Efficient Decomposition of Multi-Agent Path Finding (MAPF) Instances to Improve Computational Performance

Belangrijkste concepten

A novel approach to decompose MAPF instances into smaller solvable subproblems without compromising the overall solvability, enabling general MAPF algorithms to solve each subproblem independently and merge their solutions into a conflict-free final solution.

Samenvatting

The paper proposes a novel approach called LayeredMAPF to decompose a MAPF instance involving a large number of agents into multiple isolated subproblems with fewer agents. The key highlights are:

1. The decomposition process involves three steps:
   a. Identifying initial clusters of agents based on their dependence paths.
   b. Refining the clusters by bipartitioning them into smaller clusters.
   c. Further decomposing the clusters into levels with a specific solving order.

2. The decomposition ensures the solvability of each subproblem by verifying the existence of a solution under a simplified scenario where agents only need to avoid the targets of previous subproblems and the starts of later subproblems.

3. A framework is presented to enable general MAPF algorithms to solve each subproblem independently and merge their solutions into a conflict-free final solution. This framework handles the differences between serial and parallel MAPF methods.

4. Extensive experiments are conducted on classic MAPF benchmarks to evaluate the impact of decomposition on time cost, memory usage, success rate, and solution quality. The results demonstrate that the decomposition can significantly reduce the memory usage and time cost, particularly for serial MAPF methods.

5. The source code of the proposed algorithm is made publicly available to facilitate further research within the community.

Statistieken

The MAPF instances used in the experiments are from a classic MAPF dataset, comprising 24 typical maps with an increasing number of agents. Each number of agents is randomly selected 100 times, resulting in a total of 22,300 MAPF instances.

Citaten

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Belangrijkste Inzichten Gedestilleerd Uit

LayeredMAPF: a decomposition of MAPF instance without compromising solvability

by Zhuo Yao,Wei... om arxiv.org 04-22-2024

https://arxiv.org/pdf/2404.12773.pdf

Diepere vragen

How can the proposed decomposition method be further improved to guarantee the discovery of the optimal decomposition

To guarantee the discovery of the optimal decomposition, several enhancements can be made to the proposed method. One approach is to incorporate heuristics or optimization algorithms that can guide the decomposition process towards smaller subproblems more efficiently. By introducing criteria that prioritize the creation of subproblems with minimal size and ensuring that each step of the decomposition leads to a reduction in the overall problem complexity, the method can be refined to converge towards the optimal decomposition. Additionally, exploring advanced graph theory algorithms or machine learning techniques to analyze agent dependencies and predict the most effective decomposition strategies could further improve the method's ability to find the optimal solution.

What are the theoretical guarantees on the solution quality degradation when applying the decomposition approach to different MAPF methods

Theoretical guarantees on solution quality degradation when applying the decomposition approach to different MAPF methods can vary based on the characteristics of the methods and the specific instances being solved. In general, the decomposition of a MAPF instance may lead to a degradation in solution quality due to the division of the problem into smaller subproblems. This degradation is primarily influenced by the size and complexity of the subproblems created during the decomposition process. While the proposed method aims to maintain solvability without compromising on solution quality, the trade-off between decomposition efficiency and solution optimality may vary depending on the specific MAPF methods used and the nature of the instances being solved.

Can the decomposition technique be extended to other multi-agent coordination problems beyond MAPF

The decomposition technique used for Multi-Agent Path Finding (MAPF) instances can be extended to other multi-agent coordination problems beyond MAPF. By adapting the decomposition approach to suit the requirements and constraints of different coordination problems, such as task allocation, swarm robotics, or distributed sensor networks, the method can be applied to optimize the coordination and movement of multiple agents in various scenarios. The key lies in identifying the dependencies and interactions between agents, defining appropriate subproblems based on these dependencies, and ensuring that the decomposition process maintains solvability and efficiency while reducing the overall computational complexity of the problem. This extension can enhance the scalability and performance of algorithms designed for multi-agent coordination tasks.