Improved heuristics for optimal path-finding on game maps.

Abstract As computer game worlds get more elaborate the more visible pathfinding performance bottlenecks become. The heuristic functions typically used for guiding A * -based pathfinding are too simplistic to provide the search with the necessary guidance in such large and complex game worlds. This may result in A * -search exploring the entire game map in order to find a path between two distant locations. This article presents two effective heuristics for estimating distances between locations in large and complex game maps. The former, the dead-end heuristic, eliminates from the search map areas that are provably irrelevant for the current query, whereas the second heuristic uses so-called gateways to improve its estimates. Empirical evaluation on actual game maps shows that both heuristics reduce the exploration and time complexity of A * search significantly over a standard octile distance metric

The FastMap Algorithm for Shortest Path Computations

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic

Symmetry-Based Search Space Reduction For Grid Maps

In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles, removing from each rectangle all interior nodes and possibly some from along the perimeter. We then add a series of macro-edges between selected pairs of remaining perimeter nodes to facilitate provably optimal traversal through each rectangle. We also develop a novel online pruning technique to further speed up search. Our algorithm is fast, memory efficient and retains the same optimality and completeness guarantees as searching on an unmodified grid map

Multi-agent pathfinding for unmanned aerial vehicles

Unmanned aerial vehicles (UAVs), commonly known as drones, have become more and more prevalent in recent years. In particular, governmental organizations and companies around the world are starting to research how UAVs can be used to perform tasks such as package deliver, disaster investigation and surveillance of key assets such as pipelines, railroads and bridges. NASA is currently in the early stages of developing an air traffic control system specifically designed to manage UAV operations in low-altitude airspace. Companies such as Amazon and Rakuten are testing large-scale drone deliver services in the USA and Japan. To perform these tasks, safe and conflict-free routes for concurrently operating UAVs must be found. This can be done using multi-agent pathfinding (mapf) algorithms, although the correct choice of algorithms is not clear. This is because many state of the art mapf algorithms have only been tested in 2D space in maps with many obstacles, while UAVs operate in 3D space in open maps with few obstacles. In addition, when an unexpected event occurs in the airspace and UAVs are forced to deviate from their original routes while inflight, new conflict-free routes must be found. Planning for these unexpected events is commonly known as contingency planning. With manned aircraft, contingency plans can be created in advance or on a case-by-case basis while inflight. The scale at which UAVs operate, combined with the fact that unexpected events may occur anywhere at any time make both advanced planning and planning on a case-by-case basis impossible. Thus, a new approach is needed. Online multi-agent pathfinding (online mapf) looks to be a promising solution. Online mapf utilizes traditional mapf algorithms to perform path planning in real-time. That is, new routes for UAVs are found while inflight. The primary contribution of this thesis is to present one possible approach to UAV contingency planning using online multi-agent pathfinding algorithms, which can be used as a baseline for future research and development. It also provides an in-depth overview and analysis of offline mapf algorithms with the goal of determining which ones are likely to perform best when applied to UAVs. Finally, to further this same goal, a few different mapf algorithms are experimentally tested and analyzed

Performance Evaluation of Pathfinding Algorithms

Pathfinding is the search for an optimal path from a start location to a goal location in a given environment. In Artificial Intelligence pathfinding algorithms are typically designed as a kind of graph search. These algorithms are applicable in a wide variety of applications such as computer games, robotics, networks, and navigation systems. The performance of these algorithms is affected by several factors such as the problem size, path length, the number and distribution of obstacles, data structures and heuristics. When new pathfinding algorithms are proposed in the literature, their performance is often investigated empirically (if at all). Proper experimental design and analysis is crucial to provide an informative and non- misleading evaluation. In this research, we survey many papers and classify them according to their methodology, experimental design, and analytical techniques. We identify some weaknesses in these areas that are all too frequently found in reported approaches. We first found the pitfalls in pathfinding research and then provide solutions by creating example problems. Our research shows that spurious effects, control conditions provide solutions to avoid these pitfalls