On the Complexity of Optimal Parallel Cooperative Path-Finding

Surynek, Pavel

doi:10.3233/fi-2015-1192

Cited by 3 publications

(2 citation statements)

References 27 publications

(24 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…NP-hard even on planar graphs [23,24,41,54,62,60]. Therefore, many suboptimal solvers were developed and are usually used when m is large or when the graph is large [8,18,26,28,36,58].…”

Section: S(σ)mentioning

confidence: 99%

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

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.

show abstract

“…NP-hard even on planar graphs [23,24,41,54,62,60]. Therefore, many suboptimal solvers were developed and are usually used when m is large or when the graph is large [8,18,26,28,36,58].…”

Section: S(σ)mentioning

confidence: 99%

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

“…In other words, it is the length of the longest path from paths traveled by individual agents. It is known that finding makespan optimal solutions to CPF is a difficult problem, namely it is NP-hard [16,32,39]. Hence reducing the makespan optimal CPF to SAT is justified as both problems are at the same level in terms of the complexity.…”

Section: Introductionmentioning

confidence: 99%

A Simple Approach to Solving Cooperative Path-Finding as Propositional Satisfiability Works Well

Surynek

2014

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

The problem of makespan optimal solving of cooperative path finding (CPF) is addressed in this paper. The task in CPF is to relocate a group of agents in a non-colliding way so that each agent eventually reaches its goal location from the given initial location. The abstraction adopted in this work assumes that agents are discrete items moving in an undirected graph by traversing edges. Makespan optimal solving of CPF means to generate solutions that are as short as possible in terms of the total number of time steps required for the execution of the solution.We show that reducing CPF to propositional satisfiability (SAT) represents a viable option for obtaining makespan optimal solutions. Several encodings of CPF into propositional formulae are suggested and experimentally evaluated. The evaluation indicates that SAT based CPF solving outperforms other makespan optimal methods significantly in highly constrained situations (environments that are densely occupied by agents).

show abstract

Time-expanded graph-based propositional encodings for makespan-optimal solving of cooperative path finding problems

Surynek

2017

Ann Math Artif Intell

View full text Add to dashboard Cite

On the Complexity of Optimal Parallel Cooperative Path-Finding

Cited by 3 publications

References 27 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

A Simple Approach to Solving Cooperative Path-Finding as Propositional Satisfiability Works Well

Time-expanded graph-based propositional encodings for makespan-optimal solving of cooperative path finding problems

Contact Info

Product

Resources

About