MAPP: a Scalable Multi-Agent Path Planning Algorithm with Tractability and Completeness Guarantees (1401.3905v1)

Abstract: Multi-agent path planning is a challenging problem with numerous real-life applications. Running a centralized search such as A* in the combined state space of all units is complete and cost-optimal, but scales poorly, as the state space size is exponential in the number of mobile units. Traditional decentralized approaches, such as FAR and WHCA*, are faster and more scalable, being based on problem decomposition. However, such methods are incomplete and provide no guarantees with respect to the running time or the solution quality. They are not necessarily able to tell in a reasonable time whether they would succeed in finding a solution to a given instance. We introduce MAPP, a tractable algorithm for multi-agent path planning on undirected graphs. We present a basic version and several extensions. They have low-polynomial worst-case upper bounds for the running time, the memory requirements, and the length of solutions. Even though all algorithmic versions are incomplete in the general case, each provides formal guarantees on problems it can solve. For each version, we discuss the algorithms completeness with respect to clearly defined subclasses of instances. Experiments were run on realistic game grid maps. MAPP solved 99.86% of all mobile units, which is 18--22% better than the percentage of FAR and WHCA*. MAPP marked 98.82% of all units as provably solvable during the first stage of plan computation. Parts of MAPPs computation can be re-used across instances on the same map. Speed-wise, MAPP is competitive or significantly faster than WHCA*, depending on whether MAPP performs all computations from scratch. When data that MAPP can re-use are preprocessed offline and readily available, MAPP is slower than the very fast FAR algorithm by a factor of 2.18 on average. MAPPs solutions are on average 20% longer than FARs solutions and 7--31% longer than WHCA*s solutions.

• The paper introduces MAPP, a multi-agent path planning algorithm balancing scalability, tractability, and partial completeness guarantees.
• Experimental results show MAPP successfully solved 99.86% of units, outperforming FAR and WHCA* in fully solved instances.
• MAPP offers a promising balance for real-world applications like robotics and logistics, with potential for integration into algorithm portfolios.

MAPP: A Scalable Multi-Agent Path Planning Algorithm with Tractability and Completeness Guarantees

The paper "MAPP: A Scalable Multi-Agent Path Planning Algorithm with Tractability and Completeness Guarantees," authored by Ko-Hsin Cindy Wang and Adi Botea, addresses the problem of multi-agent path planning by introducing the MAPP algorithm. This algorithm presents a novel approach that combines theoretical tractability with partial completeness guarantees, while also performing efficiently in practice.

Overview

Multi-agent path planning involves coordinating paths for multiple units in a shared space, where each unit must navigate from a start position to a target position without colliding with others. Centralized approaches such as A* can achieve completeness and optimality but suffer from poor scalability due to the exponentially large state space when multiple agents are involved. On the other hand, decentralized approaches like FAR and WHCA* offer scalability but lack guarantees regarding solution completeness and quality.

MAPP bridges this gap by providing formal guarantees for certain subclasses of problems it can solve, with competitive performance in terms of scalability and efficiency. It systematically identifies units that are provably solvable within low polynomial time, using the concept of SLIDABLE units, which adhere to three specific conditions: alternate connectivity, initial blank position, and target isolation.

Experimental Results

Empirical evaluations were conducted on realistic game grid maps containing up to 2,000 mobile units. MAPP successfully solved 99.86% of units, outperforming FAR and WHCA* by 18-22%. Despite its incompleteness in the general case, MAPP provides formal guarantees for the units it solves. The algorithm's computational efficiency is demonstrated, particularly when preprocessed data are reused across instances on the same map.

MAPP exhibited a significant improvement in the percentage of solved units compared to established methods, such as FAR and WHCA*. Specifically, the TI+AC variant of MAPP that attempts to solve all units resulted in 84.5% fully solved instances, compared to FAR's 70.6% and WHCA*’s 58.3% (without diagonal moves). When preprocessed data are utilized, MAPP's execution time improved dramatically, making it significantly faster than WHCA* and not far behind FAR.

Implications and Future Developments

The introduction of MAPP opens up promising directions for multi-agent path planning. The algorithm's variants provide an effective balance between theoretical guarantees and practical scalability, which could be leveraged in domains requiring robust, scalable pathfinding solutions, such as robotics or logistics. Future research may focus on further extending MAPP's completeness range to tackle instances involving heterogeneous units, or improve the solution quality in terms of makespan and the total number of actions.

Moreover, MAPP's ability to detect provable instances opens opportunities for integrating it into an algorithm portfolio, where it could be applied selectively depending on the problem structure. Enhancements could also look into optimizing the repositioning strategy and increasing the reuse of precomputed paths to further reduce compute times and increase overall algorithm efficiency. These developments will contribute to advancing multi-agent path planning toward solving increasingly complex and large-scale scenarios.