LayeredMAPF: a decomposition of MAPF instance to reduce solving costs

TL;DR

This work addresses the exponential growth of multi-agent pathfinding (MAPF) solving costs by introducing Layered MAPF, a decomposition framework that progressively partitions a MAPF instance into smaller clusters and levels, solves subproblems independently, and merges results to obtain a conflict-free solution. The approach is designed to be agnostic to the underlying MAPF method, and is evaluated across classic benchmarks by applying decomposition to seven state-of-the-art MAPF algorithms, revealing substantial reductions in time and memory, with solvability loss estimated at $<1\%$. The authors define legality checks to minimize loss of solvability, and they provide a rigorous complexity analysis along with extensive experiments covering decomposition performance and cross-method applicability. The results show strong benefits for serial MAPF methods (e.g., EECBS, PBS, LNS2) in terms of runtime and memory, while parallel methods benefit less consistently due to solution-merging overheads. The work offers practical guidance for deploying MAPF in resource-constrained settings and lays groundwork for future improvements in merging strategies for parallel methods and randomized cluster restarts to further optimize decomposition outcomes.

Abstract

Multi-agent pathfinding (MAPF) holds significant utility within autonomous systems, however, the calculation and memory space required for multi-agent path finding (MAPF) grows exponentially as the number of agents increases. This often results in some MAPF instances being unsolvable under limited computational resources and memory space, thereby limiting the application of MAPF in complex scenarios. Hence, we propose a decomposition approach for MAPF instances, which breaks down instances involving a large number of agents into multiple isolated subproblems involving fewer agents. Moreover, we present a framework to enable general MAPF algorithms to solve each subproblem independently and merge their solutions into one conflict-free final solution, and avoid loss of solvability as much as possible. Unlike existing works that propose isolated methods aimed at reducing the time cost of MAPF, our method is applicable to all MAPF methods. In our results, we apply decomposition to multiple state-of-the-art MAPF methods using a classic MAPF benchmark\footnote{https://movingai.com/benchmarks/mapf.html}. The decomposition of MAPF instances is completed on average within 1s, and its application to seven MAPF methods reduces the memory usage or time cost significantly, particularly for serial methods. Based on massive experiments, we speculate the possibilty about loss of solvability caused by our method is $<$ 1\%. To facilitate further research within the community, we have made the source code of the proposed algorithm publicly available\footnote{https://github.com/JoeYao-bit/LayeredMAPF/tree/minimize\_dependence}.

Figures (30)

• Figure 1: These figures illustrate the complete process of decomposing a MAPF instance, which includes decomposing agents into initial clusters (a type of subproblem), further decomposing initial clusters into smaller clusters, and decomposing clusters into levels (another type of subproblem). For more details, please refer to Section \ref{['Methodology']}.
• Figure 2: These figures show a solvable MAPF instance (Fig. A) and an unsolvable MAPF instance (Fig. C). $S_1, S_2, S_3$ and $T_1, T_2, T_3$ represent the start and target cells of the three agents in the instance, as follows. The paths of each agent in the instance are shown in Figures B and D, respectively. The instance in Fig. A passes the solvability check, as all its agents have a path to their target. However, the instance in Fig. C does not pass the solvability check and is unsolvable because only the 3rd agent has a path to its target, while the 1st and 2nd agents have no path to their target. Grey cells represent unpassable cells, while white cells represent passable cells, as follows.
• Figure 3: This figure shows a MAPF instance that passes the mentioned solvability check but is unsolvable. $a_1$'s start $S_1$ have path to its target $T_1$ and $a_2$'s start $S_2$ have path to its target $T_2$, if another agent's start and target are passable. However, due to $a_2$ always block the path from $S_1$ to $T_1$, this instance is unsolvable.
• Figure 4: This figure illustrates three subproblems ($1, \{a_1\}; 2, \{a_2\}; 3, \{a_3\}$) of the MAPF instance shown in Fig. \ref{['solvable']} A and checks whether these three subproblems pass the solvability check under the simplified scenario. As shown in the figure, the agent in each subproblem has a solution that avoids the target state of the previous subproblem and the start state of the next subproblem. Therefore, since every subproblem passes the solvability check, the instance can be decomposed into these three subproblems.
• Figure 5: This figure shows the total solution generated by adding wait actions at the start for the MAPF instance in Fig. \ref{['layered_mapf_example']}. In the total solution, only one agent from each subproblem (denoted as $a_i$) is moving (marked with a dashed-line box), while the agents from the other subproblems stay at their start or target states. Specifically, $a_1$ (from subproblem 1) moves when $0 \leq t \leq 4$; $a_2$ (from subproblem 2) moves when $5 \leq t \leq 9$; and $a_3$ (from subproblem 3) moves when $10 \leq t \leq 13$.

Theorems & Definitions (19)

• Definition 1
• Definition 2
• Definition 3
• Theorem 1
• Proof 1
• Theorem 2
• Proof 2
• Definition 4
• Definition 5
• Definition 6