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Empirical Hardness in Multi-Agent Pathfinding: Research Challenges and Opportunities

Jingyao Ren, Eric Ewing, T. K. Satish Kumar, Sven Koenig, Nora Ayanian

TL;DR

This paper addresses the gap between MAPF's theoretical NP-hardness and its practical hardness variance across instances. It frames empirical hardness around three challenges: (1) selecting and configuring per-instance MAPF algorithms, (2) uncovering instance features and structural factors such as phase transitions and backbone/backdoor indicators that drive difficulty, and (3) generating hard instances and diverse benchmarks to robustly evaluate solvers. It surveys existing approaches to algorithm selection, feature encoding, and heuristic configuration, and discusses the lack of formal MAPF-phase-transition theory while outlining future directions for definitional work and benchmark design. Collectively, the work lays a foundation for systematic empirical hardness research in MAPF, aiming to bridge theory and practice and improve solver robustness and benchmarking practices.

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding collision-free paths for a team of agents on a map. Although MAPF is NP-hard, the hardness of solving individual instances varies significantly, revealing a gap between theoretical complexity and actual hardness. This paper outlines three key research challenges in MAPF empirical hardness to understand such phenomena. The first challenge, known as algorithm selection, is determining the best-performing algorithms for a given instance. The second challenge is understanding the key instance features that affect MAPF empirical hardness, such as structural properties like phase transition and backbone/backdoor. The third challenge is how to leverage our knowledge of MAPF empirical hardness to effectively generate hard MAPF instances or diverse benchmark datasets. This work establishes a foundation for future empirical hardness research and encourages deeper investigation into these promising and underexplored areas.

Empirical Hardness in Multi-Agent Pathfinding: Research Challenges and Opportunities

TL;DR

This paper addresses the gap between MAPF's theoretical NP-hardness and its practical hardness variance across instances. It frames empirical hardness around three challenges: (1) selecting and configuring per-instance MAPF algorithms, (2) uncovering instance features and structural factors such as phase transitions and backbone/backdoor indicators that drive difficulty, and (3) generating hard instances and diverse benchmarks to robustly evaluate solvers. It surveys existing approaches to algorithm selection, feature encoding, and heuristic configuration, and discusses the lack of formal MAPF-phase-transition theory while outlining future directions for definitional work and benchmark design. Collectively, the work lays a foundation for systematic empirical hardness research in MAPF, aiming to bridge theory and practice and improve solver robustness and benchmarking practices.

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding collision-free paths for a team of agents on a map. Although MAPF is NP-hard, the hardness of solving individual instances varies significantly, revealing a gap between theoretical complexity and actual hardness. This paper outlines three key research challenges in MAPF empirical hardness to understand such phenomena. The first challenge, known as algorithm selection, is determining the best-performing algorithms for a given instance. The second challenge is understanding the key instance features that affect MAPF empirical hardness, such as structural properties like phase transition and backbone/backdoor. The third challenge is how to leverage our knowledge of MAPF empirical hardness to effectively generate hard MAPF instances or diverse benchmark datasets. This work establishes a foundation for future empirical hardness research and encourages deeper investigation into these promising and underexplored areas.

Paper Structure

This paper contains 14 sections, 3 figures.

Table of Contents

  1. Introduction
  2. Challenge I: When to Choose Which Algorithm?
  3. Algorithm Selection
  4. Algorithm Configuration
  5. Future Directions
  6. Challenge II: Understanding the Empirical Hardness of MAPF
  7. Phase Transition
  8. Backbone and Backdoor
  9. Future Directions
  10. Challenge III: Generating Hard MAPF Instances and Benchmark Datasets
  11. Generating Hard MAPF Instances
  12. Generating Better Benchmark Datasets
  13. Future Directions
  14. Conclusion

Figures (3)

  • Figure 1: Number of instances where different MAPF algorithms are the fastest in runtime or successfully completed within the time limit across various map types.
  • Figure 2: Runtime for CBSH2-RTC li2021pairwise algorithm for different MAPF instances. Circles and squares indicate start/goal locations, and obstacles are in black. (a) MAPF instances on the same map, the same number of agents, but significantly different runtimes. (b) MAPF instances with the same number of obstacles and same start/goal locations but dramatically different runtimes. (c) Runtime variation of CBSH2-RTC algorithm using different combinations of heuristics, dashed lines show planned paths.
  • Figure 3: (a) Phase transition of 3-SAT problem. (b) The average empirical hardness of MAPF instances on different maps.