Abstract
In multi-agent path finding (MAPF) the task is to navigate agents from their starting positions to given individual goals. The problem takes place in an undirected graph whose vertices represent positions and edges define the topology. Agents can move to neighbor vertices across edges. In the standard MAPF, space occupation by agents is modeled by a capacity constraint that permits at most one agent per vertex. We suggest an extension of MAPF in this paper that permits more than one agent per vertex. Propositional satisfiability (SAT) models for these extensions of MAPF are studied. We focus on modeling capacity constraints in SAT-based formulations of MAPF and evaluation of performance of these models. We extend two existing SAT-based formulations with vertex capacity constraints: MDD-SAT and SMT-CBS where the former is an approach that builds the model in an eager way while the latter relies on lazy construction of the model.
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Notes
- 1.
The notation \(path(a_i)\) refers to path in the form of a sequence of vertices and edges connecting \(\alpha _0(a_i)\) and \(\alpha _+(a_i)\) while \(\xi \) assigns the cost to a given path.
- 2.
Dealing with objectives is out of scope of this paper. We refer the reader to [31] for more detailed discussion.
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This research has been supported by GAČR - the Czech Science Foundation, grant registration number 19-17966S.
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Surynek, P., Kumar, T.K.S., Koenig, S. (2019). Multi-agent Path Finding with Capacity Constraints. In: Alviano, M., Greco, G., Scarcello, F. (eds) AI*IA 2019 – Advances in Artificial Intelligence. AI*IA 2019. Lecture Notes in Computer Science(), vol 11946. Springer, Cham. https://doi.org/10.1007/978-3-030-35166-3_17
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