Guidance Graph Optimization for Lifelong Multi-Agent Path Finding

TL;DR

This work introduces guidance graphs as a general, optimizable representation to improve throughput in lifelong MAPF by shaping edge costs and waits. It formalizes Guidance Graph Optimization (GGO) and presents two automatic methods: direct CMA-ES optimization of edge weights and Parameterized Iterative Update (PIU), which learns a CNN-based update model to iteratively refine the graph using traffic signals from simulations. Across eight maps and multiple lifelong MAPF algorithms, both CMA-ES and PIU outperform handcrafted baselines, and PIU demonstrates transferability to larger maps with similar layouts. The results highlight potential to boost fast, distributed MAPF with offline-guided graphs, while signaling future work on reducing compute and increasing Explainability, as well as integrating online updates.

Abstract

We study how to use guidance to improve the throughput of lifelong Multi-Agent Path Finding (MAPF). Previous studies have demonstrated that, while incorporating guidance, such as highways, can accelerate MAPF algorithms, this often results in a trade-off with solution quality. In addition, how to generate good guidance automatically remains largely unexplored, with current methods falling short of surpassing manually designed ones. In this work, we introduce the guidance graph as a versatile representation of guidance for lifelong MAPF, framing Guidance Graph Optimization as the task of optimizing its edge weights. We present two GGO algorithms to automatically generate guidance for arbitrary lifelong MAPF algorithms and maps. The first method directly optimizes edge weights, while the second method optimizes an update model capable of generating edge weights. Empirically, we show that (1) our guidance graphs improve the throughput of three representative lifelong MAPF algorithms in eight benchmark maps, and (2) our update model can generate guidance graphs for as large as $93 \times 91$ maps and as many as 3,000 agents. We include the source code at: \url{https://github.com/lunjohnzhang/ggo_public}. All optimized guidance graphs are available online at: \url{https://yulunzhang.net/publication/zhang2024ggo}.

Figures (14)

• Figure 1: Comparison of no guidance, human-designed crisscross guidance, and our guidance with a simulation of 240 agents in a 33 $\times$ 36 warehouse map, shown in \ref{['fig:warehouse-large-w']}. The heatmaps show the tile-usage (the frequency that each tile is occupied). Our guidance results in the most balanced traffic with the highest throughput.
• Figure 2: CMA-ES for GGO. The edge weights are iteratively sampled from a Gaussian distribution and then evaluated by a lifelong MAPF simulator. The simulated results are used to update the Gaussian distribution towards high-throughput regions.
• Figure 3: PIU for GGO. Starting with a guidance graph with uniform edge weights, we run MAPF simulations to get the edge usage. We then use an update model $\pi_{\boldsymbol{\theta}}$ to update the edge weights. We run this process iteratively for $N_p$ iterations. The update model $\pi_{\boldsymbol{\theta}}$ is optimized using CMA-ES.
• Figure 4: Throughput with different numbers of agents. The guidance graphs are optimized with $N_a$ agents, which is indicated by the black vertical lines. In (b), the black vertical lines at 220 and 400 agents indicate $N_a$ for setups 8 and 2, respectively.
• Figure 5: Setup 10: An optimized guidance graph enables PIBT to have competitive throughput with RHCR despite the advantage of RHCR with fewer agents.

Theorems & Definitions (7)

• Definition 1: MAPF
• Definition 2: Lifelong MAPF
• Definition 3: Guidance Graph
• Definition 4: Guidance Graph Optimization (GGO)
• Definition 5: Update model
• Definition 6: Unweighted Guidance Graph
• Definition 7: Crisscross Guidance Graph