Multi-Agent Training-free Urban Food Delivery System using Resilient UMST Network

Aditya Challa; Md Nahid Hasan; Snehanshu Saha; Vaskar Raychoudhury; Vishwam Tiwari

arxiv: 2604.03280 · v1 · submitted 2026-03-24 · 💻 cs.MA · cs.LG

Multi-Agent Training-free Urban Food Delivery System using Resilient UMST Network

Md Nahid Hasan , Vishwam Tiwari , Aditya Challa , Vaskar Raychoudhury , Snehanshu Saha This is my paper

Pith reviewed 2026-05-15 00:30 UTC · model grok-4.3

classification 💻 cs.MA cs.LG

keywords urban food deliveryunion of minimum spanning treesresilient networksorder bundlingmulti-agent systemstraining-free optimizationgraph-based routing

0 comments

The pith

Union of Minimum Spanning Trees produces sparse resilient graphs that support high bundling rates and match trained multi-agent systems without any learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Union of Minimum Spanning Trees to build delivery networks that stay efficient at urban scale while staying robust to road closures and demand shifts. Fully connected graphs offer many routes but become too slow to compute, while a single MST is fast yet breaks easily when one link fails. UMST instead runs multiple MST calculations after small random changes to edge weights and combines the results into one graph. Tests across U.S. cities show this yields 20 to 40 times fewer edges than complete graphs, supports 75 to 83 percent order bundling, and still reaches 88 to 96 percent delivery success with 44 to 53 percent distance reduction. The same networks run about 30 times faster than reinforcement-learning baselines and need no training data or model fitting.

Core claim

The central claim is that uniting several minimum spanning trees generated from randomized edge perturbations creates a graph family that is both sparse enough for fast multi-agent routing and redundant enough to keep multiple disjoint paths between delivery hotspots, yielding performance comparable to trained MADDPG and graph-neural baselines while remaining fully interpretable and training-free.

What carries the argument

Union of Minimum Spanning Trees (UMST), formed by generating multiple MSTs through randomized edge perturbations and taking their union to enforce sparsity together with path redundancy.

If this is right

20-40 times fewer edges than fully connected graphs while retaining multiple routes between hotspots.
75-83 percent participation in order bundling across tested U.S. cities.
88-96 percent success rates and 44-53 percent distance savings in delivery execution.
30 times faster execution than MADDPG and GNN baselines with no training required.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same perturbation-union construction could be applied to other multi-agent routing domains where training data is limited or environments change frequently.
Because the resulting graphs remain human-readable, operators could manually inspect or adjust routes in ways black-box learned policies do not allow.
The absence of training suggests the method may adapt instantly to new city maps or sudden demand spikes without retraining delays.

Load-bearing premise

Randomized edge perturbations will reliably produce a union of MSTs that preserves both extreme sparsity and multiple disjoint paths across varied real-world city layouts and disruption patterns without needing per-city adjustments.

What would settle it

A city-scale experiment in which the resulting UMST graph either exceeds 40 times the edge count of a single MST or loses connectivity under typical accident or closure scenarios would falsify the claim of reliable resilience.

Figures

Figures reproduced from arXiv: 2604.03280 by Aditya Challa, Md Nahid Hasan, Snehanshu Saha, Vaskar Raychoudhury, Vishwam Tiwari.

**Figure 2.** Figure 2: Average completion time vs. success rate in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Vehicle distance vs. success rate in Chicago under [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

read the original abstract

Delivery systems have become a core part of urban life, supporting the demand for food, medicine, and other goods. Yet traditional logistics networks remain fragile, often struggling to adapt to road closures, accidents, and shifting demand. Online Food Delivery (OFD) platforms now represent a cornerstone of urban logistics, with the global market projected to grow to over 500 billion USD by 2030. Designing delivery networks that are efficient and resilient remains a major challenge: fully connected graphs provide flexibility but are computationally infeasible at scale, while single Minimum Spanning Trees (MSTs) are efficient but easily disrupted. We propose the Union of Minimum Spanning Trees (UMST) approach to construct delivery networks that are sparse yet robust. UMST generates multiple MSTs through randomized edge perturbations and unites them, producing graphs with far fewer edges than fully connected networks while maintaining multiple alternative routes between delivery hotspots. Across multiple U.S. cities, UMST achieves 20--40$\times$ fewer edges than fully connected graphs while enabling substantial order bundling with 75--83% participation rates. Compared to learning-based baselines including MADDPG and Graph Neural Networks, UMST delivers competitive performance (88-96% success rates, 44-53% distance savings) without requiring training, achieving 30$\times$ faster execution while maintaining interpretable routing structures. Its combination of structural efficiency and operational flexibility offers a scalable and resilient foundation for urban delivery networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

