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.

This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

The travelling thief problem (TTP) is a combination of two interdependent NP-hard components: travelling salesman problem (TSP) and knapsack problem (KP). Existing approaches for TTP typically solve the TSP and KP components in an interleaved fashion, where the solution to one component is held fixed while the other component is changed. This indicates poor coordination between solving the two components and may lead to poor quality TTP solutions. For solving the TSP component, the 2-OPT segment reversing heuristic is often used for modifying the tour. We propose an extended and modified form of the reversing heuristic in order to concurrently consider both the TSP and KP components. Items deemed as less profitable and picked in cities earlier in the reversed segment are replaced by items that tend to be equally or more profitable and not picked in the later cities. Comparative evaluations on a broad range of benchmark TTP instances indicate that the proposed approach outperforms existing state-of-the-art TTP solvers.

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the corrections frequently eliminate much of the error.

Abstraction heuristics are a leading approach for deriving admissible estimates in cost-optimal planning. However, a drawback with respect to other families of heuristics is that they require a preprocessing phase for choosing the abstraction, computing the abstract distances, and/or suitable cost-partitionings. Typically, this is performed in advance by a fixed amount of time, even though some instances could be solved much faster with little or no preprocessing. We interleave the computation of abstraction heuristics with search, avoiding a long precomputation phase and allowing information from the search to be used for guiding the abstraction selection. To evaluate our ideas, we implement them on a planner that uses a single symbolic PDB. Our results show that delaying the preprocessing is not harmful in general even when an important amount of preprocessing is required to obtain good performance.

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.

Single-agent pathfinding on grid maps can exploit online compiled knowledge produced offline and saved as a Compressed Path Database (CPD). Such a knowledge is distilled by performing repeated searches in a graph, where each node corresponds to a distinct grid cell, typically by algorithms such as Dijkstra's. All-pairs shortest paths (APSPs) are computed and the first move along a shortest path is persistently stored in the CPD. This way, an optimal move can efficiently be retrieved for any pair of source and target cells that is considered while the agent is navigating. However, a CPD supports a static grid, that is, a grid where each cell is permanently either traversable or non-traversable. Our work instead assumes that the cells in the map can undergo dynamic changes. Reasoning about the altered map would require a new CPD. As creating it from scratch is computationally expensive, we present techniques to repair an existing CPD. We prove that using our technique leads to correct and optimal solutions. Experiments demonstrate the benefits of our approach. When a single obstacle of a given size is added or removed, the repair costs often are a small fraction of a recomputation from scratch.

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms.

We examine techniques for combining generalized policies with search algorithms to exploit the strengths and overcome the weaknesses of each when solving probabilistic planning problems. The Action Schema Network (ASNet) is a recent contribution to planning that uses deep learning and neural networks to learn generalized policies for probabilistic planning problems. ASNets are well suited to problems where local knowledge of the environment can be exploited to improve performance, but may fail to generalize to problems they were not trained on. Monte-Carlo Tree Search (MCTS) is a forward-chaining state space search algorithm for optimal decision making which performs simulations to incrementally build a search tree and estimate the values of each state. Although MCTS can achieve state-of-the-art results when paired with domain-specific knowledge, without this knowledge, MCTS requires a large number of simulations in order to obtain reliable state-value estimates. By combining ASNets with MCTS, we are able to improve the capability of an ASNet to generalize beyond the distribution of problems it was trained on, as well as enhance the navigation of the search space by MCTS.

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.