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.

In a multi-agent path-finding (MAPF) problem, the task is to find 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. Guaranteeing that collisions will never occur may be impossible. An important task is to find a plan that is very likely to succeed, even though unexpected delays may occur. We propose an algorithm for finding a plan in which the probability that no collisions will occur is at least a given parameter p (p-robust plan). We show that finding an optimal p-robust plan is significantly more difficult than finding an optimal standard plan. As a practical solution, we propose a greedy algorithm based on the Conflict-Based Search framework. Our experiments show that it finds p-robust plans with cost that is relatively close to the optimal cost of the standard, non-robust plans.

The multi-agent pathfinding problem (MAPF) is the fundamental problem of planning paths for multiple agents, where the key constraint is that the agents will be able to follow these paths concurrently without colliding with each other. Applications of MAPF include automated warehouses, autonomous vehicles, and robotics. Research on MAPF has been flourishing in the past couple of years. Different MAPF research papers assume different sets of assumptions, e.g., whether agents can traverse the same road at the same time, and have different objective functions, e.g., minimize makespan or sum of agents' actions costs. These assumptions and objectives are sometimes implicitly assumed or described informally. This makes it difficult for establishing appropriate baselines for comparison in research papers, as well as making it difficult for practitioners to find the papers relevant to their concrete application. This paper aims to fill this gap and facilitate future research and practitioners by providing a unifying terminology for describing the common MAPF assumptions and objectives. In addition, we also provide pointers to two MAPF benchmarks. In particular, we introduce a new grid-based benchmark for MAPF, and demonstrate experimentally that it poses a challenge to contemporary MAPF algorithms.

Multi-agent path finding (MAPF) is the problem of moving a set of agents from their individual start locations to their individual goal locations, without collisions. This problem has practical applications in video games, traffic control, robotics, and more. In MAPF we assume that agents occupy one location each time step. However, in real life some agents have different size or shape. Hence, a standard MAPF solution may be not suited in practice for some applications. In this paper, we describe a novel algorithm, based on the CBS algorithm, that finds a plan for moving a set of train-agents, i.e., agents that occupy a sequence of two or more locations, such as trains, buses, planes, or even snakes. We prove that our solution is optimal and show experimentally that indeed such a solution can be found. Finally, we explain how our solution can also apply to agents with any geometric shape.

We present a novel search scheme for privacy-preserving multi-agent planning. Inspired by UCT search, the scheme is based on growing an asynchronous search tree by running repeated trials through the tree. We describe key differences to classical multi-agent forward search, discuss theoretical properties of the presented approach, and evaluate it based on benchmarks from the CoDMAP competition. As a secondary contribution, we describe a technique that extends the regular search approach by small explorative trials which are performed subsequent to each node expansion. We show that this technique significantly increases the number of problems solved for all algorithms considered, including MAFS.

In multi-agent planning, agents jointly compute a plan that achieves mutual goals, keeping certain information private to the individual agents. Agents' coordination is achieved through the transmission of messages, but they can be a source of privacy leakage as they can permit a malicious agent to collect information about other agents' search processes and states. In this paper, we investigate the usage of novelty techniques in the context of (decentralised) multi-agent privacy preserving planning, addressing the challenges related to the agents' privacy and performance. In particular, we show that novelty based techniques allow a significant reduction on the number of messages transmitted among agents, increasing their privacy levels and also their performances. An experimental study analyses the effectiveness of our techniques and compares them with the state of-the-art. Finally, we examine the robustness of our approach considering different delays in the messages transmission as would occur in overloaded networks, due for example to massive attacks or critical situations.

Multi-agent path finding (MAPF) deals with the problem of finding collision-free paths for a set of agents. Each agent moves from its start location to its destination location in a shared environment represented by a graph. Reduction-based solving approaches for MAPF, for example reduction to SAT, exploit a time-expended layered graph, where each layer corresponds to specific time. Hence, these approaches are natural for minimizing makespan (the shortest time till all agents reach their destinations). Modeling the other frequently used objective, namely Sum of Costs (SOC; sum of paths lengths of all agents) is more difficult as the solution with the smallest SOC may not be reached in the time-expended graph with the smallest makespan. In this paper we suggest two novel approaches to estimate the makespan, that guarantees existence of a SOC-optimal solution. The approaches are empirically compared with an existing reduction-based method as well as with the state-of-the-art search-based optimal MAPF solver.