Lecture-03-04-Uninformed_Search

Selecting a state space real world is absurdly

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Selecting a state space Real world is absurdly complex; some abstraction is necessary to allow us to reason on it… Selecting the correct abstraction and resulting state space is a difficult problem! Abstract states real-world states Abstract operators sequences or real-world actions (e.g., going from city i to city j costs Lij actually drive from city i to j) Abstract solution set of real actions to take in the real world such as to solve problem CS561 - Lectures 3-4 - Macskassy - Fall 2010
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Example: 8-puzzle State: Operators: Goal test: Path cost: start state goal state CS561 - Lectures 3-4 - Macskassy - Fall 2010
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State: integer location of tiles (ignore intermediate locations) Operators: moving blank left, right, up, down (ignore jamming) Goal test: does state match goal state? Path cost: 1 per move Example: 8-puzzle start state goal state CS561 - Lectures 3-4 - Macskassy - Fall 2010
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Example: 8-puzzle start state goal state Why search algorithms? 8-puzzle has 362,880 states 15-puzzle has 10^12 states 24-puzzle has 10^25 states So, we need a principled way to look for a solution in these huge search spaces… CS561 - Lectures 3-4 - Macskassy - Fall 2010
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Back to Vacuum World CS561 - Lectures 3-4 - Macskassy - Fall 2010
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Back to Vacuum World CS561 - Lectures 3-4 - Macskassy - Fall 2010
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Search Trees A search tree: This is a “what if” tree of plans and outcomes Start state at the root node Children correspond to successors Nodes labeled with states, correspond to PLANS to those states For most problems, can never build the whole tree So, have to find ways to use only the important parts! CS561 - Lectures 3-4 - Macskassy - Fall 2010 “N”, 1.0 “E”, 1.0
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State Space Graphs There’s a big graph where Each state is a node Each successor is an outgoing arc Important: For most problems we could never actually build this graph How many states in Pacman? CS561 - Lectures 3-4 - Macskassy - Fall 2010 b a d s p c e q h r f G Laughably tiny search graph for a tiny search problem
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States vs. Nodes Problem graphs have problem states Represent an abstracted state of the world Have successors, predecessors, can be goal / non-goal Search trees have search nodes Represent a plan (path) which results in the node’s state Have 1 parent, a length and cost, point to a problem state Expand uses successor function to create new tree nodes The same problem state in multiple search tree nodes CS561 - Lectures 3-4 - Macskassy - Fall 2010
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function T REE -S EARCH ( problem , strategy ) returns a solution , or failure initialize the search tree using the initial state problem loop do if there are no candidates for expansion then return failure choose a leaf node for expansion according to strategy if the node contains a goal state then return the corresponding solution else expand the node and add resulting nodes to the search tree end Tree search algorithms Basic idea: offline, systematic exploration of simulated state-space by generating successors of explored states CS561 - Lectures 3-4 - Macskassy - Fall 2010
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  • Fall '09
  • Moradi
  • Artificial Intelligence, Depth-first search, Search algorithms, Search algorithm, Graph algorithms, Uniform-Cost Search

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