY

  • JM coverage is the fraction of road cells passing all four service tests jointly, not a product or average of the marginal fractions.Under the chosen profile and thresholds, the valid-cell joint criterion reduces to path loss ≤106 dB and SINR ≥5 dB; this equivalence is profile-specific.Source: §B.4 · p. 16

C.1 OPTIMIZATION-BASED MODELS

  • Optimization and heuristic baselines search deployment configurations directly, while surrogate-based Bayesian optimization and TuRBO aim to improve evaluation efficiency or scale search.Their effectiveness depends on repeated objective evaluations resolving fragmented, coupled configuration spaces.Source: §C.1 · p. 17

C.2 MONTE CARLO SAMPLING

  • Monte Carlo planners explore utility-induced target distributions through weighted particles, importance sampling, or Hamiltonian dynamics.Their inference remains governed by the utility distribution defined by the underlying reward.Source: §C.2 · p. 17

C.3 DIFFUSION SAMPLING

  • Diffusion planners iteratively refine stochastic solutions, with reward- or energy-guided variants steering the reverse process toward objectives or physical constraints (Ubukata et al., 2024).Prior wireless-planning work reports that deployment quality can be limited by reward-estimation accuracy (Yuan & Cheng, 2026).Source: §C.3 · p. 17

C.4 RELATIONAL GRAPH AND STRUCTURED REWARD MODELING

  • Relational models encode transmitter interactions, while hypergraphs extend pairwise relations to collective effects and higher-order utility structures (Feng et al., 2019).The open question is which interaction structure suits different urban environments and deployment scales.Source: §C.4 · p. 17

D UTILITY MODELS AND TRAINING DETAILS

The appendix specifies scene and TX-set inputs, set-pooled and relational predictors, and a hypergraph energy model, followed by training objectives, configurations, and target-scene adaptation details.

D.1 SCENE AND TX-SET INPUTS

  • Scene rasters provide 11 channels, while normalized TX coordinates are paired with local scene features, global context, physical dimensions, and cardinality.An active-TX mask excludes padding from mean and maximum reductions.Source: §D.1 · p. 18

D.2 SET-POOLED AND RELATIONAL PREDICTORS

  • The Reward predictor pools TX embeddings, while IN and NRI add learned pairwise relation features and message aggregation.NRI predicts latent relation types without observed physical labels; its evaluation predictions use deterministic softmax probabilities.Source: §D.2 · pp. 18–19

D.3 HYPERGRAPH POTENTIAL ENERGY MODEL

  • HPEM represents singleton and higher-order TX subsets with symmetric features, aggregates order-specific energies, and predicts utility as −Eθ.Its base model enables orders 1–4; auxiliary heads predict JM, path-loss, SS-RSRP, SINR, and effective-throughput coverage.Source: §D.3 · p. 19

D.4 TRAINING OBJECTIVES AND SAMPLING

  • HPEM combines utility regression, ranking, and auxiliary coverage supervision, while Reward and IN use MSE and NRI adds a regularizer toward uniform relation-type probabilities.Ranking compares within-batch deployment pairs at a common scene and cardinality; family-membership expansion changes HPEM sample weights.Source: §D.4 · pp. 19–20

D.5 BASE-MODEL CONFIGURATION

  • Base models use AdamW with saved-run settings including seed 42, batch size at most 32, gradient clipping at 5, and a maximum of 100 epochs.HPEM uses cosine learning-rate decay and total-validation-objective checkpoint selection; other predictors use validation-MSE plateau scheduling and early stopping.Source: §D.5 · p. 20, Table 8 · p. 20

D.6 TARGET-SCENE ADAPTATION

  • Target-scene adaptation updates all parameters using base losses, first on 297 examples for 30 epochs and then on all 990 examples for 70 more epochs.The pool is separate from 200 evaluation examples; checkpoints are saved at stage end without evaluation-based selection.Source: §D.6 · p. 20

E PLANNING ALGORITHMS AND IMPLEMENTATION

The appendix specifies a shared utility-and-search interface, planner procedures, feasibility handling, and protocols for evaluating deployments and visualizing urban scenes. It distinguishes learned search scores from simulator-verified service and documents constraints that affect comparisons.

