Suboptimal Variants of the Conflict-Based Search Algorithm for the Multi-Agent Pathfinding Problem

Many existing multi-agent path finding (MAPF) solvers focus on completeness, speed, or optimization. However, completeness and rapidity are usually in conflict with each other, which makes these algorithms far from satisfactory in practical applications. Motivated by this realistic requirement, we propose an efficient decoupling method to accelerate the solution of large MAPF problems. First, we define the concept of ‘non-essential vertex’-vertices which are not needed to solve a MAPF problem, and a scheme to identify them. Then, a decoupling scheme based on ‘non-essential vertex’ is proposed, which will assign higher priorities to agents whose goal positions are non-essential vertices and lower priorities to agents whose start positions are non-essential vertices. That is, invoking our decoupling algorithm can decouple any given MAPF problem into three subproblems while maintaining the completeness of the solution. All three sub-MAPF problems can be solved sequentially by a complete solver (e.g., CBS or EECBS, etc.), and two of them can also be solved by a prioritized planning algorithm. We have conducted several experiments in different workspaces, and the statistical results show that the proposed decoupling method significantly improves the speed and success rate of existing MAPF solvers with almost no degradation in solution quality when solving problems with high agent density. In addition, the solving efficiency can be further improved if the prioritized planning algorithm is invoked to solve the first and third sub-MAPF problems.

Multi-Agent Path Finding (MAPF) is an important problem with a variety of applications. Its aim is to find collision-free paths for agents having separate start and goal positions. This work proposes a new lexicographic bi-objective MAPF considering different task types, where agents are divided into two kinds to perform critical and acritical tasks. This is common in practical intelligent warehousing scenarios where a critical/acritical-task-performing agent (called c-agent and a-agent, respectively) may represent a full-load/no-load one or the one conducting urgent/non-urgent tasks. The primary objective is to minimize the sum-of-costs of c-agents, while the secondary objective is to minimize the sum-of-costs of a-agents. Two MAPF algorithms are modified to fit and solve the concerned problem for the first time. Moreover, four improvement strategies are embedded to the proposed algorithms and proved to be effective in solving MAPF problems with different task types.

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.

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.

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p1464.pdf **Abstract:** With the rising demand of deploying robot teams in autonomous warehouses and factories, the Multi-agent Path Finding (MAPF) problem has drawn more and more attention. However, the classical MAPF problem focuses on navigating agent teams to reach single goal locations while avoiding collisions, and thus it cannot plan the case in which each agent is associated with a sequence of goal locations, and precedence constraints across goal sequences should be respected. Planning with these goal sequences and precedence constraints is important in real-world multi-agent systems. For example, a mobile robot needs to move an inventory pod to several stations for delivering different packages, which is captured by a sequence of goal locations, and another robot can only pick up a package after it has been delivered to the corresponding station, which can be modeled as precedence constraints across goal sequences. In this paper, we formalize the Multi-Agent Path Finding with Precedence Dependency (MAPF-PD) problem along with two algorithms to systematically solve this problem: Conflict-Based Search with Precedence Dependency (CBS-PD) is a complete and optimal algorithm; and Priority-Based Search with Precedence Dependency (PBS-PD) is an incomplete and suboptimal algorithm but shows great scalability and obtains near-optimal solutions in practice. Our experimental results show that our algorithms can scale to dozens of agents with hundreds of goal locations and precedence constraints.

With the rising demand for deploying robot teams in autonomous warehouses and factories, the Multi-Agent Path Finding (MAPF) problem has drawn more and more attention. The classical MAPF problem and most of its variants focus on navigating agent teams to goal locations while avoiding collisions. However, they do not take into account any precedence constraints that agents should respect when reaching their goal locations. Planning with precedence constraints is important for real-world multi-agent systems. For example, a mobile robot can only pick up a package at a station after it has been delivered by another robot. In this paper, we study the Multi-Agent Path Finding with Precedence Constraints (MAPF-PC) problem, in which agents need to visit sequences of goal locations while satisfying precedence constraints between the goal locations. We propose two algorithms for solving this problem systematically: Conflict-Based Search with Precedence Constraints (CBS-PC) is complete and optimal, and Priority-Based Search with Precedence Constraints (PBS-PC) is incomplete but more efficient in finding near-optimal solutions in practice. Our experimental results show that CBS-PC scales to dozens of agents and hundreds of goal locations and precedence constraints, and PBS-PC scales to hundreds of agents, around one thousand goal locations, and hundreds of precedence constraints.

Multi-Robot-Arm Motion Planning (M-RAMP) is a challenging problem featuring complex single-agent planning and multi-agent coordination. Recent advancements in extending the popular Conflict-Based Search (CBS) algorithm have made large strides in solving Multi-Agent Path Finding (MAPF) problems. However, fundamental challenges remain in applying CBS to M-RAMP. A core challenge is the existing reliance of the CBS framework on conservative "complete" constraints. These constraints ensure solution guarantees but often result in slow pruning of the search space -- causing repeated expensive single-agent planning calls. Therefore, even though it is possible to leverage domain knowledge and design incomplete M-RAMP-specific CBS constraints to more efficiently prune the search, using these constraints would render the algorithm itself incomplete. This forces practitioners to choose between efficiency and completeness. In light of these challenges, we propose a novel algorithm, Generalized ECBS, aimed at removing the burden of choice between completeness and efficiency in MAPF algorithms. Our approach enables the use of arbitrary constraints in conflict-based algorithms while preserving completeness and bounding sub-optimality. This enables practitioners to capitalize on the benefits of arbitrary constraints and opens a new space for constraint design in MAPF that has not been explored. We provide a theoretical analysis of our algorithms, propose new "incomplete" constraints, and demonstrate their effectiveness through experiments in M-RAMP.

