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Artificial Intelligence for Games Uninformed search

Artificial Intelligence for Games Uninformed search. Patrick Olivier p.l.olivier@ncl.ac.uk. Simple problem solving agent. Roadmap of Romania…. Example: Romanian holiday. On holiday in Romania (currently in Arad) Flight leaves tomorrow from Bucharest Formulate goal: be in Bucharest

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Artificial Intelligence for Games Uninformed search

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  1. Artificial Intelligence for GamesUninformed search Patrick Olivier p.l.olivier@ncl.ac.uk

  2. Simple problem solving agent

  3. Roadmap of Romania…

  4. 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…

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

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

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

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

  9. Tree search: implementation

  10. 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 ∞)

  11. 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)

  12. 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

  13. Old queue: [ ] New queue: [A]

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

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

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

  17. Properties of breadth-first search • Complete? • Yes (if b is finite) • Time: • b+b2+b3+… +bd + (bd+1-b) = O(bd+1) • Space: • O(bd+1) …keeps every node in memory • Optimal? • If the cost is the same per step • Space is the problem (more than time)

  18. 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

  19. Old queue: [ ] New queue: [A]

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

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

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

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

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

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

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

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

  28. 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(bm): 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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