Modelling Multi-Agent Pathfinding Problems by Integrating Connectivity and No-Collision Constraints

Jiri Svancara, Roman Barták, Ian Miguel, Joan Espasa

Keywords: Multi-agent pathfinding, SAT, SMT, graph propagators

TL;DR: In this paper, we explore a novel SMT-based encoding for MAPF based on graph propagators.

Abstract: Multi-agent pathfinding (MAPF) is the problem of finding collision-free paths for a set of agents in a shared environment, typically represented as a graph. One of the approaches to solving MAPF represents the problem as a Boolean satisfiability problem. However, due to the encoding required to represent the valid paths, this method can produce extremely large Boolean formulas, both in terms of variables and clauses. Herein, we propose two encodings of MAPF designed for SAT Modulo Theories solvers. Our approach delegates all the valid path reasoning to a monotonic theory supporting source-target connectivity. This is then combined with a 2-SAT Boolean formula to prevent collisions between agents. Together, these components create an effective separation of concerns: the SAT solver focuses on resolving conflicts, while the theory solver handles the connectivity constraints. Our experiments are conducted in both makespan and sum of costs optimisation settings, empirically demonstrating a notable reduction in both the size of the MAPF encoding and the time required to generate it. In addition, when fixing the SAT solver across experiments, results demonstrate considerable performance improvements when transitioning from pure SAT to our proposed SMT encodings.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 37