E.1 SHARED PLANNING INTERFACE AND CONSTRAINTS

E.2 DIFFUSION-BASED PLANNING

  • The diffusion planner derives a score from learned utility gradients, applies decreasing noise scales, and retains the best visited state without guaranteeing exact sampling.Its score uses Gaussian perturbations and does not require a separately trained denoiser.Source: §E.2 · p. 21

E.3 MONTE CARLO PLANNING

  • Monte Carlo planners include annealed particle methods with Gaussian or Langevin mutations, NUTS in logit coordinates, and BR-SNIS resampling that returns a concrete candidate.BR-SNIS selects among the retained deployment and new uniform proposals using probabilities proportional to exp(βrS).Source: §E.3 · p. 22

E.4 DERIVATIVE-FREE OPTIMIZATION

  • Derivative-free search includes beam-based Greedy construction, PSO, a genetic algorithm, and TuRBO, each proposing and updating deployments through different search procedures.Greedy queries utility on partial as well as complete deployments; TuRBO uses a Gaussian-process trust region.Source: §E.4 · p. 22

E.5 CANDIDATE SELECTION AND FEASIBILITY REPAIR

  • Candidate selection maps scored coordinates to road locations, checks distinctness and minimum separation, and uses a finite repair heuristic when direct mapping fails.The repair heuristic need not find the globally nearest feasible deployment; simulator outcomes do not rerank candidates.Source: §E.5 · pp. 22–23

E.6 ALGORITHM CONFIGURATIONS

  • Reference configurations do not imply equal compute budgets, and iteration counts alone do not equate computation across planners.Score evaluations, gradients, and simulator calls are recorded as distinct operations.Source: §E.6 · p. 23, Table 9 · p. 23

F EVALUATION PROTOCOLS AND METRICS

  • Fixed-cardinality evaluation compares verified utility and marginal coverage under matched conditions; target planning reports success alongside TX counts conditional on success.A missing result at a smaller tested count does not establish minimality across that gap.Source: §F.1 · pp. 23–24, §F.2 · p. 24, §F.4 · p. 24

G.1 URBAN SCENE VISUALIZATIONS ACROSS SIX CITIES

  • Transfer records distinguish geographic-group, external, and held-out scenes, while the visualization appendix shows aligned city imagery and individual planner deployments with radio maps.Continuous metric maps retain per-panel color scales, so their numerical colorbars should be consulted for comparisons.Source: §F.3 · p. 24, §G.1 · p. 24, §G.2 · p. 31

H SIMULATION RESULTS WITH FIXED TX NUMBER

The supplied tables compare performance across TX deployment scales in three city scenes and report mean±std, highlighting the top three and worst results for each evaluation metric.

H SIMULATION RESULTS WITH FIXED TX NUMBER

  • Table 10 compares deployment scales in a 128 m × 128 m Sydney scene and reports mean±std with top-three and worst results marked for each metric.The supplied passage does not identify the table’s metric columns or values.Source: Table 10 · p. 38
  • Table 11 compares deployment scales in a 256 m × 256 m Paris scene and reports mean±std with top-three and worst results marked for each metric.The supplied passage does not identify the table’s metric columns or values.Source: Table 11 · p. 39
  • Table 12 compares deployment scales in a 512 m × 512 m Tokyo scene and reports mean±std with top-three and worst results marked for each metric.The supplied passage does not identify the table’s metric columns or values.Source: Table 12 · p. 40

I SIMULATION RESULTS WITH TARGET JM COVERAGE

The target-coverage tables report HPEM planning metrics for three fixed-scene targets, while the cross-city tables compare adaptation regimes and relational models. Their accompanying descriptions report benefits from few-shot adaptation and higher-order modeling, with transfer and complexity varying by setting.