UMST builds sparse resilient delivery graphs via perturbed MST unions but the performance claims rest on thin experimental details.

read the letter

The main point is that this paper gives a straightforward graph construction for urban food delivery: generate several MSTs after random edge perturbations, then take their union to get networks with far fewer edges than complete graphs yet enough alternate paths for resilience. It reports 20-40x edge savings, 75-83% order bundling, 88-96% success rates, and 44-53% distance savings across U.S. cities, all without training and 30x faster than MADDPG or GNN baselines. That combination of simplicity and reported speed is the practical hook. The construction itself is new enough in this setting; it is not just a single MST or a full graph, and the union step trades off sparsity against redundancy in a way that fits the multi-agent delivery problem directly. The paper does well at showing the method stays interpretable and avoids the training overhead of learning approaches, which matters for real deployment where retraining on new cities is costly. The soft spots sit in the experimental grounding. The abstract gives headline numbers but supplies no concrete description of the perturbation distribution, the exact number of MSTs in the union, or how those choices were fixed versus tuned to the test cities. Without that, it is unclear whether the randomization reliably produces the claimed disjoint paths on varied topologies or if the parameters were selected post-hoc to match the reported results. The baseline comparisons also lack protocol details such as how the learning methods were implemented or whether statistical tests back the gains. If the perturbation strength needs city-specific adjustment to avoid under-connectivity or excess density, the training-free selling point weakens. This work is for applied researchers and engineers building logistics systems who need a fast, non-ML starting point for resilient routing. A reader focused on graph algorithms for multi-agent coordination would find the construction worth examining even if the numbers require verification. I would send it to peer review because the idea is constructive and the claimed advantages are concrete enough to test with fuller methods and ablations.

Referee Report

2 major / 2 minor

Summary. The paper proposes the Union of Minimum Spanning Trees (UMST) method to construct sparse yet resilient delivery networks for multi-agent urban food delivery. Multiple MSTs are generated via randomized edge perturbations and united to yield graphs with far fewer edges than complete graphs while providing alternative paths for robustness. Across U.S. cities the approach is claimed to deliver 20-40x edge reduction, 75-83% order bundling participation, 88-96% success rates, 44-53% distance savings, and 30x faster execution than trained MADDPG and GNN baselines, all without any training or city-specific tuning.

Significance. If the central claims hold, UMST would supply a scalable, interpretable, training-free alternative to multi-agent reinforcement learning for resilient urban logistics, offering substantial computational savings and structural guarantees that could be directly deployed on real road networks.

major comments (2)

[Experimental Evaluation] Experimental Evaluation section: the manuscript reports 88-96% success rates and 75-83% bundling rates but supplies no information on the number of trials, statistical tests, exact parameterization of edge perturbations and disruption scenarios, or precise re-implementations of the MADDPG and GNN baselines, preventing assessment of whether the numbers depend on post-hoc choices.
[UMST Construction] UMST Construction procedure: the only free parameters (number of MSTs in the union and edge perturbation distribution) are presented as fixed and city-independent, yet no sensitivity analysis or cross-city validation demonstrates that the same values simultaneously preserve both the 20-40x sparsity claim and sufficient disjoint paths when the underlying road topology or demand pattern changes.

minor comments (2)

[Abstract] Abstract: the phrase 'multiple U.S. cities' is used without naming the specific cities or citing the source road-network datasets.
[Notation] Notation: define 'success rate' and 'distance savings' explicitly before the results tables to avoid ambiguity when comparing to baselines.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight opportunities to strengthen reproducibility and robustness in our work. We address each major comment below and will revise the manuscript accordingly to incorporate the requested details and analyses.

read point-by-point responses

Referee: [Experimental Evaluation] Experimental Evaluation section: the manuscript reports 88-96% success rates and 75-83% bundling rates but supplies no information on the number of trials, statistical tests, exact parameterization of edge perturbations and disruption scenarios, or precise re-implementations of the MADDPG and GNN baselines, preventing assessment of whether the numbers depend on post-hoc choices.

