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Search Part I Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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Introduction Let’s review a goal-based agent called a “problem-solving agent” They have two characteristics: 1.Find sequences of actions to reach a goal. 2.They are uninformed.
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Preliminaries We need to define two things: Goal Formulation Define objectives Problem Formulation Define actions and states
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Problem Formulation Four components: 1.The initial state 2.Actions (successor function) 3.Goal test 4.Path Cost
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Problem Formulation Comments: a. Removing detail from a representation is called “abstraction”. b. Good abstractions are key to solving problems. c. A solution is a path from initial state to goal.
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Example
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Other Examples Toy Problems: Vacuum World 8-puzzle 8-queens problem
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Other Examples Real Problems Route-Finding Problem Robot Navigation Automatic Assembly Sequencing Protein Design Internet Searching
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Problem Solving By Searching Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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Solutions We search through a search tree We expand new nodes to grow the tree There are different search strategies Nodes contain the following: state parent node action path cost depth
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Search Tree Initial state Expanded nodes
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Performance Four elements of performance: Completeness (guaranteed to find solution) Optimality (optimal solution?) Time Complexity Space Complexity
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Performance Complexity requires three elements: a.Branching factor b b.Depth of the shallowest goal node d c.Maximum length of any path m
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Problem Solving By Searching Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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Breadth-First Search Root is expanded first Then all successors at level 2. Then all successors at level 3, etc. Properties: Complete (if b and d are finite) Optimal (if path cost increases with depth) Complexity is O(b d+1 )
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Search
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Implemented as a FIFO Queue
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Uniform-Cost Search Like breadth-first search Expand node with lowest path cost. Properties: Complete (if b and d are finite) Optimal (if path cost increases with depth) Could be worse than breadth first search
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Search
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Depth-First Search Expand the deepest node at the bottom of the tree. Properties: Incomplete suboptimal Time complexity is O(b m ) Space complexity is only O(bm)
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Search Failure in infinite spaces…
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Search
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Depth-Limited Like depth-first search but with depth limit L. Properties: Incomplete (if L < d) Nonoptimal (if L > d) Time complexity is O(b L ) Space complexity is O(bL)
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Iterative Deepening A combination of depth and breadth-first search. Gradually increases the limit L Properties: Complete (if b and d are finite) Optimal if path cost increases with depth Time complexity is O(b d )
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Search
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Bidirectional Search Run two searches – one from the initial state and one backward from the goal. We stop when the two searches meet. Motivation: Time complexity: (b d/2 + b d/2 ) < b d Searching backwards not easy.
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Problem Solving By Searching Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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Avoiding Repeated States In some problems repeated states are unavoidable (example 8-Puzzle) Solution: Store all nodes already generated on a hash table.
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Avoiding Repeated States
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Problem Solving By Searching Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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Partial Information Knowledge of states or actions is incomplete. a.Sensorless problems b.Contingency Problems c.Exploration Problems
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Problem Solving By Searching Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States Partial Information Summary
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To search we need goal and problem formulation. A problem has initial state, actions, goal test, and path function. Performance measures: completeness, optimality, time and space complexity.
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Summary Uninformed search has no additional knowledge of states: breadth and depth-first search, depth-limited, iterative deepening, bidirectional search. It is important to eliminate repeated states. In partially observable environments, one can deal with belief states.
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