Where Paths Collide: A Comprehensive Survey of Classic and Learning-Based Multi-Agent Pathfinding

Multi-Agent Path Finding (MAPF) is a fundamental problem in artificial intelligence and robotics, requiring the computation of collision-free paths for multiple agents navigating from their start locations to designated goals. As autonomous systems become increasingly prevalent in warehouses, urban transportation, and other complex environments, MAPF has evolved from a theoretical challenge to a critical enabler of real-world multi-robot coordination. This comprehensive survey bridges the long-standing divide between classical algorithmic approaches and emerging learning-based methods in MAPF research. We present a unified framework that encompasses search-based methods (including Conflict-Based Search, Priority-Based Search, and Large Neighborhood Search), compilation-based approaches (SAT, SMT, CSP, ASP, and MIP formulations), and data-driven techniques (reinforcement learning, supervised learning, and hybrid strategies). Through systematic analysis of experimental practices across 200+ papers, we uncover significant disparities in evaluation methodologies, with classical methods typically tested on larger-scale instances (up to 200 by 200 grids with 1000+ agents) compared to learning-based approaches (predominantly 10-100 agents). We provide a comprehensive taxonomy of evaluation metrics, environment types, and baseline selections, highlighting the need for standardized benchmarking protocols. Finally, we outline promising future directions including mixed-motive MAPF with game-theoretic considerations, language-grounded planning with large language models, and neural solver architectures that combine the rigor of classical methods with the flexibility of deep learning. This survey serves as both a comprehensive reference for researchers and a practical guide for deploying MAPF solutions in increasingly complex real-world applications.