# Judgelight: Trajectory-Level Post-Optimization for Multi-Agent Path Finding via Closed-Subwalk Collapsing

arXiv: https://arxiv.org/abs/2601.19388 · HTML: https://mlsanity.com/paper/2601.19388/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2026.

## Built on by (most cited first, 1 of 1)

- [Divide and Collapse: MAPF-Collapse via Exact Decomposition into Independent Sub-Instances](https://mlsanity.com/paper/2609.39559/) (2026)

## Abstract (arXiv)

Multi-Agent Path Finding (MAPF) is an NP-hard problem with applications in warehouse automation and multi-robot coordination. Learning-based MAPF solvers offer fast and scalable planning but often produce feasible trajectories that contain unnecessary or oscillatory movements. We propose Judgelight, a post-optimization layer that improves trajectory quality after a MAPF solver generates a feasible schedule. Judgelight collapses closed subwalks in agents' trajectories to remove redundant movements while preserving all feasibility constraints. We formalize this process as MAPF-Collapse, prove that it is NP-hard, and present an exact optimization approach by formulating it as integer linear programming (ILP) problem. Experimental results show Judgelight consistently reduces solution cost by around 20%, particularly for learning-based solvers, producing trajectories that are better suited for real-world deployment.