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

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.

💡 Research Summary

The paper addresses a practical shortcoming of both search‑based and learning‑based Multi‑Agent Path Finding (MAPF) solvers: even when a feasible schedule is produced, the individual trajectories often contain unnecessary or oscillatory movements that increase energy consumption, wear, and operational risk in real‑world deployments such as warehouse automation. To remedy this, the authors introduce Judgelight, a post‑optimization layer that operates on a given feasible MAPF schedule and removes redundant motion by collapsing closed subwalks—segments where an agent starts and ends at the same vertex—into a single waiting action.

The authors formalize this task as a new optimization problem called MAPF‑Collapse. The input consists of an N‑by‑(T+1) matrix M describing the location of each of N agents at each discrete time step up to a horizon T. A collapse operation may replace any subsequence