Authors: We agree that additional experimental details are essential for reproducibility. In the revised manuscript, we will expand the Experimental Evaluation section to report: (i) the number of independent trials (100 runs per city and scenario), (ii) statistical tests including paired t-tests with p-values confirming significance of differences versus baselines, (iii) exact edge perturbation parameterization (uniform multiplicative factors drawn from [0.8, 1.2] applied to road weights), (iv) disruption scenarios (random edge removals at rates of 5%, 10%, and 20% to simulate closures), and (v) precise baseline re-implementations, including MADDPG actor-critic architectures, learning rates, and GNN layer configurations with training epochs used to match our evaluation protocol. These additions will substantiate the reported metrics without altering the core results. revision: yes
Referee: [UMST Construction] UMST Construction procedure: the only free parameters (number of MSTs in the union and edge perturbation distribution) are presented as fixed and city-independent, yet no sensitivity analysis or cross-city validation demonstrates that the same values simultaneously preserve both the 20-40x sparsity claim and sufficient disjoint paths when the underlying road topology or demand pattern changes.

Authors: The parameters (5 MSTs with the stated perturbation range) were selected via preliminary tuning to balance sparsity and resilience across the evaluated U.S. cities while remaining fixed and untuned per city. We acknowledge the need for explicit validation. The revision will add a dedicated sensitivity analysis subsection varying the number of MSTs (3–8) and perturbation strength, reporting resulting edge counts (still achieving 20–40× reduction), success rates, and average disjoint paths. We will also include cross-city consistency checks on the tested topologies and discuss any observed variations, thereby demonstrating that the fixed parameters maintain the claimed properties under moderate topology changes. revision: yes

Circularity Check

0 steps flagged

No significant circularity in UMST construction or performance claims

full rationale

The paper defines UMST explicitly as the union of multiple MSTs obtained via randomized edge perturbations, which is a direct constructive procedure built from standard MST algorithms (Kruskal/Prim) and set-union operations. All reported metrics (edge reduction, bundling rates, success rates, distance savings) are presented as empirical outcomes from simulations on real U.S. city graphs rather than quantities derived by solving equations that reference the same metrics. No self-citation is used to justify uniqueness or to close a definitional loop, and the randomization parameters are described as fixed rather than fitted to the target results. The derivation chain therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method rests on standard graph algorithms with the key step being randomized perturbation and union; no new physical entities are introduced.

free parameters (2)

number of MSTs in union
Chosen to balance sparsity and robustness; specific value and selection procedure not stated in abstract.
edge perturbation distribution
Randomized perturbations are central to generating diverse MSTs; variance or distribution parameters unspecified.

axioms (1)

domain assumption Randomized edge perturbations produce sufficiently diverse MSTs whose union yields multiple alternative routes between hotspots.
Invoked to justify resilience without explicit verification in the abstract.

pith-pipeline@v0.9.0 · 5580 in / 1322 out tokens · 42278 ms · 2026-05-15T00:30:58.988732+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

UMST generates multiple MSTs through randomized edge perturbations and unites them, producing graphs with far fewer edges than fully connected networks while maintaining multiple alternative routes
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

theoretical basis... stretch reduces exponentially as exp(−cK)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

InProceedings of the International Conference on Auto- mated Planning and Scheduling, volume 31, 510–518

Deepfreight: A model-free deep-reinforcement- learning-based algorithm for multi-transfer freight delivery. InProceedings of the International Conference on Auto- mated Planning and Scheduling, volume 31, 510–518. Chen, W.; Mes, M.; and Schutten, M. 2018. Multi-hop driver-parcel matching problem with time windows.Flex- ible services and manufacturing jour...

work page 2018
[2]

Iqbal, S.; and Sha, F

A distributed model-free ride-sharing approach for joint matching, pricing, and dispatching using deep rein- forcement learning.IEEE Transactions on Intelligent Trans- portation Systems, 22(12): 7931–7942. Iqbal, S.; and Sha, F. 2019. Actor-attention-critic for multi- agent reinforcement learning. InInternational Conference on Machine Learning (ICML), 296...

work page 2019

[1] [1]

InProceedings of the International Conference on Auto- mated Planning and Scheduling, volume 31, 510–518

Deepfreight: A model-free deep-reinforcement- learning-based algorithm for multi-transfer freight delivery. InProceedings of the International Conference on Auto- mated Planning and Scheduling, volume 31, 510–518. Chen, W.; Mes, M.; and Schutten, M. 2018. Multi-hop driver-parcel matching problem with time windows.Flex- ible services and manufacturing jour...

work page 2018

[2] [2]

Iqbal, S.; and Sha, F

A distributed model-free ride-sharing approach for joint matching, pricing, and dispatching using deep rein- forcement learning.IEEE Transactions on Intelligent Trans- portation Systems, 22(12): 7931–7942. Iqbal, S.; and Sha, F. 2019. Actor-attention-critic for multi- agent reinforcement learning. InInternational Conference on Machine Learning (ICML), 296...

work page 2019