Integration of Independence Detection into SAT-based Optimal Multi-Agent Path Finding - A Novel SAT-based Optimal MAPF Solver

Surynek, Pavel; Švancara, Jiří; Felner, Ariel; Boyarski, Eli

doi:10.5220/0006126000850095

Cited by 6 publications

(3 citation statements)

References 22 publications

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“…In this section, we describe how to integrate independence detection for MAPF (Standley, 2010b;Standley & Korf, 2011) into MDD-SAT. We summarize here and extend the results originally published as conference papers (Surynek et al, 2017b(Surynek et al, , 2017c.…”

Section: Independence Detection In Sat-based Approachsupporting

confidence: 76%

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

Surynek¹,

Stern²,

Boyarski³

et al. 2022

jair

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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.

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Section: Independence Detection In Sat-based Approachsupporting

confidence: 76%

“…Results presented in this work partly appeared in several conference papers (Surynek, Felner, Stern, & Boyarski, 2016a, 2016b, 2017aSurynek, Svancara, Felner, & Boyarski, 2017c, 2017b.…”

Section: Current Shortcomings and Contributionmentioning

confidence: 75%

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

Surynek¹,

Stern²,

Boyarski³

et al. 2022

jair

Self Cite

View full text Add to dashboard Cite

show abstract

“…Therefore, there are numerous heuristic approaches that allow us to efficiently obtain a useful solution for the given input; see, e.g., the survey (Stern 2019) for overview of such results. A multitude of techniques was used to tackle MAPF-A*-based algorithms (Hart, Nilsson, and Raphael 1968), SAT-based algorithms (Surynek et al 2017), scheduling approach (Barták, Švancara, and Vlk 2018), SMTsolvers (Surynek 2019(Surynek , 2020, to name just a few. Our work focuses on exact algorithms, that is, the aim is to return an optimal solution and the central question is on which kinds of inputs this can be done in an efficient way and where this is unlikely.…”

Section: Introductionmentioning

confidence: 99%

Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology

Fioravantes,

Knop,

Křištan

et al. 2024

AAAI

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In the Multiagent Path Finding (MAPF for short) problem, we focus on efficiently finding non-colliding paths for a set of k agents on a given graph G, where each agent seeks a path from its source vertex to a target. An important measure of the quality of the solution is the length of the proposed schedule l, that is, the length of a longest path (including the waiting time). In this work, we propose a systematic study under the parameterized complexity framework. The hardness results we provide align with many heuristics used for this problem, whose running time could potentially be improved based on our Fixed-Parameter Tractability (FPT) results. We show that MAPF is W[1]-hard with respect to k (even if k is combined with the maximum degree of the input graph). The problem remains NP-hard in planar graphs even if the maximum degree and the makespan l are fixed constants. On the positive side, we show an FPT algorithm for k+l. As we continue, the structure of G comes into play. We give an FPT algorithm for parameter k plus the diameter of the graph G. The MAPF problem is W[1]-hard for cliquewidth of G plus l while it is FPT for treewidth of G plus l.

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Variants of Independence Detection in SAT-Based Optimal Multi-agent Path Finding

Surynek

Švancara

Felner

et al. 2018

Lecture Notes in Computer Science

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Integration of Independence Detection into SAT-based Optimal Multi-Agent Path Finding - A Novel SAT-based Optimal MAPF Solver

Cited by 6 publications

References 22 publications

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

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

Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology

Variants of Independence Detection in SAT-Based Optimal Multi-agent Path Finding

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