Pathfinding

Abstract: Cooperative Pathfinding is a multi-agent path planning problem where agents must find non-colliding routes to separate destinations, given full information about the routes of other agents. This paper presents three new algorithms for efficiently solving this problem, suitable for use in Real-Time Strategy games and other real-time environments. The algorithms are decoupled approaches that break down the problem into a series of single-agent searches. Cooperative A* (CA*) searches space-time for a non-colliding route. Hierarchical Cooperative A* (HCA*) uses an abstract heuristic to boost performance. Finally, Windowed Hierarchical Cooperative A* (WHCA*) limits the space-time search depth to a dynamic window, spreading computation over the duration of the route. The algorithms are applied to a series of challenging, maze-like environments, and compared to A* with Local Repair (the current video-games industry standard). The results show that the new algorithms, especially WHCA*, are robust and efficient solutions to the Cooperative Pathfinding problem, finding more successful routes and following better paths than Local Repair A*.

Abstract: AI and Games Introduction What Is AI? Model of Game AI Algorithms, Data Structures, and Representations On the Website Layout of the Book Game AI The Complexity Fallacy The Kind of AI in Games Speed and Memory The AI Engine Techniques Movement The Basics of Movement Algorithms Kinematic Movement Algorithms Steering Behaviors Combining Steering Behaviors Predicting Physics Jumping Coordinated Movement Motor Control Movement in the Third Dimension Pathfinding The Pathfinding Graph Dijkstra A* World Representations Improving on A* Hierarchical Pathfinding Other Ideas in Pathfinding Continuous Time Pathfinding Movement Planning Decision Making Overview of Decision Making Decision Trees State Machines Behavior Trees Fuzzy Logic Markov Systems Goal-Oriented Behavior Rule-Based Systems Blackboard Architectures Scripting Action Execution Tactical and Strategic AI Waypoint Tactics Tactical Analyses Tactical Pathfinding Coordinated Action Learning Learning Basics Parameter Modification Action Prediction Decision Learning Naive Bayes Classifiers Decision Tree Learning Reinforcement Learning Artificial Neural Networks Board Games Game Theory Minimaxing Transposition Tables and Memory Memory-Enhanced Test Algorithms Opening Books and Other Set Plays Further Optimizations Turn-Based Strategy Games Supporting Technologies Execution Management Scheduling Anytime Algorithms Level of Detail World Interfacing Communication Getting Knowledge Efficiently Event Managers Polling Stations Sense Management Tools and Content Creation Knowledge for Pathfinding and Waypoint Tactics Knowledge for Movement Knowledge for Decision Making The Toolchain Designing Game AI Designing Game AI The Design Shooters Driving Real-Time Strategy Sports Turn-Based Strategy Games AI-Based Game Genres Teaching Characters Flocking and Herding Games Appendix Books, Periodicals, and Papers Games

Abstract: A common algorithm to solve the shortest path problem (SPP) is the Dijkstra algorithm. In this paper, a generalized Dijkstra algorithm is proposed to handle SPP in an uncertain environment. Two key issues need to be addressed in SPP with fuzzy parameters. One is how to determine the addition of two edges. The other is how to compare the distance between two different paths with their edge lengths represented by fuzzy numbers. To solve these problems, the graded mean integration representation of fuzzy numbers is adopted to improve the classical Dijkstra algorithm. A numerical example of a transportation network is used to illustrate the efficiency of the proposed method.

Abstract: We present a new speedup technique for route planning that exploits the hierarchy inherent in real world road networks. Our algorithm preprocesses the eight digit number of nodes needed for maps of the USA or Western Europe in a few hours using linear space. Shortest (i.e. fastest) path queries then take around eight milliseconds to produce exact shortest paths. This is about 2 000 times faster than using Dijkstra’s algorithm.