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.

翻译：多智能体路径寻找（MAPF）是一个NP难问题，在仓库自动化和多机器人协调等领域具有应用。基于学习的MAPF求解器能够提供快速且可扩展的规划，但其生成的可行轨迹往往包含不必要的或振荡的运动。我们提出了Judgelight，这是一个后优化层，用于在MAPF求解器生成可行调度后提升轨迹质量。Judgelight通过折叠智能体轨迹中的闭合子游走来消除冗余运动，同时保持所有可行性约束。我们将此过程形式化为MAPF-Collapse问题，证明其是NP难的，并通过将其表述为整数线性规划（ILP）问题提出了一种精确优化方法。实验结果表明，Judgelight能持续将求解成本降低约20%，尤其对于基于学习的求解器，能生成更适用于实际部署的轨迹。