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

2026-01-27

AI Summary

This work addresses the inefficiency of trajectories generated by learning-based multi-agent path finding (MAPF) methods, which often contain redundant or oscillatory actions that hinder real-world deployment. The study formally introduces the MAPF-Collapse problem for the first time, proves its NP-hardness, and proposes a post-optimization approach based on integer linear programming (ILP). This method identifies and collapses closed subpaths in agent trajectories while preserving all feasibility constraints, thereby eliminating unnecessary movements. The approach is highly general and can be seamlessly integrated with various learning-based MAPF solvers. Experimental results across multiple benchmarks demonstrate an average reduction of approximately 20% in trajectory cost, significantly enhancing both trajectory smoothness and practical utility.

Technology Category

• Multiagent Systems: Multiagent Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Multi-Agent Path Finding
• trajectory optimization
• redundant movements
• oscillatory trajectories
• post-optimization

Innovation

• closed-subwalk collapsing
• trajectory post-optimization
• multi-agent path finding
• integer linear programming
• MAPF-Collapse