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Implementing Search

Implementing Search. Lecture 2-2 January 14 th /19 th , 1999 CS250. 8-Puzzle. States? Operators? Goal test? Path cost?. 8-Queens. Place 8 queens on a chess board, with no one attacking any other Goal test? Path cost? States Operators?. Cryptarithmetic.

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Implementing Search

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  1. Implementing Search Lecture 2-2 January 14th/19th, 1999 CS250 CS250: Intro to AI/Lisp

  2. 8-Puzzle • States? • Operators? • Goal test? • Path cost? CS250: Intro to AI/Lisp

  3. 8-Queens • Place 8 queens on a chess board, with no one attacking any other • Goal test? • Path cost? • States • Operators? CS250: Intro to AI/Lisp

  4. Cryptarithmetic • Puzzles with numbers replaced by letters FORTY + TEN + TEN ===== SIXTY CS250: Intro to AI/Lisp

  5. Missionaries & Cannibals • Three missionaries and three cannibals wish to cross a river in a boat that won’t hold all three • States? • Operators? • Goal test? • Path cost? CS250: Intro to AI/Lisp

  6. Real-World Problems • Route finding • TSP • VLSI • Robot navigation • Paint booth scheduling CS250: Intro to AI/Lisp

  7. Search Trees CS250: Intro to AI/Lisp

  8. What’s in a Node? • State - what state are we in? • Parent - Which node generated the current node? • Operator - Action which generated node from parent • Node depth - Number of nodes from root • Cost - Path cost from initial node CS250: Intro to AI/Lisp

  9. Lieutenant Node & General Search function GENERAL-SEARCH(problem, QUEUEING-FN) returns solution or failure nodes  MAKE-QUEUE(MAKE-NODE(INITIAL-STATE[problem])) loop do ifnodes is empty thenreturn failure node  REMOVE-FRONT(nodes) if GOAL-TEST[problem] applied to STATE(node) succeeds then return node nodes  QUEUING-FN(nodes, EXPAND(node, OPERATORS[problem])) end CS250: Intro to AI/Lisp

  10. Coding Goals • Create the initial node list • Need the right ordering • Write a loop • If test • Functions for: • QUEUEING-FN, REMOVE-FRONT, GOAL-TEST, EXPAND, MAKE-NODE CS250: Intro to AI/Lisp

  11. In Lisp... (defun general-search (problem queuing-fn) "Expand nodes according to the specification of PROBLEM until we find a solution or run out of nodes to expand. The QUEUING-FN decides which nodes to look at first. [p 73]” (let ((nodes (make-initial-queue problem queuing-fn)) node) (loop (if (empty-queue? nodes) (RETURN nil)) (setq node (remove-front nodes)) (if (goal-test problem (node-state node)) (RETURN node)) (funcall queuing-fn nodes (expand node problem))))) CS250: Intro to AI/Lisp

  12. A Few Lisp Ends special form: A list (but not a macro), which is a form with special syntax or special evaluation rules or both, possibly manipulating the evaluation environment or control flow or both. The first element of a special form is a special operator. (setq var1 form1 var2 form2 ...) return terminates a loop and returns the value of the specified expression as the value of the loop CS250: Intro to AI/Lisp

  13. Dumb & Smart Searching • Does the search algorithm use information beyond GOAL-TEST? • Uninformed/blind searching does not • Informed/heuristic search does CS250: Intro to AI/Lisp

  14. Factors in Search Strategy • Completeness - Are we guaranteed to find a solution, if one exists? • Time complexity - How long does it take? • Space complexity - How much memory? • Optimality - Find the best of several solutions? CS250: Intro to AI/Lisp

  15. Different Strokes for Different Searches • Why is GENERAL-SEARCH general? CS250: Intro to AI/Lisp

  16. Breadth-First Search • Go sideways before you go down • How do we do this in GENERAL-SEARCH? • How good is it? • Completeness? • How long does it take? • How much memory? • Optimality? CS250: Intro to AI/Lisp

  17. Uniform Cost • BFS: No shorter path is a solution, but what about cost? • Uniform cost expands the lowest cost node • When is BFS also uniform? g(node) = DEPTH(node) CS250: Intro to AI/Lisp

  18. Depth-first Search • Go down before you go sideways • Saves memory over BFS - why? • How good is it? • Completeness? • How long does it take? • Optimality? • Depth-limited search CS250: Intro to AI/Lisp

  19. Iterative Deepening Search • Repeated depth-limited search • Depth 0, depth 1, depth 2, … • Same states expanded multiple times • Higher branching factors make repeated expansion less important • How good is it? • Good choice when: • Big search space • Unknown solution depth CS250: Intro to AI/Lisp

  20. Bidirectional Search • Start from the beginning and the end, meet in the middle • Divide and conquer • Cut the depth of each search in half • From O(bd) to O(2bd/2) • For b = 10, d = 6: • BFS searches 1,111,111 • Bidirectional searches 2,222 CS250: Intro to AI/Lisp

  21. Sounds Great, Where do I Sign Up? • Searching backwards? • Calculating predecessors can be tricky • Many goal states are a problem • Generate a node and ask, “Is it in the other half of the tree?” • Different halves can have different searches CS250: Intro to AI/Lisp

  22. Search Comparison d = depth of the goal m = max tree depth l = depth limit CS250: Intro to AI/Lisp

  23. And the Winner is... • Depth-first iterative deepening • Asymptotically optimal in time • Asymptotically optimal in space among blind searches that find optimal solutions CS250: Intro to AI/Lisp

  24. Constraint Satisfaction Search • Constraint Satisfaction Problem (CPS): additional structural properties • States are values of a set of variables • Goal test specifies constraints on variable values • Unary - cryptarithmetic • Binary - 8-Queens • 3rd and higher-order • Absolute or just nice to have CS250: Intro to AI/Lisp

  25. Why Bother? • Less general than the notion of ‘problem’ • More efficient algorithms • Constraints are fine-grained CS250: Intro to AI/Lisp

  26. Domains • Variables Vi have domains, Di • Discrete or continuous? CS250: Intro to AI/Lisp

  27. AIMA Code (for homework) • Code from AIMA /courses/current/CS250/Code/AIMA/doc/overview.html CS250: Intro to AI/Lisp

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