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Artificial Intelligence for Games Uninformed search Patrick Olivier

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Simple problem solving agent

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Roadmap of Romania…

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Example: Romanian holiday On holiday in Romania (currently in Arad) Flight leaves tomorrow from Bucharest Formulate goal: –be in Bucharest Formulate problem: –states: various cities –actions: drive between cities Find solution: –sequence of cities, e.g., Arad, Sibiu, Fagaras…

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Example: 8 puzzle states? –locations of tiles actions? –move blank left, right, up, down goal test? –goal state (given) path cost? –1 per move

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Example: robot assembly states? –joint angles + parts actions? –joint motions goal test? –complete assembly path cost? –time to execute

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Example: NPC path planning states? –discretised world actions? –character motions goal test? –destination reached path cost? –cumulative motion cost

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Tree search algorithms simulated (offline) exploration of state space generating successors of already-explored states

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Tree search: implementation

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Search strategies strategy defined by order of node expansion strategies evaluated according to: –completeness: always find a solution if one exists? –time complexity: number of nodes generated –space complexity: maximum nodes in memory –optimality: always finds a least-cost solution? time & space complexity measured in terms of: –b: maximum branching factor of the search tree –d: depth of the least-cost solution –m: maximum depth of the state space (may be ∞)

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Uninformed search strategies only use information in the problem definition (uninformed): –breadth-first search –uniform-cost search –depth-first search –depth-limited search –iterative deepening search improve using informed search (next week)

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Breadth-first search Expand shallowest unexpanded node Implementation: fringe is a FIFO queue –add newly expanded nodes to back of queue –expand nodes at the front of the queue

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Old queue:[ ] New queue:[A]

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Old queue:[A] New queue:[B C]

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Old queue:[B C] New queue:[C D E]

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Old queue:[C D E] New queue:[D E F G]

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Properties of breadth-first search Complete? –Yes (if b is finite) Time: –b+b 2 +b 3 +… +b d + (b d+1 -b) = O(b d+1 ) Space: –O(b d+1 ) …keeps every node in memory Optimal? –If the cost is the same per step Space is the problem (more than time)

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Depth-first search Expand deepest unexpanded node Implementation: fringe is a LIFO queue –add newly expanded nodes to front of queue –expand node at the front of queue

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Old queue:[ ] New queue:[A]

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Old queue:[A] New queue:[B C]

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Old queue:[B C] New queue:[D E C]

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Old queue:[D E C] New queue:[H I E C]

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Old queue:[H I E C] New queue:[I E C]

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Old queue:[I E C] New queue:[E C]

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Old queue:[E C] New queue:[J K C]

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Old queue:[J K C] New queue:[K C]

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Old queue:[K C] New queue:[C]

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Properties of depth-first search Complete? –No – fails in infinite-depth spaces (or with loops) –modify to avoid repeated states along path –complete in finite spaces Time: –O(b m ): bad if m much larger than d of shallowest goal –if solutions are dense, much faster than breadth-first Space: –O(bm), i.e. linear space Optimal? –No

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