Xiaoyu He , Xueyan Tang , Wentong Cai , Jingning Li
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引用次数: 0
摘要
多代理路径查找(MAPF)是一个经典的 NP 难问题,它考虑同时为多个代理规划无碰撞路径。MAPF 问题通常是通过处理一系列单个代理路径查找子问题来解决的,在这些子问题中,A⁎ 等经过充分研究的算法是适用的。然而,基于这一思想的现有方法依赖于穷举搜索,因此只能保证渐进性能。在本文中,我们提供了一种建模范式,将 MAPF 问题转换为随机过程,并采用基于置信度约束的规则来寻找最优状态转换策略。我们提出了一种随机算法来解决这一随机过程,该算法结合了基于冲突的搜索和蒙特卡罗树搜索的思想。我们证明,所提出的方法几乎肯定是最优的,同时享有非渐近性能保证。特别是,在解决 N 个单代理子问题后,所提出的方法可以产生一个可行解,其次优化性的边界为 O(1/N)。基于网格图的几个数值实验验证了理论结果。
A stochastic process approach for multi-agent path finding with non-asymptotic performance guarantees
Multi-agent path finding (MAPF) is a classical NP-hard problem that considers planning collision-free paths for multiple agents simultaneously. A MAPF problem is typically solved via addressing a sequence of single-agent path finding subproblems in which well-studied algorithms such as are applicable. Existing methods based on this idea, however, rely on an exhaustive search and therefore only have asymptotic performance guarantees. In this article, we provide a modeling paradigm that converts a MAPF problem into a stochastic process and adopts a confidence bound based rule for finding the optimal state transition strategy. A randomized algorithm is proposed to solve this stochastic process, which combines ideas from conflict based search and Monte Carlo tree search. We show that the proposed method is almost surely optimal while enjoying non-asymptotic performance guarantees. In particular, the proposed method can, after solving N single-agent subproblems, produce a feasible solution with suboptimality bounded by . The theoretical results are verified by several numerical experiments based on grid maps.
期刊介绍:
The Journal of Artificial Intelligence (AIJ) welcomes papers covering a broad spectrum of AI topics, including cognition, automated reasoning, computer vision, machine learning, and more. Papers should demonstrate advancements in AI and propose innovative approaches to AI problems. Additionally, the journal accepts papers describing AI applications, focusing on how new methods enhance performance rather than reiterating conventional approaches. In addition to regular papers, AIJ also accepts Research Notes, Research Field Reviews, Position Papers, Book Reviews, and summary papers on AI challenges and competitions.