On SAT-Based Approaches for Multi-Agent Path Finding with the Sum-of-Costs Objective

Barták, Roman; Švancara, Jiří

doi:10.1609/socs.v10i1.18497

Cited by 5 publications

(6 citation statements)

References 15 publications

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“…The paper [36] investigates MAPF with continuous time, which removes the assumption that transitions between nodes are uniform. A SATbased solver described in the paper [37] can also deal with this extension. SMT-based MAPF solver for MAPF with continuous time and geometric agents is described in [38].…”

Section: Related Workmentioning

confidence: 99%

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

Rajaratnam¹,

Schaub

Wanko

et al. 2023

Algorithms

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A warehouse delivery problem consists of a set of robots that undertake delivery jobs within a warehouse. Items are moved around the warehouse in response to events. A solution to a warehouse delivery problem is a collision-free schedule of robot movements and actions that ensures that all delivery jobs are completed and each robot is returned to its docking station. While the warehouse delivery problem is related to existing research, such as the study of multi-agent path finding (MAPF), the specific industrial requirements necessitated a novel approach that diverges from these other approaches. For example, our problem description was more suited to formalizing the warehouse in terms of a weighted directed graph rather than the more common grid-based formalization. We formalize and encode the warehouse delivery problem in Answer Set Programming (ASP) extended with difference constraints. We systematically develop and study different encoding variants, with a view to computing good quality solutions in near real-time. In particular, application specific criteria are contrasted against the traditional notion of makespan minimization as a measure of solution quality. The encoding is tested against both crafted and industry data and experiments run using the Hybrid ASP solver clingo[dl].

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Section: Related Workmentioning

confidence: 99%

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

Rajaratnam¹,

Schaub

Wanko

et al. 2023

Algorithms

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“…We follow a two-phase approach similar to the one described by Barták and Svancara (2019) and Gómez, Hernández, and Baier (2021). Phase 1 finds a Makespanminimal with minimum cost.…”

Section: Soc-optimal Mapf Via Maxsatmentioning

confidence: 99%

“…While the former (e.g., Sharon et al 2012;Felner et al 2018;Li et al 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 et al 2016;Barták et al 2017; Barták and Svancara 2019), answer set programming (ASP) (e.g., Erdem et al 2013;Gebser et al 2018;Nguyen et al 2017;Gómez, Hernández, and 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.…”

Section: Introductionmentioning

confidence: 99%

A New Boolean Encoding for MAPF and its Performance with ASP and MaxSAT Solvers

Achá¹,

López²,

Hagedorn³

et al. 2021

SOCS

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Multi-agent pathfinding (MAPF) is an NP-hard problem. As such, dense maps may be very hard to solve optimally. In such scenarios, compilation-based approaches, via Boolean satisfiability (SAT) and answer set programming (ASP), have proven to be most effective. In this paper, we propose a new encoding for MAPF, which we implement and solve using both ASP and MaxSAT solvers. Our encoding builds on a recent ASP encoding for MAPF but changes the way agent moves are encoded. This allows to represent swap and follow conflicts with binary clauses, which are known to work well along with conflict-based clause learning. For MaxSAT, we study different ways in which we may combine the MSU3 and LSU algorithms for maximum performance. Our results, over grid and warehouse maps, show that the ASP solver scales better when the number of agents is increased on grids with few obstacles, while the MaxSAT solver performs better in scenarios with more obstacles and fewer agents.

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“…When MAPF tasks are relatively small and dense, the approaches that perform best in practice are compilation-based. One successful strategy, applicable to SAT-, ASP-, and MIP-based solvers (Barták and Svancara 2019;Gómez, Hernández, and Baier 2021;Asín Achá et al 2022), involves two phases: first, finding a solution Π min of minimum makespan (i.e., minimum time-to-completion), and second, using a theoretical result to compute an upper bound T * for the makespan of a cost-optimal solution. By encoding the problem for makespan T * , a minimum-cost solution is guaranteed to be cost-optimal.…”

Section: Introductionmentioning

confidence: 99%

A New Upper Bound for the Makespan of Cost-Optimal Solutions for Multi-Agent Path Finding (Extended Abstract)

López,

Asín-Achá,

Baier

2024

SOCS

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A well-known approach to solving Multi-Agent Path Finding (MAPF) optimally is compilation to Boolean Satisfiability or Answer Set Programming (ASP). Such compilation-based approaches are superior to other approaches on dense, relatively small instances and may invoke the solver multiple times, each with an encoding of the same instance for a different makespan. Critical to their performance is the runtime of the last solver invocation, whose input is the instance encoded with a theoretical upper bound of the makespan of the optimal solution. In this paper, we propose a new theoretical upper bound for such a last invocation. Unlike the previously known bound, when given a MAPF instance P, our bound requires a solution to P_1, a version of P where one of its agents is removed. We prove that our bound is correct and experimentally significantly tighter than the previously known bound. We propose a recursive parallel approach that allows us to exploit our new bound effectively. Our evaluation of warehouses and random MAPF benchmarks of varied sizes shows that our bound is, on average, 21.2% smaller than the previous bound. This allows for generating grounded ASP formulas around 33.45% smaller and solving 4.9% more instances.

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On SAT-Based Approaches for Multi-Agent Path Finding with the Sum-of-Costs Objective

Cited by 5 publications

References 15 publications

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

Solving an Industrial-Scale Warehouse Delivery Problem with Answer Set Programming Modulo Difference Constraints

A New Boolean Encoding for MAPF and its Performance with ASP and MaxSAT Solvers

A New Upper Bound for the Makespan of Cost-Optimal Solutions for Multi-Agent Path Finding (Extended Abstract)

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