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Search Problems

Search Problems. Russell and Norvig: Chapter 3, Sections 3.1 – 3.3 Slides adapted from: robotics.stanford.edu/~latombe/cs121/2003/home.htm by Prof. Jean-Claude Latombe. Why Search?.

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Search Problems

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  1. Search Problems Russell and Norvig: Chapter 3, Sections 3.1 – 3.3 Slides adapted from: robotics.stanford.edu/~latombe/cs121/2003/home.htm by Prof. Jean-Claude Latombe

  2. Why Search? • In many tasks, we know what a solution looks like, but do not have an algorithm that produces a solution. • Goal + preferences • Search is a general problem solving technique for this kind of situations. • Search Problem: • Input: Initial State + Goal (utility) + actions (state transitions) • Output: A sequence of actions to reach the goal.

  3. Example: Travel Task

  4. Clean House Task

  5. Vacuum Cleaner Space

  6. Search Problem • State space • Initial state • Successor function • Goal test • Path cost

  7. Example: 8-queens Place 8 queens in a chessboard so that no two queens are in the same row, column, or diagonal. A solution Not a solution

  8. Example: 8-queens • Formulation #1: • States: any arrangement of • 0 to 8 queens on the board • Initial state: 0 queens on the • board • Successor function: add a • queen in any square • Goal test: 8 queens on the • board, none attacked  648 states with 8 queens

  9. Example: 8-queens • Formulation #2: • States: any arrangement of • k = 0 to 8 queens in the k • leftmost columns with none • attacked • Initial state: 0 queens on the • board • Successor function: add a • queen to any square in the leftmost empty column such that it is not attacked • by any other queen • Goal test: 8 queens on the • board  2,067 states

  10. Example: Robot navigation What is the state space?

  11. Cost of one horizontal/vertical step = 1 Cost of one diagonal step = 2 Example: Robot navigation

  12. Example: Robot navigation

  13. Example: Robot navigation

  14. Example: Robot navigation Cost of one step = ???

  15. Example: Robot navigation

  16. Example: Robot navigation

  17. Cost of one step: length of segment Example: Robot navigation

  18. Example: Robot navigation

  19. Complex function: it must find if a collision-free merging motion exists • Successor function: • Merge two subassemblies Example: Assembly Planning Initial state Goal state

  20. Example: Assembly Planning

  21. Example: Assembly Planning

  22. Assumptions in Basic Search • The environment is static • The environment is discretizable • The environment is observable • The actions are deterministic  open-loop solution

  23. Search Problem Formulation • Real-world environment  Abstraction • Validity: • Can the solution be executed?

  24. Search Problem Formulation • Real-world environment  Abstraction • Validity: • Can the solution be executed? • Does the state space contain the solution? • Usefulness • Is the abstract problem easier than the real-world problem? • Without abstraction an agent would be swamped by the real world

  25. Search Problem Variants • One or several initial states • One or several goal states • The solution is the path or a goal node • In the 8-puzzle problem, it is the path to a goal node • In the 8-queen problem, it is a goal node • Any, or the best, or all solutions

  26. Multi-state Search • In vacuum problem, what if we don’t have sensors to tell us whether the floor is clean or not, and which room are we in?

  27. Important Parameters • Number of states in state space • Size of memory needed to store a state • Running time of the successor function

  28. Applications • Route finding: airline travel, telephone/computer networks • Pipe routing, VLSI routing • Pharmaceutical drug design • Robot motion planning • Video games

  29. Summary • Problem-solving agent • State space, successor function, search • Examples: Travel Task, house cleaning, 8-queens, robot navigation, assembly planning • Assumptions of basic search • Important parameters

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