Counterexample Guided Abstraction Refinement with Non-Refined Abstractions for Multi-Agent Path Finding

Counterexample guided abstraction refinement (CEGAR) represents a powerful symbolic technique for various tasks such as model checking and reachability analysis. Recently, CEGAR combined with Boolean satisfiability (SAT) has been applied for multi-agent path finding (MAPF), a problem where the task is to navigate agents from their start positions to given individual goal positions so that the agents do not collide with each other. The recent CEGAR approach used the initial abstraction of the MAPF problem where collisions between agents were omitted and were eliminated in subsequent abstraction refinements. We propose in this work a novel CEGAR-style solver for MAPF based on SAT in which some abstractions are deliberately left non-refined. This adds the necessity to post-process the answers obtained from the underlying SAT solver as these answers slightly differ from the correct MAPF solutions. Non-refining however yields order-of-magnitude smaller SAT encodings than those of the previous approach and speeds up the overall solving process making the SAT-based solver for MAPF competitive again in relevant benchmarks

Efficient Declarative Solutions in Picat for Optimal Multi-Agent Pathfinding

The multi-agent pathfinding (MAPF) problem has attracted considerable attention because of its relation to practical applications. The majority of solutions for MAPF are algorithmic. Recently, declarative solutions that reduce MAPF to encodings for off-the-shelf solvers have achieved remarkable success. We present a constraint-based declarative model for MAPF, together with its implementation in Picat, which uses SAT and MIP. We consider both the makespan and the sum-of-costs objectives, and propose a preprocessing technique for improving the performance of the model. Experimental results show that the implementation using SAT is highly competitive. We also analyze the high performance of the SAT solution by relating it to the SAT encoding algorithms that are used in the Picat compiler

Lifelong Multi-Agent Path Finding in Large-Scale Warehouses

Multi-Agent Path Finding (MAPF) is the problem of moving a team of agents to their goal locations without collisions. In this paper, we study the lifelong variant of MAPF, where agents are constantly engaged with new goal locations, such as in large-scale automated warehouses. We propose a new framework Rolling-Horizon Collision Resolution (RHCR) for solving lifelong MAPF by decomposing the problem into a sequence of Windowed MAPF instances, where a Windowed MAPF solver resolves collisions among the paths of the agents only within a bounded time horizon and ignores collisions beyond it. RHCR is particularly well suited to generating pliable plans that adapt to continually arriving new goal locations. We empirically evaluate RHCR with a variety of MAPF solvers and show that it can produce high-quality solutions for up to 1,000 agents (= 38.9\% of the empty cells on the map) for simulated warehouse instances, significantly outperforming existing work.Comment: Published at AAAI 202