I SIMULATION RESULTS WITH TARGET JM COVERAGE

  • The HPEM target-coverage tables report TX count, success rate, best joint coverage, per-metric coverage, and runtime over 15 trials in Shanghai, New York, and London.The targets are 85%, 75%, and 55% joint coverage, respectively.Source: Table 13 · p. 41, Table 14 · p. 41, Table 15 · p. 42

J ENERGY MODEL PERFORMANCE WITH A FIXED NUMBER OF TXS

  • Across fixed-TX cross-city tests, few-shot adaptation narrows transfer gaps, while higher-order relational models improve coverage with moderately increased inference time.In the Tokyo and Paris settings, greater scene complexity is associated with lower joint coverage and more pronounced transfer gaps; few-shot adaptation recovers some of the gap.Source: Table 16 · p. 43, Table 17 · p. 43, Table 18 · p. 44

K ENERGY MODEL PERFORMANCE WITH TARGET JM COVERAGE

  • In cross-city target-coverage tests, higher targets require more TXs and longer planning time, while few-shot adaptation reduces transfer gaps and in-distribution evaluation performs strongest overall.The London and Shanghai descriptions report lower success and more required TXs in more complex settings, especially at aggressive targets.Source: Table 19 · p. 45, Table 20 · p. 46, Table 21 · p. 47

L ABLATION STUDIES

The ablations show that useful utility representation depends on physical coupling, while model capacity and search effort do not improve planning uniformly. As TX density and interaction grow, service trade-offs and representation preferences shift across deployment regimes.

L.1 POTENTIAL MODEL CAPACITY

  • The 256/64 potential configuration yields the lowest error across five service targets, while further enlarging the hypernetwork degrades prediction despite similar runtime.The result suggests capacity allocation matters more than parameter count alone.Source: §L.1 · p. 48

L.2 INFERENCE BUDGET AND INTERACTION ORDER

  • Higher interaction order consistently improves coverage across tested budgets, with a larger gap at greater budgets; particles or sampling steps also improve coverage within each order.The higher-order advantage persists at matched inference budgets, indicating it is not solely attributable to stronger search.Source: §L.2 · p. 48, Table 23 · p. 49

M.2 SENSITIVITY TO UTILITY REPRESENTATION

  • The preferred utility representation changes with deployment regime: relational models can compete at low TX cardinality, while higher-order structure becomes more useful under stronger coupling.The same reward replacement can help one planner but offer little gain to another.Source: §M.2 · p. 48

M.1 PHYSICAL SCALING AND SERVICE COUPLING

  • Additional TXs generally improve serving-link coverage, but SINR and JM responses vary by scene as co-channel interference can offset coverage gains in compact deployments.Larger regions can remain predominantly coverage-limited over the evaluated TX range.Source: §M.1 · p. 48, Figure 18 · p. 49

M.3 QUALITY, EFFICIENCY, AND STABILITY

Planning methods trade off simulator-verified JM coverage and time differently across deployment scales. Several sampling methods also combine high average coverage with relatively small variation across random seeds.

M.3 QUALITY, EFFICIENCY, AND STABILITY

  • Several sampling methods combine high average JM coverage with relatively small variation across random seeds, so stochastic search does not necessarily imply unstable outcomes.The results motivate evaluating methods jointly by quality, cost, and stability rather than on a single performance axis.Source: §M.3 · pp. 49–50
  • The empirical quality–efficiency Pareto frontier changes with deployment scale: fast local procedures remain competitive in simpler settings, while structured stochastic exploration is more valuable under stronger coupling.Figure 20 compares median planning time with mean simulator-verified JM coverage.Source: §M.3 · p. 49, Figure 20 · p. 50
  • Figure 20 plots mean simulator-verified JM coverage against median planning time on a logarithmic scale across six cities, four utility representations, and five random seeds.Source: Figure 20 · p. 50
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