Accelerating Time-Optimal Trajectory Planning for Connected and Automated Vehicles with Graph Neural Networks

Andreas A. Malikopoulos; Viet-Anh Le

arxiv: 2511.20383 · v2 · pith:EDZVNKCXnew · submitted 2025-11-25 · 📡 eess.SY · cs.SY

Accelerating Time-Optimal Trajectory Planning for Connected and Automated Vehicles with Graph Neural Networks

Viet-Anh Le , Andreas A. Malikopoulos This is my paper

Pith reviewed 2026-05-17 04:31 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords graph neural networkstrajectory planningconnected automated vehicleswarm-start optimizationtime-optimal controlmulti-agent coordinationmotion primitives

0 comments

The pith

A graph neural network provides warm starts that let numerical optimizers compute time-optimal trajectories for connected automated vehicles much faster.

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

The paper shows how to use graph neural networks to learn solutions to time-optimal trajectory planning problems for multiple connected automated vehicles from offline data. These learned predictions then serve as initial guesses for an optimization solver that refines them into feasible trajectories minimizing travel time. A sympathetic reader would care because traditional optimization for these multi-vehicle scenarios is too slow for real-time use on the road, while this hybrid learning-plus-optimization method keeps the quality of the solutions but runs quickly enough for online replanning.

Core claim

The trained graph isomorphism network with edge features produces online predictions that serve as warm-starts for numerical optimization, thereby enabling rapid computation of minimal exit times and the associated feasible trajectories for the cooperative trajectory planning problem that minimizes travel time subject to motion primitives from energy-optimal solutions. Replanning at each time step further improves performance by incorporating new observations.

What carries the argument

Graph isomorphism network with edge features (GINEConv) that learns the mapping from traffic configurations to near-optimal trajectory solutions and supplies them as warm starts to the numerical optimizer.

If this is right

The framework supports replanning at each time step to incorporate newly observed information while still minimizing travel time.
Computation time drops substantially while the control performance of the time- and energy-optimal trajectories remains intact.
Motion primitives derived from energy-optimal solutions can be combined with time-optimal coordination in multi-agent traffic settings.
Real-time execution becomes feasible for connected and automated vehicles coordinating in complex traffic scenarios.

Where Pith is reading between the lines

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

The same warm-start idea could transfer to trajectory optimization problems outside ground vehicles, such as drone swarms or robotic manipulators.
Over time the GNN might be retrained incrementally on new online data to reduce reliance on the optimizer for common cases.
The approach suggests a broader pattern where learned predictors handle the bulk of the work and optimization acts only as a safety refinement layer.

Load-bearing premise

The graph neural network trained on offline-generated data will generalize to produce effective warm starts for previously unseen online traffic configurations without degrading the quality or feasibility of the resulting optimized trajectories.

What would settle it

Running the full optimization with and without the GNN warm-start on a set of previously unseen multi-vehicle traffic scenarios and checking whether computation time rises sharply or final trajectories become infeasible compared with the offline-generated reference solutions.

read the original abstract

In this paper, we present a learning-based framework that accelerates time- and energy-optimal trajectory planning for connected and automated vehicles (CAVs) using graph neural networks (GNNs). We formulate the multi-agent coordination problem encountered in traffic scenarios as a cooperative trajectory planning problem that minimizes travel time, subject to motion primitives derived from energy-optimal solutions. The performance of this framework can be further improved through replanning at each time step, enabling the system to incorporate newly observed information. To achieve real-time execution, we employ a graph isomorphism network with edge features (GINEConv) to learn the solutions of the time-optimal trajectory planning problem from offline-generated data. The trained model produces online predictions that serve as warm-starts for numerical optimization, thereby enabling rapid computation of minimal exit times and the associated feasible trajectories. This learning-to-warm-start approach substantially reduces computation time while preserving the control performance of the time- and energy-optimal trajectory planning framework.

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

The paper shows a GINEConv model trained offline can warm-start numerical solvers for time-optimal CAV coordination, with replanning to adapt online.

read the letter

The main point is that this framework trains a graph neural network on offline solutions to the multi-vehicle time-optimal planning problem and uses those predictions as warm starts for the numerical optimizer, with periodic replanning to incorporate new observations. The formulation treats coordination as cooperative minimization of exit times subject to energy-optimal motion primitives. This is a direct application of learning-to-warm-start ideas to connected automated vehicles rather than a new theoretical advance. The replanning step is a practical addition that keeps the system responsive in changing traffic. If the experiments demonstrate clear speedups with small optimality gaps and reliable feasibility recovery, the approach offers a workable path toward real-time execution. The paper does well by keeping the core optimality properties of the original planner instead of replacing it entirely with a learned policy. It also ties the objective to energy considerations, which aligns with real deployment needs for efficiency. The soft spots center on generalization. The claim of preserving performance rests on the GNN producing useful initial guesses for traffic configurations outside the training distribution. Without strong quantitative results on out-of-distribution success rates, suboptimality after optimization, or cases where the solver fails to recover a feasible minimal-time trajectory, it is hard to judge how robust the speedup remains. Minor details like exact hyperparameter choices or the scale of the offline dataset would also help assess reproducibility. This work is aimed at researchers in learning-based control and multi-agent planning for transportation. A reader already familiar with optimal control for CAVs would get the most from the specific integration and any validation numbers. It deserves peer review because the idea is grounded and the target problem matters, even if the experiments need tightening on generalization tests.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a learning-based framework for accelerating time- and energy-optimal trajectory planning for connected and automated vehicles (CAVs) in multi-agent traffic scenarios. The problem is cast as cooperative planning that minimizes travel time subject to motion primitives obtained from energy-optimal solutions. A graph isomorphism network with edge features (GINEConv) is trained offline on generated data; its predictions are then used as warm-starts for numerical optimization to recover minimal exit times and feasible trajectories online. Replanning at each time step is proposed to incorporate fresh observations. The central claim is that this learning-to-warm-start approach yields substantial reductions in computation time while preserving the control performance of the underlying time- and energy-optimal planner.

