Meta-Agent Conflict-Based Search For Optimal Multi-Agent Path Finding.

The task in the multi-agent path finding problem (MAPF) is to find paths for multiple agents, each with a different start and goal position, such that agents do not collide. It is possible to solve this problem optimally with algorithms that are based on the A* algorithm. Recently, we proposed an alternative algorithm called Conflict-Based Search (CBS) (Sharon et al. 2012), which was shown to outperform the A*-based algorithms in some cases. CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. While in some cases CBS is very efficient, in other cases it is worse than A*-based algorithms. This paper focuses on the latter case by generalizing CBS to Meta-Agent CBS (MA-CBS). The main idea is to couple groups of agents into meta-agents if the number of internal conflicts between them exceeds a given bound. MACBS acts as a framework that can run on top of any complete MAPF solver. We analyze our new approach and provide experimental results demonstrating that it outperforms basic CBS and other A*-based optimal solvers in many cases. Introduction and Background In the multi-agent path finding (MAPF) problem, we are given a graph, G(V,E), and a set of k agents labeled a1 . . . ak. Each agent ai has a start position si ∈ V and goal position gi ∈ V . At each time step an agent can either move to a neighboring location or can wait in its current location. The task is to return the least-cost set of actions for all agents that will move each of the agents to its goal without conflicting with other agents (i.e., without being in the same location at the same time or crossing the same edge simultaneously in opposite directions). MAPF has practical applications in robotics, video games, vehicle routing, and other domains (Silver 2005; Dresner and Stone 2008). In its general form, MAPF is NPcomplete, because it is a generalization of the sliding tile puzzle, which is NP-complete (Ratner and Warmuth 1986). There are many variants to the MAPF problem. In this paper we consider the following common setting. The cumulative cost function to minimize is the sum over all agents of the number of time steps required to reach the goal location (Standley 2010; Sharon et al. 2011a). Both move and Copyright c © 2012, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. wait actions cost one. A centralized computing setting with a single CPU that controls all the agents is assumed. Note that a centralized computing setting is logically equivalent to a decentralized setting where each agent has its own computing power but agents are fully cooperative with full knowledge sharing and free communication. There are two main approaches for solving the MAPF in the centralized computing setting: the coupled and the decoupled approaches. In the decoupled approach, paths are planned for each agent separately. Algorithms from the decoupled approach run relatively fast, but optimality and even completeness are not always guaranteed (Silver 2005; Wang and Botea 2008; Jansen and Sturtevant 2008). New complete (but not optimal) decoupled algorithms were recently introduced for trees (Khorshid, Holte, and Sturtevant 2011) and for general graphs (Luna and Bekris 2011). Our aim is to solve the MAPF problem optimally and therefore the focus of this paper is on the coupled approach. In this approach MAPF is formalized as a global, singleagent search problem. One can activate an A*-based algorithm that searches a state space that includes all the different ways to permute the k agents into |V | locations. Consequently, the state space that is searched by the A*-based algorithms grow exponentially with the number of agents. Hence, finding the optimal solutions with A*-based algorithms requires significant computational expense. Previous optimal solvers dealt with this large search space in several ways. Ryan (2008; 2010) abstracted the problem into pre-defined structures such as cliques, halls and rings. He then modeled and solved the problem as a CSP problem. Note that the algorithm Ryan proposed does not necessarily returns the optimal solutions. Standley (2010; 2011) partitioned the given problem into smaller independent problems, if possible. Sharon et. al. (2011a; 2011b) suggested the increasing cost search tree (ICTS) a two-level framework where the high-level phase searches a tree with exact path costs for each of the agents and the low-level phase aims to verify whether there is a solution of this cost. In this paper we focus on the new Conflict Based Search algorithm (CBS) (Sharon et al. 2012) which optimally solves MAPF. CBS is a two-level algorithm where the high-level search is performed on a constraint tree (CT) whose nodes include constraints on time and locations of a single agent. At each node in the constraint tree a low-level search is per97 Proceedings of the Fifth Annual Symposium on Combinatorial Search