# Optimizing Two-Truck Platooning with Deadlines

arXiv: https://arxiv.org/abs/2210.01889 · HTML: https://mlsanity.com/paper/2210.01889/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2022.

## Built on by (most cited first, 2 of 2)

- [An Automated Reinforcement Learning Reward Design Framework with Large Language Model for Cooperative Platoon Coordination](https://mlsanity.com/paper/2504.19480/) (2025)
- [Multi-Agent Bayesian Optimization with Coupled Black-Box and Affine Constraints](https://mlsanity.com/paper/2310.00962/) (2023)

## Abstract (arXiv)

We study a transportation problem where two heavy-duty trucks travel across the national highway from separate origins to destinations, subject to individual deadline constraints. Our objective is to minimize their total fuel consumption by jointly optimizing path planning, speed planning, and platooning configuration. Such a two-truck platooning problem is pervasive in practice yet challenging to solve due to hard deadline constraints and enormous platooning configurations to consider. We first leverage a unique problem structure to significantly simplify platooning optimization and present a novel formulation. We prove that the two-truck platooning problem is weakly NP-hard and admits a Fully Polynomial Time Approximation Scheme (FPTAS). The FPTAS can achieve a fuel consumption within a ratio of (1+ε) to the optimal (for any ε>0) with a time complexity polynomial in the size of the transportation network and 1/ε. These results are in sharp contrast to the general multi-truck platooning problem, which is known to be APX-hard and repels any FPTAS. As the FPTAS still incurs excessive running time for large-scale cases, we design an efficient dual-subgradient algorithm for solving large-/national- scale instances. It is an iterative algorithm that always converges. We prove that each iteration only incurs polynomial-time complexity, albeit it requires solving an integer linear programming problem optimally. We characterize a condition under which the algorithm generates an optimal solution and derive a posterior performance bound when the condition is not met. Extensive simulations based on real-world traces show that our joint solution of path planning, speed planning, and platooning saves up to 24% fuel as compared to baseline alternatives.