[Paper Review] LaCAM: Search-Based Algorithm for Quick Multi-Agent Pathfinding

Keisuke Okumura|arXiv (Cornell University)|Nov 24, 2022

Robotic Path Planning Algorithms4 citations

TL;DR

LaCAM is a novel, complete, and efficient search-based algorithm for multi-agent pathfinding (MAPF) that uses a two-level search: high-level configuration search with lazy constraint generation from low-level agent-specific pathfinding. It achieves sub-second planning times even for 10,000 agents on large, dense grids, outperforming state-of-the-art sub-optimal solvers in speed, success rate, and solution quality.

ABSTRACT

We propose a novel complete algorithm for multi-agent pathfinding (MAPF) called lazy constraints addition search for MAPF (LaCAM). MAPF is a problem of finding collision-free paths for multiple agents on graphs and is the foundation of multi-robot coordination. LaCAM uses a two-level search to find solutions quickly, even with hundreds of agents or more. At the low-level, it searches constraints about agents' locations. At the high-level, it searches a sequence of all agents' locations, following the constraints specified by the low-level. Our exhaustive experiments reveal that LaCAM is comparable to or outperforms state-of-the-art sub-optimal MAPF algorithms in a variety of scenarios, regarding success rate, planning time, and solution quality of sum-of-costs.

Motivation & Objective

• To develop a fast, complete, and scalable algorithm for multi-agent pathfinding (MAPF) that handles hundreds to thousands of agents in real-time.
• To address the trade-off between solution quality and planning speed in large-scale MAPF applications, especially where optimal algorithms are too slow.
• To enable efficient planning in dense, complex environments such as automated warehouses with high agent counts and obstacle density.
• To design a modular, extensible framework that can integrate modern single-agent planners for configuration generation.
• To demonstrate that lazy constraint addition at the low-level can drastically reduce search effort while maintaining solution completeness.

Proposed method

• LaCAM employs a two-level search: high-level exploration of agent configurations and low-level search for agent-specific movement constraints.
• At the high-level, each node represents a full configuration (agent locations at a time step), and successors are generated lazily using constraints from the low-level.
• The low-level performs single-agent pathfinding to determine which agent moves where in the next configuration, generating positive constraints (e.g., 'agent i goes to vertex v').
• Constraints are added incrementally and only when needed, reducing the branching factor and search space compared to full configuration enumeration.
• The algorithm uses A* with a heuristic based on sum-of-costs and integrates external planners (e.g., PIBT) as configuration generators.
• It maintains completeness by systematically exploring configurations and resolving conflicts through constraint addition, similar to CBS but with a reversed constraint direction (positive vs. negative).

Experimental results

Research questions

• RQ1 Can a two-level search with lazy constraint addition achieve both completeness and high speed in large-scale MAPF?
• RQ2 How does LaCAM compare to state-of-the-art sub-optimal MAPF algorithms in terms of planning time, success rate, and solution quality?
• RQ3 Can LaCAM scale to 10,000 agents on large, dense grids within real-time constraints?
• RQ4 What is the impact of using positive constraints (who goes where) versus negative constraints (who cannot go where) on search efficiency?
• RQ5 To what extent can the branching factor be reduced through lazy, incremental successor generation in high-level configurations?

Key findings

• LaCAM solved all 400-agent instances on a 32×32 grid with 20% obstacles from the MAPF benchmark in a median time of 1 second, outperforming baseline sub-optimal algorithms that failed under 30-second timeouts.
• On a large 1491×656 four-connected grid, LaCAM successfully solved instances with up to 10,000 agents in tens of seconds, demonstrating strong scalability.
• In dense scenarios with high agent-to-space ratios, LaCAM maintained high success rates and low planning times, where other solvers often failed or timed out.
• The use of positive constraints in the low-level search reduced the search space compared to negative constraint approaches, leading to faster convergence.
• LaCAM’s lazy successor generation suppressed the effective branching factor, enabling fast convergence even with large agent counts.
• The algorithm achieved competitive sum-of-costs (SOC) values, indicating high solution quality despite being sub-optimal, and showed strong robustness across diverse map types and agent densities.