分而治之：通过精确分解为独立子实例实现MAPF-Collapse

中文摘要 AI 辅助

在这项工作中，我们研究了MAPFC问题，这是多智能体路径规划（MAPF）计划的后优化步骤，其中给定一个由现代MAPF求解器生成的可行计划，任务是在保持可行性的同时移除可避免的移动。当使用基于学习的最先进（SOTA）求解器时，这些求解器生成的计划包含可移除的冗余移动，因此这个NP难问题自然出现。最近，Tang等人提出了Judgelight，它使用整数线性规划（ILP）来解决MAPFC。重要的是，ILP是在所有智能体联合构建的，因此其成本由整个实例决定，而不是由实际需要联合推理的小型耦合残差决定。我们的关键见解（激励了这项工作）是MAPFC实例自然分解为独立的子问题，其中大多数涉及单个智能体，可以在没有任何智能体间推理的情况下解决。为此，我们首先识别哪些智能体需要协调其运动，并相应地将实例划分为子问题。对于不需要协调的情况，我们引入了一个极其轻量级的求解器，其速度比Judgelight快约1,900倍。对于需要协调的情况，可以使用Judgelight，但我们引入了一种替代的CBS类求解器，在较简单的问题上更高效。由此产生的框架是精确的，不使用商业ILP求解器，并且在协调较轻的大多数实例上运行速度显著更快，同时匹配Judgelight的质量；在协调较重的实例上，我们提出了一种基于机制感知的混合规划器，回退到Judgelight。在所有测试的基准上，该规划器实现了比Judgelight每实例中位数10.5倍的加速。

英文摘要

In this work we study the problem of MAPFC, a post-optimization step for Multi-Agent Path Finding (MAPF) plans where we are given a feasible plan produced by a modern MAPF solver and are tasked with removing avoidable moves while preserving feasibility. This NP-hard problem naturally arises when using learning-based state-of-the-art (SOTA) solvers which construct plans that contain redundant moves that can be removed. Recently, Tang et al. presented Judgelight, which uses Integer Linear Programming (ILP) to solve MAPFC. Importantly, the ILP is constructed over all agents jointly, so its cost is governed by the full instance rather than by the small coupled residue that actually requires joint reasoning. Our key insight, motivating this work, is that MAPFC instances naturally decompose into independent sub-problems, most of which involve a single agent and can be solved without any inter-agent reasoning. To this end, we first identify which agents need to coordinate their motion and partition the instance into sub-problems accordingly. For the cases where no coordination is required, we introduce an extremely lightweight solver that is $\approx\!1{,}900\times$ faster than Judgelight. For cases where coordination is required, Judgelight can be used but we introduce an alternative CBS-like solver which is more efficient on easier problems. The resulting framework is exact, uses no commercial ILP solver, and matches Judgelight's quality while running substantially faster on the coordination-light majority of instances; on the coordination-heavy instances we propose a regime-aware hybrid planner that falls back to Judgelight. Over all benchmarks tested, this planner achieves a median $10.5\times$ per-instance speedup over Judgelight.

发表机构

• Technion – Israel Institute of Technology（以色列理工学院）

机构由 AI 辅助整理，请以论文原文为准。