Branch-and-Cut-and-Price for Multi-Agent Pathfinding

Lam, Edward; Bodic, Pierre Le; Harabor, Daniel; Stuckey, Peter J.

doi:10.24963/ijcai.2019/179

Cited by 71 publications

(69 citation statements)

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“…Multi-agent path finding (MAPF) is a problem of MAPP in discrete spaces, with the objective of finding a set of timed paths on graphs while preventing collisions with other agents [58]. MAPF has been studied extensively over the last decade and has produced numerous powerful algorithms (e.g., [4,34,45,51]). More recently, some works have attempted to leverage machine-learning techniques for solving MAPF.…”

Section: Related Workmentioning

confidence: 99%

“…Over the last decade, significant progress has been made on MAPP in discretized environments, which is also known as multi-agent path finding (MAPF), aimed at finding a set of conflict-free paths on a graph given a priori, typically as a grid. Despite its optimization intractability in various criteria [2,42,63], recent work has shown MAPF can obtain near-optimal solutions in a short amount of time (e.g., less than a minute), even for hundreds of agents [34,37,46].…”

Section: Introductionmentioning

confidence: 99%

“…We extensively evaluate our approach on a variety of MAPP problems with several different setups in terms of the number of agents (21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40), the presence of obstacles, and the heterogeneity in agent sizes and motion speeds. Our results consistently demonstrate that, compared to standard roadmap construction strategies, planning by learning to construct CTRMs is several orders of magnitude more efficient in the planning effort (e.g., assessed by search node expansions or runtime), while maintaining a comparable planning success rate and solution quality, with acceptable overheads.…”

Section: Introductionmentioning

confidence: 99%

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CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces

Okumura¹,

Yonetani²,

Nishimura³

et al. 2022

Preprint

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Multi-agent path planning (MAPP) in continuous spaces is a challenging problem with significant practical importance. One promising approach is to first construct graphs approximating the spaces, called roadmaps, and then apply multi-agent pathfinding (MAPF) algorithms to derive a set of conflict-free paths. While conventional studies have utilized roadmap construction methods developed for single-agent planning, it remains largely unexplored how we can construct roadmaps that work effectively for multiple agents. To this end, we propose a novel concept of roadmaps called cooperative timed roadmaps (CTRMs). CTRMs enable each agent to focus on its important locations around potential solution paths in a way that considers the behavior of other agents to avoid inter-agent collisions (i.e., "cooperative"), while being augmented in the time direction to make it easy to derive a "timed" solution path. To construct CTRMs, we developed a machine-learning approach that learns a generative model from a collection of relevant problem instances and plausible solutions and then uses the learned model to sample the vertices of CTRMs for new, previously unseen problem instances. Our empirical evaluation revealed that the use of CTRMs significantly reduced the planning effort with acceptable overheads while maintaining a success rate and solution quality comparable to conventional roadmap construction approaches. †

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces

Okumura¹,

Yonetani²,

Nishimura³

et al. 2022

Preprint

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“…Gange et al (2019) replaced the high-level solver of CBS with a lazily constructed constraint programming model with nogoods (Lazy CBS). Lam et al (2019) solved MAPF using a decomposition framework developed for mathematical optimization called branch-and-cut-and-price (BCP).…”

Section: A Declarative Solutionmentioning

confidence: 99%

Robust Multi-Agent Path Finding and Executing

Atzmon

Stern

Felner

et al. 2020

jair

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Multi-agent path-finding (MAPF) is the problem of finding a plan for moving a set of agents from their initial locations to their goals without collisions. Following this plan, however, may not be possible due to unexpected events that delay some of the agents. In this work, we propose a holistic solution for MAPF that is robust to such unexpected delays. First, we introduce the notion of a k-robust MAPF plan, which is a plan that can be executed even if a limited number (k) of delays occur. We propose sufficient and required conditions for finding a k-robust plan, and show how to convert several MAPF solvers to find such plans. Then, we propose several robust execution policies. An execution policy is a policy for agents executing a MAPF plan. An execution policy is robust if following it guarantees that the agents reach their goals even if they encounter unexpected delays. Several classes of such robust execution policies are proposed and evaluated experimentally. Finally, we present robust execution policies for cases where communication between the agents may also be delayed. We performed an extensive experimental evaluation in which we compared different algorithms for finding robust MAPF plans, compared different ro- bust execution policies, and studied the interplay between having a robust plan and the performance when using a robust execution policy.

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“…Nevertheless, given its high utility, especially in e-commerce applications [46,32,45] that are expected to grow significantly [8,1], many algorithmic solutions have been proposed for optimally solving MRPP. Among these, combinatorialsearch based solvers [24] have been demonstrated to be fairly effective. MRPP solvers may be classified as being optimal or suboptimal.…”

Section: Introductionmentioning

confidence: 99%

Sub-1.5 Time-Optimal Multi-Robot Path Planning on Grids in Polynomial Time

Yu¹

2022

Preprint

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It is well-known that graph-based multi-robot path planning (MRPP) is NP-hard to optimally solve. In this work, we propose the first low polynomial-time algorithm for MRPP achieving 1-1.5 asymptotic optimality guarantees on solution makespan (i.e., the time it takes to complete a reconfiguration of the robots) for random instances under very high robot density, with high probability. Specifically, on an m1 ×m2 gird, m1 ≥ m2, our RTH (Rubik Table with Highways) algorithm computes solutions for routing up to m 1 m 2 3 robots with uniformly randomly distributed start and goal configurations with a makespan of m1 + 2m2 + o(m1), with high probability. Because the minimum makespan for such instances is m1 + m2 − o(m1), also with high probability, RTH guarantees m 1 +2m 2 m 1 +m 2 optimality as m1 → ∞ for random instances with up to 1 3 robot density, with high probability. m 1 +2m 2 m 1 +m 2 ∈ (1, 1.5]. Alongside the above-mentioned key result, we also establish:(1) for completely filled grids, i.e., m1m2 robots, any MRPP instance may be solved in polynomial time under a makespan of 7m1 + 14m2, (2) for m 1 m 2 3 robots, RTH solves arbitrary MRPP instances with makespan of 3m1 + 4m2 + o(m1), (3) for m 1 m 2 2 robots, a variation of RTH solves a random MRPP instance with the same 1-1.5 optimality guarantee, and (4) the same m 1 +2m 2 m 1 +m 2 optimality guarantee holds for regularly distributed obstacles at 1 9 density together with 2m 1 m 2 9 randomly distributed robots; such settings directly map to real-world parcel sorting scenarios.Moreover, we have developed effective, principled heuristics that further improve the computed optimality of RTH algorithms. In extensive numerical evaluations, RTH and its variants demonstrate exceptional scalability as compared with methods including ECBS and DDM, scaling to over 450 × 300 grids with 45, 000 robots, and consistently achieves makespan around 1.5 optimal or better, as predicted by our theoretical analysis.• The same m1+2m2 m1+m2 optimality guarantee may be achieved on grids with up to m1m2 9 regularly distributed obstacles together with 2m1m2 9 robots using RTH (e.g., Fig. 1(b)).

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Branch-and-Cut-and-Price for Multi-Agent Pathfinding

Cited by 71 publications

References 1 publication

CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces

CTRMs: Learning to Construct Cooperative Timed Roadmaps for Multi-agent Path Planning in Continuous Spaces

Robust Multi-Agent Path Finding and Executing

Sub-1.5 Time-Optimal Multi-Robot Path Planning on Grids in Polynomial Time

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