We describe an attempt to unify search-based and compilation-based approaches to multi-agent path finding (MAPF) through satisfiability modulo theories (SMT). The task in MAPF is to navigate agents in an undirected graph to given goal vertices so that they do not collide. We rephrase Conflict-Based Search (CBS), one of the state-of-the-art algorithms for optimal MAPF solving, in the terms of SMT. This idea combines SAT-based solving known from MDD-SAT, a SAT-based optimal MAPF solver, at the low level with conflict elimination of CBS at the high level. Where the standard CBS branches the search after a conflict occurs, we refine the propositional model with a disjunctive constraint instead. Our novel algorithm called SMT-CBS hence does not branch at the high-level but incrementally extends the propositional model that is consulted with the SAT solver at each iteration. We experimentally compare SMT-CBS with CBS and MDD-SAT.

This paper addresses a variant of multi-agent path finding (MAPF) in continuous space and time. We present a new solving approach based on satisfiability modulo theories (SMT) to obtain makespan optimal solutions. The standard MAPF is a task of navigating agents in an undirected graph from given starting vertices to given goal vertices so that agents do not collide with each other in vertices of the graph. In the continuous version (MAPF-R) agents move in an n-dimensional Euclidean space along straight lines that interconnect predefined positions. For simplicity, we work with circular omni-directional agents having constant velocities in the 2D plane. As agents can have different sizes and move smoothly along lines, a non-colliding movement along certain lines with small agents can result in a collision if the same movement is performed with larger agents. Our SMT-based approach for MAPF-R called SMT-CBS-R reformulates the Conflict-based Search (CBS) algorithm in terms of SMT concepts. We suggest lazy generation of decision variables and constraints. Each time a new conflict is discovered, the underlying encoding is extended with new variables and constraints to eliminate the conflict. We compared SMT-CBS-R and adaptations of CBS for the continuous variant of MAPF experimentally.

In Multi-Agent Path Finding (MAPF), a team of agents needs to find collision-free paths from their starting locations to their respective targets. Combined Target Assignment and Path Finding (TAPF) extends MAPF by including the problem of assigning targets to agents as a precursor to the MAPF problem. A limitation of both models is their assumption that the number of agents and targets are equal, which is invalid in some applications. We address this limitation by generalizing TAPF to allow for (1) unequal number of agents and tasks; (2) tasks to have deadlines by which they must be completed; (3) ordering of groups of tasks to be completed; and (4) tasks that are composed of a sequence of checkpoints that must be visited in a specific order. Further, we model the problem using answer set programming (ASP) to show that customizing the desired variant of the problem is simple -- one only needs to choose the appropriate combination of ASP rules to enforce it. We also demonstrate experimentally that if problem specific information can be incorporated into the ASP encoding then ASP based methods can be efficient and can scale up to solve practical applications.

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for well-formed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities. This paper was published at AAAI 2019.

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time. This paper was published at AAAI 2019.

Multi-Agent Path Finding (MAPF) has been widely studied in the AI community. For example, Conflict-Based Search (CBS) is a state-of-the-art MAPF algorithm based on a two-level tree-search. However, previous MAPF algorithms assume that an agent occupies only a single location at any given time, e.g., a single cell in a grid. This limits their applicability in many real-world domains that have geometric agents in lieu of point agents. Geometric agents are referred to as “large” agents because they can occupy multiple points at the same time. In this paper, we formalize and study LAMAPF, i.e., MAPF for large agents. We first show how CBS can be adapted to solve LA-MAPF. We then present a generalized version of CBS, called Multi-Constraint CBS (MC-CBS), that adds multiple constraints (instead of one constraint) for an agent when it generates a high-level search node. We introduce three different approaches to choose such constraints as well as an approach to compute admissible heuristics for the high-level search. Experimental results show that all MC-CBS variants outperform CBS by up to three orders of magnitude in terms of runtime. The best variant also outperforms EPEA* (a state-of-the-art A*-based MAPF solver) in all cases and MDD-SAT (a state-of-the-art reduction-based MAPF solver) in some cases.

We describe a new way of reasoning about symmetric collisions for Multi-Agent Path Finding (MAPF) on 4-neighbor grids. We also introduce a symmetry-breaking constraint to resolve these conflicts. This specialized technique allows us to identify and eliminate, in a single step, all permutations of two currently assigned but incompatible paths. Each such permutation has exactly the same cost as a current path, and each one results in a new collision between the same two agents. We show that the addition of symmetry-breaking techniques can lead to an exponential reduction in the size of the search space of CBS, a popular framework for MAPF, and report significant improvements in both runtime and success rate versus CBSH and EPEA* – two recent and state-of-the-art MAPF algorithms.

Conflict-Based Search (CBS) and its enhancements are among the strongest algorithms for Multi-Agent Pathfinding. Recent work introduced an admissible heuristic to guide the high-level search of CBS. In this work, we prove the limitation of this heuristic, as it is based on cardinal conflicts only. We then introduce two new admissible heuristics by reasoning about the pairwise dependency between agents. Empirically, CBS with both new heuristics significantly improves the success rate over CBS with the recent heuristic and reduces the number of expanded nodes and runtime by up to a factor of 50, yielding a new state-of-the-art CBS-based algorithm.

Multi-Agent Pathfinding (MAPF) over grids is the problem of finding n non-conflicting paths that lead n agents from a given initial cell to a given goal cell. Cost-optimal MAPF in addition minimizes the total number of actions performed by each agent before stopping at the goal. Being a combinatorial problem in nature, a number of compilations from MAPF to Answer Set Programming (ASP) exist. In this paper we propose a new one, which unlike existing ASP approaches (1) produces cost-optimal solutions, (2) exploits information that can be pre-computed quickly using Dijkstra's algorithm, and (3) when grounded, produces a number of clauses that grows linearly with the number of agents. In our empirical evaluation, in which we use the clasp solver, we show that our approach is superior to heuristic-search-based algorithms in various settings.

The Coalition Structure Generation (CSG) problem is a partitioning of a set of agents into exhaustive and disjoint coalitions to maximize social welfare. This NP-complete problem arises in many practical scenarios. Prominent examples are included in the field of transportation, e-Commerce, distributed sensor networks, and others. The fastest exact algorithm to solve the CSG problem is ODP-IP, which is a hybrid version of two previously established algorithms, namely Improved Dynamic Programming (IDP) and IP. In this paper, we show that the ODP-IP algorithm performs many redundant operations. To improve ODP-IP, we propose a faster abortion mechanism to speed up IP’s search. Our abortion mechanism decides at runtime which of the IP's operations are redundant to skip them. Then, we propose a modified version of IDP (named MIDP) and an improved version of IP (named IIP). Based on these two improved algorithms, we develop a hybrid version (MIDP-IIP) to solve the CSG problem. After a detailed description of the new algorithm MIDP-IIP, an experimental comparison is conducted against ODP-IP. Our analysis shows that MIDP-IIP performs fewer operations than ODP-IP. In addition, MIDP-IIP reduced significantly many problem instances running times (11% to 37 %), and improved drastically some of them.