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arxiv: 2605.20618 · v1 · pith:M5CZOQ4Jnew · submitted 2026-05-20 · 💻 cs.AI

COAgents: Multi-Agent Framework to Learn and Navigate Routing Problems Search Space

Oleksandr Yakovenko , Mahdi Mostajabdaveh , Cheikh Ahmed , Abdullah Ali Sivas , Xiaorui Li , Zirui Zhou , Mao Kun This is my paper

Pith reviewed 2026-05-21 05:21 UTC · model grok-4.3

classification 💻 cs.AI
keywords multi-agent frameworkvehicle routing problempartial search graphcombinatorial optimizationVRPTWsearch intensificationdiversificationlearning-based solver
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The pith

COAgents trains agents on a partial search graph to guide solution search for vehicle routing problems.

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

The paper presents COAgents as a way to solve vehicle routing problems by treating the search for better routes as a graph navigation task. Solutions are nodes in a graph, connected by either small improvements or big changes called jumps. A partial version of this graph is built on the fly while searching, and three agents learn to pick which solution to work on next, which improvement to apply, and when to make a jump to escape poor areas. This setup keeps the learning of how to search separate from the details of the routing problem itself. A sympathetic reader would care because traditional methods need lots of custom rules for each problem type, and this learned approach could make solvers more flexible for real logistics challenges.

Core claim

COAgents is a cooperative multi-agent framework that models the search process as a graph where nodes represent solutions and edges correspond to local refinements or large perturbations for diversification. It dynamically constructs a Partial Search Graph during search to train a Node Selection Agent and a Move Selection Agent for intensification as well as a Jump Agent to trigger explorations of new regions. The framework separates problem-agnostic search control from compact domain-specific encoding to improve adaptability.

What carries the argument

Partial Search Graph (PSG) dynamically built from solutions during search, used to train Node Selection, Move Selection, and Jump agents that control intensification and diversification.

If this is right

  • COAgents sets a new state of the art among learning-based methods on VRPTW instances.
  • Reduces the gap to the best-known solutions by 14% at N=100 and 44% at N=50 relative to POMO.
  • Reduces the gap by 21% at N=100 and 40% at N=50 relative to ALNS.
  • Remains competitive with several learn-to-search baselines on CVRP.
  • The separation of search control from domain encoding supports adaptability across different tasks.

Where Pith is reading between the lines

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

  • The approach could be tested on other combinatorial optimization problems that use local search and diversification strategies.
  • Learned jump timing might help in problems where manual diversification rules are hard to design.

Load-bearing premise

Dynamically constructing a Partial Search Graph and training specialized agents on it will reliably guide both intensification and diversification across diverse VRP instances without needing extensive problem-specific handcrafted rules.

What would settle it

Evaluating COAgents on a fresh collection of VRPTW instances of size 50 and 100 and measuring whether the optimality gap reductions match or exceed the claimed 44% and 14% improvements over POMO would confirm or refute the performance advantage.

Figures

Figures reproduced from arXiv: 2605.20618 by Abdullah Ali Sivas, Cheikh Ahmed, Mahdi Mostajabdaveh, Mao Kun, Oleksandr Yakovenko, Xiaorui Li, Zirui Zhou.

Figure 1
Figure 1. Figure 1: The COAgents which defines how our three agents are collaborating to orches [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of a PSG during the al￾gorithm. s denotes solutions and m are moves. In this study, we propose a method that learns how to guide the exploration of the search space from previous experiences and how to generate jumps during exploration. We will use PSGs to identify patterns in solution exploration and to guide further exploration, improving search efficiency by focusing on unexplored or promising… view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the general architecture of agents [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of optimality gap for a test set of VRPTW instances. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Node & Move Selection training sample. Left: Three PSGs converging from distinct perturbed solutions. Right: A training sample with three sub-graphs sampled from the PSGs on the left with labels. Jump Agent Dataset For our jump model, using the same training instances, we generate multiple trajectories per instance by running ALNS [13] from different random starts until convergence to a local optimum. We r… view at source ↗
read the original abstract

Although Vehicle Routing Problems (VRP) are essential to many real-world systems, they remain computationally intractable at scale due to their combinatorial complexity. Traditional heuristics rely on handcrafted rules for local improvements and occasional \textit{jumps} to escape local minima, but often struggle to generalize across diverse instances. We introduce \textbf{COAgents}, a cooperative multi-agent framework that models the search process as a graph: nodes represent solutions, and edges correspond to either local refinements or large perturbations for diversification (i.e., jumps). A \textit{Partial Search Graph} (PSG) is dynamically constructed during search, enabling COAgents to train a Node Selection Agent and a Move Selection Agent to guide intensification, and a Jump Agent to trigger well-timed explorations of new regions. Unlike end-to-end learning approaches, COAgents cleanly separates problem-agnostic search control from compact domain-specific encoding, facilitating adaptability across tasks. Extensive experiments on the CVRP and VRPTW benchmarks show that COAgents remains competitive with several learn-to-search baselines on CVRP and sets a new state of the art among learning-based methods on the more challenging VRPTW instances, reducing the gap to the best-known solutions by 14\% at $N\!=\!100$ and 44\% at $N\!=\!50$ relative to the strongest neural solver (POMO), and by 21\% and 40\% respectively relative to ALNS. Code is available at https://github.com/mahdims/COAgents.

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.

