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Algorithm Selection for Optimal Multi-Agent Path Finding via Graph Embedding

Carmel Shabalin, Omri Kaduri, Roni Stern

TL;DR

This work tackles the problem of selecting the fastest optimal MAPF solver for a given instance. It introduces MAG, a graph-embedding–based algorithm selection approach that encodes MAPF problems with FG2V and G2V graph representations, embeds them via FEATHER, and combines these with MAPF-specific features to train a multi-class classifier using XGBoost. MAG demonstrates superior or competitive performance across in-grid and in-grid-type tasks, with notable improvements in average regret over strong baselines, and reveals limits in between-grid tasks, highlighting cross-topology generalization challenges. The study underscores the practical viability of graph embeddings for MAPF AS and points to future work merging graph-embedding methods with image-based representations for broader applicability.

Abstract

Multi-agent path finding (MAPF) is the problem of finding paths for multiple agents such that they do not collide. This problem manifests in numerous real-world applications such as controlling transportation robots in automated warehouses, moving characters in video games, and coordinating self-driving cars in intersections. Finding optimal solutions to MAPF is NP-Hard, yet modern optimal solvers can scale to hundreds of agents and even thousands in some cases. Different solvers employ different approaches, and there is no single state-of-the-art approach for all problems. Furthermore, there are no clear, provable, guidelines for choosing when each optimal MAPF solver to use. Prior work employed Algorithm Selection (AS) techniques to learn such guidelines from past data. A major challenge when employing AS for choosing an optimal MAPF algorithm is how to encode the given MAPF problem. Prior work either used hand-crafted features or an image representation of the problem. We explore graph-based encodings of the MAPF problem and show how they can be used on-the-fly with a modern graph embedding algorithm called FEATHER. Then, we show how this encoding can be effectively joined with existing encodings, resulting in a novel AS method we call MAPF Algorithm selection via Graph embedding (MAG). An extensive experimental evaluation of MAG on several MAPF algorithm selection tasks reveals that it is either on-par or significantly better than existing methods.

Algorithm Selection for Optimal Multi-Agent Path Finding via Graph Embedding

TL;DR

This work tackles the problem of selecting the fastest optimal MAPF solver for a given instance. It introduces MAG, a graph-embedding–based algorithm selection approach that encodes MAPF problems with FG2V and G2V graph representations, embeds them via FEATHER, and combines these with MAPF-specific features to train a multi-class classifier using XGBoost. MAG demonstrates superior or competitive performance across in-grid and in-grid-type tasks, with notable improvements in average regret over strong baselines, and reveals limits in between-grid tasks, highlighting cross-topology generalization challenges. The study underscores the practical viability of graph embeddings for MAPF AS and points to future work merging graph-embedding methods with image-based representations for broader applicability.

Abstract

Multi-agent path finding (MAPF) is the problem of finding paths for multiple agents such that they do not collide. This problem manifests in numerous real-world applications such as controlling transportation robots in automated warehouses, moving characters in video games, and coordinating self-driving cars in intersections. Finding optimal solutions to MAPF is NP-Hard, yet modern optimal solvers can scale to hundreds of agents and even thousands in some cases. Different solvers employ different approaches, and there is no single state-of-the-art approach for all problems. Furthermore, there are no clear, provable, guidelines for choosing when each optimal MAPF solver to use. Prior work employed Algorithm Selection (AS) techniques to learn such guidelines from past data. A major challenge when employing AS for choosing an optimal MAPF algorithm is how to encode the given MAPF problem. Prior work either used hand-crafted features or an image representation of the problem. We explore graph-based encodings of the MAPF problem and show how they can be used on-the-fly with a modern graph embedding algorithm called FEATHER. Then, we show how this encoding can be effectively joined with existing encodings, resulting in a novel AS method we call MAPF Algorithm selection via Graph embedding (MAG). An extensive experimental evaluation of MAG on several MAPF algorithm selection tasks reveals that it is either on-par or significantly better than existing methods.
Paper Structure (18 sections, 1 equation, 4 figures, 3 tables)

This paper contains 18 sections, 1 equation, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. MAPF
  4. AS for MAPF
  5. Graph Embedding Algorithms
  6. Method
  7. Encoding MAPF as a Graph
  8. Embedding the Graph
  9. Feature Extraction and Learning
  10. Experimental Results
  11. Experimental Setup
  12. Baselines
  13. Metrics
  14. In-Grid Results
  15. In-Grid-Type and Between-Grid-Type Results
  16. ...and 3 more sections

Figures (4)

  • Figure 1: An example of the $\textit{G2V}$ and $\textit{FG2V}$ encoding methods.
  • Figure 2: Diagram of the $\textit{MAG}$ feature extraction and training process.
  • Figure 3: An example grid from each of the grid types in our benchmark, From left to right: empty, random, warehouse, game, city, maze, and room.
  • Figure 4: Feature importance for the XGBoost model created for $\textit{MAG}$ in the in-grid (top), in-grid-type (middle), and between-grid (bottom) setups.