Multi-Agent Path Finding (MAPF) deals with finding conflict-free paths for a set of agents from an initial configuration to a given target configuration. The Lifelong MAPF (LMAPF) problem is a well-studied online version of MAPF in which an agent receives a new target when it reaches its current target. The common approach for solving LMAPF is to treat it as a sequence of MAPF problems, periodically replanning from the agents’ current configurations to their current targets. A significant drawback of this approach is that in MAPF the agents must reach a configuration in which all agents are at their targets simultaneously. Coordinating the agents’ paths such that they occupy their targets at the same time is needlessly restrictive for LMAPF. Techniques have been proposed to indirectly mitigate this drawback. In this position paper, we describe cases where these mitigation techniques fail. As an alternative, we propose to solve LMAPF problems by solving a sequence of modified MAPF problems, in which the objective is for each agent to eventually visit its target, but not necessarily for all agents to do so simultaneously. We refer to this MAPF variant as MAPF for Lifelong (MAPF4L) and propose how to solve it by modifying several existing MAPF algorithms. A limited experimental evaluation identifies some cases where using a MAPF4L algorithm can improve the system throughput significantly.

In Multi-Agent Path Finding (MAPF), we are asked to plan collision-free paths for teams of moving agents. Among the leading methods for optimal MAPF is Conflict-Based Search (CBS), an algorithmic family which has received intense attention in recent years and for which large advancements in efficiency and effectiveness have been reported. Yet all of the recent CBS gains come from reasoning over pairs of agents only. In this paper, we show how to further improve CBS by reasoning about more than two agents at the same time. Our new cluster reasoning techniques allow us to generate stronger bounds for CBS and to identify more bypasses (alternative cost-equivalent paths), which reduce the number of nodes in the CBS conflict tree.

We address conflict reasoning in generalizations of multi-agent path finding (MAPF). We assume items placed in vertices of an undirected graph with at most one item per vertex. Items can be relocated across edges while various constraints depending on the concrete type of MAPF must be satisfied. We recall a general problem formulation that encompasses known types of item relocation problems such as multi-agent path finding (MAPF) and token swapping (TSWAP). We show how to express new types of relocation problems in the general problem formulation. We thoroughly evaluate a novel solving method for item relocation that combines satisfiability modulo theory (SMT) with conflict-based search (CBS). CBS is interpreted in the SMT framework where we start with the basic model and refine the model with a collision resolution constraint whenever a collision between items occurs. The key difference between the standard CBS and the SMT-based modification of CBS (SMT-CBS) is that the standard CBS branches the search to resolve the collision while SMT-CBS iteratively adds a single disjunctive collision resolution constraint. Our experimental evaluation revealed that although SMT-CBS performs better than CBS in small densely occupied instances of variants of MAPF, it is outperformed on large sparsely occupied environments. The performed analysis shows that individual paths in large environments of relocation instances can be found faster using simple A*-based algorithm than by the SMT solver. On the other hand the SMT solver performs better when many conflicts between items need to be resolved.

We study practical approaches to solving the token swapping (TSWAP) problem optimally in this paper. In TSWAP, we are given an undirected graph with colored vertices. A colored token is placed in each vertex. A pair of tokens can be swapped between adjacent vertices. The goal is to perform a sequence of swaps so that token and vertex colors agree across the graph. The minimum number of swaps is required in the optimization variant of the problem. We observed similarities between the TSWAP problem and multi-agent path finding (MAPF) where instead of tokens we have multiple agents that need to be moved from their current vertices to given unique target vertices. The difference between both problems consists in local conditions that state transitions (swaps/moves) must satisfy. We developed two algorithms for solving TSWAP optimally by adapting two different approaches to MAPF - conflict-based search (CBS) and SAT-based approach that uses multi-value decision diagrams (MDD-SAT). This constitutes the first attempt to design optimal solving algorithms for TSWAP. Experimental evaluation on various types of graphs shows that the reduction to SAT scales better than CBS in optimal TSWAP solving. It has been also demonstrated that TSWAP instances are easier to solve than corresponding similar MAPF instances.

Conflict-Based Search (CBS) is a leading two-level algorithm for optimal Multi-Agent Path Finding (MAPF). At its high level, CBS expands nodes by resolving conflicts. In recent years, admissible heuristics were added to the high level of CBS. We enhance all known heuristic functions for CBS by using information about the cost of resolving certain conflicts, with only a small computational overhead. We experimentally demonstrate that the improved heuristics contribute to making CBS even more efficient.

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 Path Finding (MAPF) is the problem of finding non-colliding paths for multiple agents. The classical problem assumes that all agents are homogeneous, with a fixed size and behavior. However, in reality agents are heterogeneous, with different sizes and behaviors. In this paper, we generalize MAPF to G-MAPF for the case of heterogeneous agents. We then show how two previous settings of large agents and k-robust agents are special cases of G-MAPF. Finally, we introduce G-CBS, a variant of the Conflict-Based Search (CBS) algorithm for G-MAPF, which does not cause significant extra overhead.

Optimal planning and heuristic search systems solve state-space searchproblems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e. without actually finding a solution path of that cost. We present an efficient algorithm, BiSS, based on ideas of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. Our method is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity.We show empirically that our method makes accurate predictions in several domains. In addition, we show that our method scales to state spaces much larger than can be solved optimally. In particular, we estimate the average solution cost for the 6x6, 7x7, and 8x8 Sliding-Tile Puzzle and provide indirect evidence that these estimates are accurate.