Referee Report

3 major / 2 minor

Summary. The paper introduces COAgents, a cooperative multi-agent framework for routing problems that dynamically constructs a Partial Search Graph (PSG) during search. Nodes represent solutions and edges represent local moves or jumps; three specialized agents (Node Selection, Move Selection, and Jump) are trained to guide intensification and diversification. The approach separates problem-agnostic search control from domain encoding. Experiments on CVRP and VRPTW benchmarks claim competitiveness with learn-to-search baselines on CVRP and new state-of-the-art results among learning-based methods on VRPTW, with gap reductions to best-known solutions of 14% (N=100) and 44% (N=50) versus POMO and 21%/40% versus ALNS.

Significance. If the empirical claims hold under matched budgets and proper controls, the clean separation of search control from domain encoding and the multi-agent PSG mechanism could provide a more generalizable alternative to end-to-end neural solvers for combinatorial optimization. The open-source code is a positive contribution that aids reproducibility. However, the significance is currently limited by the absence of detailed experimental protocols needed to confirm that gains arise from the proposed framework rather than unequal computational resources.

major comments (3)
  1. [Abstract / Experiments] Abstract and experimental results section: The headline SOTA claims (14% gap reduction at N=100 and 44% at N=50 versus POMO on VRPTW) are presented without any reported details on the number of independent runs, statistical significance tests, variance across instances, or hyperparameter tuning protocol. This information is load-bearing for verifying that the reported improvements are robust and not the result of post-hoc selection or favorable random seeds.
  2. [Method / Experiments] Method and experimental sections: No ablation is described that disables the Jump Agent while retaining the Node/Move Selection agents on the PSG. Without this control, it is impossible to isolate whether the cooperative multi-agent structure (rather than any competent search procedure given extra budget) is responsible for the claimed diversification benefits and gap reductions.
  3. [Experiments] Experiments section: The manuscript does not report explicit matching of search budgets (total local moves, perturbation frequency, wall-clock time, or function evaluations) against the POMO and ALNS baselines. Because the framework description emphasizes problem-agnostic control, the absence of such controls leaves open the possibility that any search procedure with equivalent extra effort could achieve similar gap closures.
minor comments (2)
  1. [Method] The notation distinguishing the three agents and the PSG construction steps would benefit from an explicit diagram or pseudocode listing in the method section to improve readability.
  2. [Abstract / Introduction] A few sentences in the abstract and introduction repeat the same performance numbers; consolidating them would reduce redundancy.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments highlight important aspects of experimental rigor that will improve the manuscript. We respond to each major comment below and indicate the planned revisions.

read point-by-point responses

  1. Referee: [Abstract / Experiments] Abstract and experimental results section: The headline SOTA claims (14% gap reduction at N=100 and 44% at N=50 versus POMO on VRPTW) are presented without any reported details on the number of independent runs, statistical significance tests, variance across instances, or hyperparameter tuning protocol. This information is load-bearing for verifying that the reported improvements are robust and not the result of post-hoc selection or favorable random seeds.

    Authors: We agree that these details are essential for substantiating the claims. In the revised manuscript we will report the number of independent runs, include standard deviations and variance across instances, add statistical significance tests (such as paired t-tests or Wilcoxon tests), and describe the hyperparameter tuning protocol in the Experiments section. revision: yes

  2. Referee: [Method / Experiments] Method and experimental sections: No ablation is described that disables the Jump Agent while retaining the Node/Move Selection agents on the PSG. Without this control, it is impossible to isolate whether the cooperative multi-agent structure (rather than any competent search procedure given extra budget) is responsible for the claimed diversification benefits and gap reductions.

    Authors: This is a fair request to isolate component contributions. We will add an ablation study in the revised Experiments section in which the Jump Agent is disabled while retaining the Node Selection and Move Selection agents on the PSG, and we will report the resulting performance to demonstrate the Jump Agent's role in diversification. revision: yes

  3. Referee: [Experiments] Experiments section: The manuscript does not report explicit matching of search budgets (total local moves, perturbation frequency, wall-clock time, or function evaluations) against the POMO and ALNS baselines. Because the framework description emphasizes problem-agnostic control, the absence of such controls leaves open the possibility that any search procedure with equivalent extra effort could achieve similar gap closures.

    Authors: We acknowledge the need for explicit budget matching. In the revision we will report detailed search budgets (local moves, perturbations, wall-clock time) for COAgents and the baselines. Where direct equivalence is not already present we will either adjust the experimental protocol or clearly document the differences and their implications. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical SOTA claims rest on external baseline comparisons

full rationale

The paper proposes a multi-agent framework (COAgents) that dynamically builds a Partial Search Graph and trains Node/Move Selection and Jump Agents to guide VRP search. Central claims of gap reductions (14%/44% vs POMO, 21%/40% vs ALNS on VRPTW at N=50/100) are presented as outcomes of experiments on standard CVRP/VRPTW benchmarks. These rest on direct performance comparisons to independent external solvers rather than any internal prediction, fitted parameter, or derivation that reduces to the method's own inputs by construction. No equations, uniqueness theorems, or ansatzes are invoked that loop back to self-defined quantities. The separation of problem-agnostic control from domain encoding supplies independent methodological content, rendering the reported results self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions from heuristic search and reinforcement learning plus typical ML hyperparameters; no new physical entities are postulated.

free parameters (1)
  • Agent network architectures and training hyperparameters
    Standard in multi-agent RL; these are chosen or tuned during development to achieve the reported benchmark performance.
axioms (1)
  • domain assumption The solution search process for VRPs can be effectively modeled as a graph with edges for local refinements and large perturbations.
    Core modeling choice described in the abstract for enabling agent-guided navigation.

pith-pipeline@v0.9.0 · 5828 in / 1369 out tokens · 60718 ms · 2026-05-21T05:21:53.624300+00:00 · methodology

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