A Compact Answer Set Programming Encoding of Multi-Agent Pathfinding

Abstract

Multi-agent pathfinding (MAPF) is the problem of finding k non-colliding paths connecting k given initial positions with k given goal positions on a given map. In its sum-of-costs variant, the total number of moves and wait actions performed by agents before they definitely reach the goal is minimized. Not surprisingly, since MAPF is combinatorial, a number of compilations to Boolean Satisfiability (SAT) and Answer Set Programming (ASP) exist. In this paper, we describe in detail the first family of compilations to ASP that solve sum-of-costs MAPF over 4-connected grids. Compared to existing ASP compilations, a distinguishing feature of our compilation is that the number of total clauses (after grounding) grow linearly with the number of agents, while existing compilations grow quadratically. In addition, the optimization objective is such that its size after grounding does not depend on the size of the grid. In our experimental evaluation, we show that our approach outperforms search-based sum-of-costs MAPF solvers when grids are congested with agents. We also show that our approach is competitive with a SAT-based approach when follow conflicts are taken into account. We also explore the potential of our solver when finding makespanoptimal solutions, in which makespan is minimized first and then cost is minimized. Our results show that makespan-optimal solutions are slightly suboptimal in most benchmarks. Moreover, our MAPF solver, when run in that mode, is faster and scales better.

An Adaptive Agent-Specific Sub-Optimal Bounding Approach for Multi-Agent Path Finding

“…While the edge conflict can be defined by (a i , u, t) → (a i , v, t + 1), where agent a i tries to go to vertex v ∈ V from u ∈ V between time-steps t and t + 1. At the same time-step t, another agent a j tries to go to vertex u ∈ V from v ∈ V incurring head-to-head conflict in t + 1; that is, (a j , v, t) → (a j , u, t + 1) [39]- [41].…”

Multi-Agent Path Finding: A New Boolean Encoding

“…While the former (e.g., Sharon, Stern, Felner, & Sturtevant, 2012;Felner, Li, Boyarski, Ma, Cohen, Kumar, & Koenig, 2018;Li, Felner, Boyarski, Ma, & Koenig, 2019a) can scale to large maps, they do not perform very well in relatively small, dense maps. Compilation-based techniques, instead, translate the MAPF instance to an instance of another problem, for example Boolean satisfiability (SAT) (e.g., Surynek, Felner, Stern, & Boyarski, 2016;Barták, Zhou, Stern, Boyarski, & Surynek, 2017;Barták & Svancara, 2019;Surynek, Stern, Boyarski, & Felner, 2022), answer set programming (ASP) (e.g., Erdem, Kisa, Öztok, & Schüller, 2013;Gebser, Obermeier, Otto, Schaub, Sabuncu, Nguyen, & Son, 2018;Nguyen, Obermeier, Son, Schaub, & Yeoh, 2017;Gómez, Hernández, & Baier, 2021), or Mixed-Integer Programming (MIP) (e.g., Barták et al, 2017). They do perform better than search-based solvers in dense, rather small maps, but do not scale to large maps.…”

“…The efficiency of compilation-based approaches depends on a number of factors, including the base SAT/ASP/MIP solver, but also on the encoding used. Recently, Gómez et al (2021) showed that focusing on generating a smaller encoding, linear on the number of agents rather than quadratic, yielded significant benefits in practice.…”

“…In this paper, we propose a new Boolean encoding for sum-of-costs MAPF and show how it can be implemented in both MaxSAT and ASP. Our encoding shares common aspects with the encoding introduced by Gómez et al (2021) for their ASP-MAPF solver. However, ours encodes decisions in a different way, allowing to represent swap and follow conflicts using binary clauses involving two decision variables.…”

Formalisation of Action with Durations in Answer Set Programming

“…ASP is already used in time-related solving in a lot of different contexts, from planning trains [2] to moving robots in wharehouse [25] [18]. There exist some dedicated tools like Telingo [6] that are used for planning.…”