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Learning Objectives At the end of the class you should be able to: justify why depth-bounded search is useful demonstrate how iterative-deepening works for a particular problem demonstrate how depth-first branch-and-bound works for a

  1. Learning Objectives At the end of the class you should be able to: justify why depth-bounded search is useful demonstrate how iterative-deepening works for a particular problem demonstrate how depth-first branch-and-bound works for a particular problem � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 1

  2. Bounded Depth-first search A bounded depth-first search takes a bound (cost or depth) and does not expand paths that exceed the bound. I explores part of the search graph I uses space linear in the depth of the search. How does this relate to other searches? How can this be extended to be complete? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 2

  3. Which shaded goal will a depth-bounded search find first? Q W R T Y U V � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 3

  4. Iterative-deepening search Iterative-deepening search: I Start with a bound b = 0. I Do a bounded depth-first search with bound b I If a solution is found return that solution I Otherwise increment b and repeat. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 4

  5. Iterative-deepening search Iterative-deepening search: I Start with a bound b = 0. I Do a bounded depth-first search with bound b I If a solution is found return that solution I Otherwise increment b and repeat. This will find the same first solution as what other method? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 5

  6. Iterative-deepening search Iterative-deepening search: I Start with a bound b = 0. I Do a bounded depth-first search with bound b I If a solution is found return that solution I Otherwise increment b and repeat. This will find the same first solution as what other method? How much space is used? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 6

  7. Iterative-deepening search Iterative-deepening search: I Start with a bound b = 0. I Do a bounded depth-first search with bound b I If a solution is found return that solution I Otherwise increment b and repeat. This will find the same first solution as what other method? How much space is used? What happens if there is no path to a goal? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 7

  8. Iterative-deepening search Iterative-deepening search: I Start with a bound b = 0. I Do a bounded depth-first search with bound b I If a solution is found return that solution I Otherwise increment b and repeat. This will find the same first solution as what other method? How much space is used? What happens if there is no path to a goal? Surely recomputing paths is wasteful!!! � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 8

  9. Iterative Deepening Complexity Complexity with solution at depth k & branching factor b : level breadth-first iterative deepening # nodes 1 1 k b b 2 2 1 k − 1 . . . . . . . . . . . . b k − 1 k − 1 1 2 b k k 1 1 total � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 9

  10. Iterative Deepening Complexity Complexity with solution at depth k & branching factor b : level breadth-first iterative deepening # nodes 1 1 k b b 2 2 1 k − 1 . . . . . . . . . . . . b k − 1 k − 1 1 2 b k k 1 1 ⌘ 2 ≤ b k ⇣ ≥ b k b total b − 1 � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 10

  11. Depth-first Branch-and-Bound combines depth-first search with heuristic information. finds optimal solution. most useful when there are multiple solutions, and we want an optimal one. uses the space of depth-first search. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 11

  12. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 12

  13. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? p can be pruned. What can we do if a non-pruned path to a goal is found? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 13

  14. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? p can be pruned. What can we do if a non-pruned path to a goal is found? bound can be set to the cost of p , and p can be remembered as the best solution so far. Why should this use a depth-first search? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 14

  15. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? p can be pruned. What can we do if a non-pruned path to a goal is found? bound can be set to the cost of p , and p can be remembered as the best solution so far. Why should this use a depth-first search? Uses linear space. What can be guaranteed when the search completes? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 15

  16. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? p can be pruned. What can we do if a non-pruned path to a goal is found? bound can be set to the cost of p , and p can be remembered as the best solution so far. Why should this use a depth-first search? Uses linear space. What can be guaranteed when the search completes? It has found an optimal solution. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 16

  17. Depth-first Branch-and-Bound Suppose we want to find a single optimal solution. Suppose bound is the cost of the lowest-cost path found to a goal so far. What if the search encounters a path p such that cost ( p ) + h ( p ) ≥ bound ? p can be pruned. What can we do if a non-pruned path to a goal is found? bound can be set to the cost of p , and p can be remembered as the best solution so far. Why should this use a depth-first search? Uses linear space. What can be guaranteed when the search completes? It has found an optimal solution. How should the bound be initialized? � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 17

  18. Depth-first Branch-and-Bound: Initializing Bound The bound can be initialized to ∞ . The bound can be set to an estimate of the optimal path cost. After depth-first search terminates either: � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 18

  19. Depth-first Branch-and-Bound: Initializing Bound The bound can be initialized to ∞ . The bound can be set to an estimate of the optimal path cost. After depth-first search terminates either: I A solution was found. I No solution was found, and no path was pruned I No solution was found, and a path was pruned. � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 19

  20. Which shaded goals will be best solutions so far? Q W R T Y U V � D. Poole and A. Mackworth 2010 c Artificial Intelligence, Lecture 3.5, Page 20

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