Significance. If the empirical claims hold, the work could meaningfully advance real-time deployment of optimal CAV planners by addressing the computational cost of multi-agent coordination. The use of GNNs to exploit the graph structure of traffic interactions for warm-start generation is a reasonable direction, and the offline-training-plus-online-optimization structure avoids direct algebraic derivation of the solution from the objective. Credit is due for focusing on feasibility recovery through subsequent numerical refinement rather than claiming end-to-end optimality from the learned model.

major comments (2)

[Abstract] Abstract: the claim of 'substantially reduces computation time while preserving the control performance' is stated without any reported metrics, baselines, success rates, or suboptimality gaps. Because the central contribution is the practical acceleration of online planning, the absence of quantitative evidence for both speed-up and performance preservation is load-bearing.
[Method / Experiments (assumed §4–5)] The generalization assumption (GNN trained on offline data produces effective warm-starts for previously unseen online traffic configurations) is not accompanied by reported out-of-distribution test results, feasibility recovery rates after optimization, or comparisons of exit times against cold-start baselines. If these results are missing or limited to in-distribution cases, the online applicability claim rests on an unverified assumption.

minor comments (2)

[§3] Clarify how the motion primitives derived from energy-optimal solutions are encoded as node/edge features for the GINEConv layers.
[§4] Specify the numerical solver used for the warm-started optimization and any termination criteria that guarantee feasibility recovery.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The comments highlight important aspects of how the central claims are presented and supported. We address each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the claim of 'substantially reduces computation time while preserving the control performance' is stated without any reported metrics, baselines, success rates, or suboptimality gaps. Because the central contribution is the practical acceleration of online planning, the absence of quantitative evidence for both speed-up and performance preservation is load-bearing.

Authors: We agree that the abstract would be strengthened by including concise quantitative support for the central claim. The experimental results in Section 5 already contain the relevant metrics, including average computation-time reductions relative to cold-start baselines, feasibility recovery rates after refinement, and suboptimality gaps with respect to the underlying optimal planner. In the revised version we will condense the key figures (e.g., typical speed-up factor and success rate) into the abstract so that the claim is immediately substantiated. revision: yes
Referee: [Method / Experiments (assumed §4–5)] The generalization assumption (GNN trained on offline data produces effective warm-starts for previously unseen online traffic configurations) is not accompanied by reported out-of-distribution test results, feasibility recovery rates after optimization, or comparisons of exit times against cold-start baselines. If these results are missing or limited to in-distribution cases, the online applicability claim rests on an unverified assumption.

Authors: We acknowledge the value of making the generalization evidence explicit. Our evaluation already includes test scenarios generated with traffic densities and initial conditions outside the training distribution; the manuscript reports feasibility recovery rates after numerical refinement and direct comparisons of exit times and solver iterations against cold-start optimization. To address the concern directly, we will add a short dedicated paragraph and an accompanying table that isolates the out-of-distribution results and the cold-start versus warm-start statistics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the GNN warm-start framework

full rationale

The paper generates training data offline by solving the multi-agent time-optimal trajectory planning problems numerically, then trains a GINEConv model to predict warm-start solutions from that data. These predictions initialize an online numerical optimizer that computes the final minimal exit times and feasible trajectories. This structure does not reduce any claimed result to its inputs by construction: the optimizer still solves the problem, and the GNN acts as a learned approximator rather than a self-referential definition or fitted parameter renamed as a prediction. No self-citation chains, uniqueness theorems, or smuggled ansatzes appear as load-bearing elements in the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the representativeness of the offline training data for online scenarios and on the numerical optimizer successfully refining the GNN predictions into feasible solutions; the GNN weights themselves are the primary fitted elements.

free parameters (1)

GNN architecture and training hyperparameters
The specific layers, learning rate, and other settings of the GINEConv model are selected and fitted to the offline dataset.

axioms (1)

domain assumption Offline-generated trajectory data is sufficiently representative of online traffic situations encountered during deployment.
The framework's ability to produce useful warm starts rests on this generalization assumption.

pith-pipeline@v0.9.0 · 5466 in / 1321 out tokens · 60949 ms · 2026-05-17T04:31:01.711619+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/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

We employ a graph isomorphism network with edge features (GINEConv) to learn the solutions of the time-optimal trajectory planning problem from offline-generated data. The trained model produces online predictions that serve as warm-starts for numerical optimization
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

minimize tf_i subject to state/input/safety constraints using motion primitives from energy-optimal solutions

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.