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Case-based subgoaling in real-time heuristic search for video game pathfinding
(2010) Bulitko, Vadim; Björnsson, Yngvi; Lawrence, Ramon; Department of Computer Science
Real-time heuristic search algorithms satisfy a constant bound on the amount of planning per action, independent of problem size. As a result, they scale up well as problems become larger. This property would make them well suited for video games where Artificial Intelligence controlled agents must react quickly to user commands and to other agents' actions. On the downside, real-time search algorithms employ learning methods that frequently lead to poor solution quality and cause the agent to appear irrational by re-visiting the same problem states repeatedly. The situation changed recently with a new algorithm, D LRTA*, which attempted to eliminate learning by automatically selecting subgoals. D LRTA* is well poised for video games, except it has a complex and memory-demanding pre-computation phase during which it builds a database of subgoals. In this paper, we propose a simpler and more memory-efficient way of pre-computing subgoals thereby eliminating the main obstacle to applying state-of-the-art real-time search methods in video games. The new algorithm solves a number of randomly chosen problems off-line, compresses the solutions into a series of subgoals and stores them in a database. When presented with a novel problem on-line, it queries the database for the most similar previously solved case and uses its subgoals to solve the problem. In the domain of pathfinding on four large video game maps, the new algorithm delivers solutions eight times better while using 57 times less memory and requiring 14% less pre-computation time.
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Automated discovery of search-extension features
(2010) Skowronski, Pálmi; Björnsson, Yngvi; Winands, Mark H.M.; Department of Computer Science
One of the main challenges with selective search extensions is designing effective move categories (features). Usually, it is a manual trial-and-error task, which requires both intuition and expert human knowledge. Automating this task potentially enables the discovery of both more complex and more effective move categories. The current work introduces Gradual Focus, an algorithm for automatically discovering interesting move categories for selective search extensions. The algorithm iteratively creates new more refined move categories by combining features from an atomic feature set. Empirical data is presented for the game Breakthrough showing that Gradual Focus looks at a number of combinations that is two orders of magnitude fewer than a brute-force method does, while preserving adequate precision and recall.
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Improved heuristics for optimal pathfinding on game maps
(AAAI Press, 2006) Björnsson, Yngvi; Halldórsson, Káari; Department of Computer Science
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.
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Solving 7×7 Hex : Virtual connections and game-state reduction
(Springer New York LLC, 2004) Hayward, R.; Björnsson, Y.; Johanson, M.; Kan, M.; Po, N.; van Rijswijck, J.; Department of Computer Science
We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough to solve arbitrary 7×7 game-states; in particular, we use it to determine the outcome of a 7 × 7 Hex game after each of the 49 possible opening moves, in each case finding an explicit proof-tree for the winning player.
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Differences in epicentral location of Mexican earthquakes between local and global catalogs : An update
(2016) Hjörleifsdóttir, Vala; Singh, Shri Krishna; Husker, Allen; Department of Engineering
Differences in epicentral locations between local and global catalogs for earthquakes in the Mexican subduction zone were first observed to be biased in the 1980s, based on a few well studied events. In this study we compare locations between two local catalogs; (1) a recent high precision catalog of events in the state of Guerrero and (2) the catalog of the Servicio Sismológico Nacional (SSN), to the global catalog of the United States Geological Service (USGS). We find that on average epicentral locations in the global catalog of earthquakes larger than M 5 in the Mexican subduction zone are 26 km towards N54°E of those in the local catalogs. We investigate how the errors vary for different types of earthquakes in Guerrero, and how they vary along the trench, from the state of Jalisco to the state of Chiapas. The average differences are largest for thrust events occurring close to the trench, and for events in Michoacán. The differences are greater on average for large earthquakes than for small. There is a tradeoff between the distance from the trench and timing, suggesting a poor resolution of these parameters, due to the lack of stations the Pacific Ocean. We attribute the differences in locations to systematic patterns in the velocity structure of the mantle, with consistently fast paths to the northeast and relatively slow paths towards the southwest.

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