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Artificial Intelligence

Artificial Intelligence. Lecture 5 Uninformed Search. Overview. Searching for Solutions Uninformed Search BFS UCS DFS DLS IDS. Searching for Solutions. Tree Search Algorithms. Tree Search Example. Implementation: State vs. Nodes. and state. General Tree Search. Search Strategies.

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Artificial Intelligence

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  1. Artificial Intelligence Lecture 5 Uninformed Search

  2. Overview • Searching for Solutions • Uninformed Search • BFS • UCS • DFS • DLS • IDS

  3. Searching for Solutions

  4. Tree Search Algorithms

  5. Tree Search Example

  6. Implementation:State vs. Nodes and state

  7. General Tree Search

  8. Search Strategies

  9. Uninformed Search

  10. Uninformed Search Strategies • Use only the information available in the problem definition • Breadth-first search • Uniform-cost search • Depth-first search • Depth-limit search • Iterative deepening search

  11. Breadth-First Search • Expand shallowest unexpanded node • Implementation: fringe is a FIFO queue, that is new successors go at end

  12. Properties of BFS • Complete? • Yes. (if b is finite) • Time? • 1+b+b2+…+b(bd-1)=O(bd+1), exp in d • Space? • O(bd+1) (keeps every node in memory) • Optimal? • Yes, if cost = 1 per step; not optimal in general when actions have different cost • Space is the big problem; can easily generate nodes at 10MB/sec, so 24hrs = 860GB

  13. Uniform-Cost Search

  14. Depth-First Search • Expanded deepest unexpanded node • Implementation: • Fringe = LIFO queue, i.e. put successors at front

  15. Properties of DFS • Complete? • No. Fails in infinite-depth spaces, spaces with loops • Modify to avoid repeated states along path => complete in finite space • Time? • O(bm), terrible if m is much larger than d, but if solutions are dense, may be much faster than BFS • Space? • O(bm), linear space • Optimal? • No

  16. Depth-Limit Search • Depth-first search with depth limit L, that is nodes at depth L have no successors

  17. Depth-Limited search • Is DF-search with depth limit l. • i.e. nodes at depth l have no successors. • Problem knowledge can be used • Solves the infinite-path problem. • If l < d then incompleteness results. • If l > d then not optimal. • Time complexity: • Space complexity:

  18. Depth-Limit Search • Algorithm

  19. Iterative Deepening Search • Iterative deepening search • A general strategy to find best depth limit l. • Goals is found at depth d, the depth of the shallowest goal-node. • Often used in combination with DF-search • Combines benefits of DF- en BF-search

  20. Iterative Deepening Search

  21. Properties of IDS

  22. Bidirectional search • Two simultaneous searches from start an goal. • Motivation: • Check whether the node belongs to the other fringe before expansion. • Space complexity is the most significant weakness. • Complete and optimal if both searches are BF.

  23. How to search backwards? • The predecessor of each node should be efficiently computable. • When actions are easily reversible.

  24. Summary of Algorithms

  25. Repeated States

  26. Graph Search

  27. Summary • Searching for Solutions • Uninformed Search • BFS • UCS • DFS • DLS • IDS

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