Migrating Techniques from Search-based Multi-Agent Path Finding Solvers to SAT-based Approach

Abstract

In the multi-agent path finding problem (MAPF) we are given a set of agents each with respective start and goal positions. The task is to find paths for all agents while avoiding collisions, aiming to minimize a given objective function. Many MAPF solvers were introduced in the past decade for optimizing two specific objective functions: sum-of-costs and makespan. Two prominent categories of solvers can be distinguished: search-based solvers and compilation-based solvers. Search-based solvers were developed and tested for the sum-of-costs objective, while the most prominent compilation-based solvers that are built around Boolean satisfiability (SAT) were designed for the makespan objective. Very little is known on the performance and relevance of solvers from the compilation-based approach on the sum-of-costs objective. In this paper, we start to close the gap between these cost functions in the compilation-based approach. Our main contribution is a new SAT-based MAPF solver called MDD-SAT, that is directly aimed to optimally solve the MAPF problem under the sum-of-costs objective function. Using both a lower bound on the sum-of-costs and an upper bound on the makespan, MDD-SAT is able to generate a reasonable number of Boolean variables in our SAT encoding. We then further improve the encoding by borrowing ideas from ICTS, a search-based solver. In addition, we show that concepts applicable in search-based solvers like ICTS and ICBS are applicable in the SAT-based approach as well. Specifically, we integrate independence detection, a generic technique for decomposing an MAPF instance into independent subproblems, into our SAT-based approach, and we design a relaxation of our optimal SAT-based solver that results in a bounded suboptimal SAT-based solver. Experimental evaluation on several domains shows that there are many scenarios where our SAT-based methods outperform state-of-the-art sum-of-costs search-based solvers, such as variants of the ICTS and ICBS algorithms.

Multi-Agent Path Finding: A New Boolean Encoding

“…We briefly review relevant aspects of the two most related compilation-based approaches: MDD-SAT (Surynek et al, 2016(Surynek et al, , 2022 and ASP-MAPF (Gómez et al, 2021). Both approaches encode the problem using propositional variables relative to a certain time instant.…”

“…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.…”