Speedup Techniques for Switchable Temporal Plan Graph Optimization

TL;DR

This work addresses scalable optimization of Switchable Temporal Plan Graphs for MAPF under execution delays. It introduces Improved GSES (IGSES), which combines stronger admissible heuristics, maximal edge-grouping, prioritized branching, and incremental longest-path computations to efficiently find acyclic STPGs with minimum execution cost. Empirical results show IGSES consistently doubles GSES’ success rate and achieves up to 10–30× speedups on problems solved by both methods, with edge grouping preprocessing contributing to substantial search-space reduction. The approach advances robust, scalable MAPF execution by exploiting the STPG structure, enabling faster planning in dynamic environments while maintaining optimality with respect to the STPG objective.

Abstract

Multi-Agent Path Finding (MAPF) focuses on planning collision-free paths for multiple agents. However, during the execution of a MAPF plan, agents may encounter unexpected delays, which can lead to inefficiencies, deadlocks, or even collisions. To address these issues, the Switchable Temporal Plan Graph provides a framework for finding an acyclic Temporal Plan Graph with the minimum execution cost under delays, ensuring deadlock- and collision-free execution. Unfortunately, existing optimal algorithms, such as Mixed Integer Linear Programming and Graph-Based Switchable Edge Search (GSES), are often too slow for practical use. This paper introduces Improved GSES, which significantly accelerates GSES through four speedup techniques: stronger admissible heuristics, edge grouping, prioritized branching, and incremental implementation. Experiments conducted on four different map types with varying numbers of agents demonstrate that Improved GSES consistently achieves over twice the success rate of GSES and delivers up to a 30-fold speedup on instances where both methods successfully find solutions.

Figures (12)

• Figure 1: (a) shows an example of a MAPF problem. In the initial MAPF plan, Agent $1$ moves from $A$ to $H$ (red arrows) and visits $G$ first. Agent $2$ moves from $E$ to $D$ (blue arrows) and visits $G$ after Agent $1$. (b) shows the TPG of the initial plan. Each row of vertices encodes an agent's path with superscripts $1,2$ differentiating agents. The black arrow encodes the precedence that agent $2$ can only visit $G^2$ after agent $1$ arrives $H^1$. The bold number near a vertex $v^i$ shows the earliest possible time for agent $i$ to arrive at this vertex. The execution cost below the TPG shows the overall cost of these two agents. (c) shows the TPG with a $2$-timestep delay at vertex $A^1$, which is encoded by two dashed vertices.
• Figure 2: (a) is the STPG built from the TPG in \ref{['fig: delayed_TPG']}. The only switchable edge $(H^1,G^2)$ is dashed. It can be fixed to edge $(H^1,G^2)$ as in (b) or reversed to edge $(C^2,G^1)$ as in (c). The different choices result in different execution costs. Notably, when computing the execution cost of STPG (defined in \ref{['subsection: baseline']}), the dashed switchable edge will be ignored.
• Figure 3: Edge grouping examples. The upper graphs show the partial MAPF trajectories. The lower graphs show the partial STPG with switchable edges that can be grouped. In (a), Agent $2$ (blue arrows) visits the same sequence of locations, $A,B,C$, as Agent $1$ (red arrows). In a successful execution, one agent must visit each location before the other agent. Namely, the visiting orders of each location must be the same. Therefore, these edges must always have the same direction and are groupable. In (b), Agent $2$ traverses Agent $1$'s trajectory reversely, but the conclusion remains the same. (c) can be regarded as a mixture of (a) and (b).
• Figure 4: An example of finding all the switchable edges groupable with a certain switchable edge $e$. (a) is a complete STPG for the parallel pattern in \ref{['fig: parallel']}. We want to find all the switchable edges groupable with $(B^1,A^2)$ in (a). We must consider two possible directions of it. (b), (c), (d) illustrate the reasoning for the case we fix it. Specifically, in (b), we fix $(B^1,A^2)$ (marked black) and temporarily reverse other switchable edges (marked green) to reason whether they must follow the same direction as $(B^1,A^2)$ based on the constraint that there should be no cycle in the graph. Since there is a cycle $C^2\rightarrow B^1\rightarrow A^2$ in (b), we know $(C^1,B^2)$ in (a) must be fixed instead of reversed. Then, we obtain (c). Similarly, there is a cycle $B^2 \rightarrow F^2 \rightarrow C^1$. So, $(D^1,C^2)$ must also be fixed. Then, we obtain (d). As a result, we find both edges $(C^1,B^2)$ and $(D^1,C^2)$ need to follow the same direction as $(B^1,A^2)$ if it is fixed. (e), (f), (g) illustrate the reasoning for the case that we reverse the switchable edge $(B^1,A^2)$. We confirm that both edges $(C^1,B^2)$ and $(D^1,C^2)$ need to follow the same direction as $(B^1,A^2)$ if it is reversed. Therefore, these three switchable edges must always select the same direction. Namely, they are groupable.
• Figure 5: Success rates of IGSES and other baselines on four maps. An instance is considered successfully solved if an optimal solution is returned within the time limit. The shading areas indicate the standard deviations of different runs. They are multiplied by 10 for illustration. In each figure, the top-left corner shows the corresponding map, and the top-right corner shows the range of agent numbers.

Theorems & Definitions (19)

• Definition 1: MAPF
• Definition 2: TPG
• Theorem 1
• Definition 3: EAT
• Theorem 2
• Definition 4: STPG
• Definition 5: Reduced TPG
• Definition 6: Edge Slack
• Definition 7: Vertex Slack
• Definition 8: Ordered-Pairwise Subgraph $\mathcal{G}_{i,j}^S$