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Problem Solving Agents
Blind and Informed Searches
Problem Solving Agent
Problem Types
 Well defined
 Initial state
 Operator(Successor and predecessor Functions)
 Goal Test
 Path cost function
 Non well defined
 Missing at least on criteria
Example 1: TSM In Romania
 On holiday in Romania; currently in Arad.
 Formulate goal:
 be in Bucharest
 Formulate problem:
 states: various cities
 actions: drive between cities
 Find solution:
 sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest
 Goal Test> Are we in Bucharest.
 Cost Function> Sum of road lengths to the destination
TSM In Romania
Example 2: 8-Puzzel
Example 2: 8-Puzzel
 states??: integer locations of tiles (ignore intermediate positions)
 actions??: move blank left, right, up, down (ignore unjamming etc.)
 transition model??: effect of the actions
 goal test??: = goal state (given)
 path cost??: 1 per move
 [Note: optimal solution of n-Puzzle family is NP-hard]
Example Problems
 Toy problems
 vacuum cleaner agent
 8-puzzle
 8-queens
 Crypt arithmetic
 missionaries cannibals
 Real-world problems
 route finding
 traveling salesperson
 VLSI layout
 robot navigation
 assembly sequencing
Search
 Know the fundamental search strategies and algorithms
 uninformed search
 breadth-first, depth-first, uniform-cost, iterative deepening, bidirectional
 informed search
 best-first (greedy, A*), heuristics, memory-bounded
 Evaluate the suitability of a search strategy for a problem
 completeness, optimality, time & space complexity
Searching for Solutions
 Traversal of some search space from the initial state to a goal state
legal sequence of actions as defined by operators
 The search can be performed on
 On a search tree derived from
expanding the current state using the possible operators
Tree-Search algorithm
 A graph representing
the state space
Graph-Search algorithm
Searching for Solutions
Uninformed search strategies
 Uninformed strategies use only the information available in the problem
definition
 Breadth-first search
 Uniform-cost search
 Depth-first search
 Depth-limited search
 Iterative deepening search
 Bidirectional Search
BFS
 Expand shallowest unexpanded node (shortest path in the frontier)
Evaluation
Evaluation
 Complete?? Yes (if b is finite)
 Optimal?? Yes (if cost = 1 per step); not optimal in general
 Time?? b^d
 Number of nodes generated: 1 + b + b^2 + … + b^d
 Space?? b^d
Space is the big problem; can easily generate nodes at 100MB/sec so 24hrs =
8640GB.
Uniform-cost search
 Expand first least-cost path (Equivalent to breadth-first if step costs all equal)
 Implementation:
fringe = priority queue ordered by path cost, lowest first
Depth First Search
DFS
 Depth first search is another way of traversing graphs, which is closely related
to preorder traversal of a tree. Recall that preorder traversal simply visits
each node before its children. It is most easy to program as a recursive
routine.
 Complete?? No
 Optimal?? No
 Time?? b^d
 Space?? b*d
Depth limited search
 A version of DFS in which l is defined by an expert
 There is a chance of converging to local optima
 Complete?? Yes(if l>d)
 Optimal?? Yes
 Time?? b^l
 Space?? b*l
Iterative Deeping Search(IDS)
This search strategy always expands one node to the deepest level of the tree.
Only when a dead-end is encountered does the search backup and expand nodes
at shallower levels.
N=(d+1)1+(d)b+(d-1)b2+...+(3)bd-2+(2)bd-1+bd
IDS Evaluation
 Complete?? Yes
 Optimal?? Yes
 Time?? b^d
 Space?? b.d
Bidirectional search
 Idea: Run two simultaneous searches.
 One Forward from initial state
 One Backward from goal state
 Until two fingers met
Summary

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13256181.ppt

  • 1. Problem Solving Agents Blind and Informed Searches
  • 3. Problem Types  Well defined  Initial state  Operator(Successor and predecessor Functions)  Goal Test  Path cost function  Non well defined  Missing at least on criteria
  • 4. Example 1: TSM In Romania  On holiday in Romania; currently in Arad.  Formulate goal:  be in Bucharest  Formulate problem:  states: various cities  actions: drive between cities  Find solution:  sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest  Goal Test> Are we in Bucharest.  Cost Function> Sum of road lengths to the destination
  • 7. Example 2: 8-Puzzel  states??: integer locations of tiles (ignore intermediate positions)  actions??: move blank left, right, up, down (ignore unjamming etc.)  transition model??: effect of the actions  goal test??: = goal state (given)  path cost??: 1 per move  [Note: optimal solution of n-Puzzle family is NP-hard]
  • 8. Example Problems  Toy problems  vacuum cleaner agent  8-puzzle  8-queens  Crypt arithmetic  missionaries cannibals  Real-world problems  route finding  traveling salesperson  VLSI layout  robot navigation  assembly sequencing
  • 9. Search  Know the fundamental search strategies and algorithms  uninformed search  breadth-first, depth-first, uniform-cost, iterative deepening, bidirectional  informed search  best-first (greedy, A*), heuristics, memory-bounded  Evaluate the suitability of a search strategy for a problem  completeness, optimality, time & space complexity
  • 10. Searching for Solutions  Traversal of some search space from the initial state to a goal state legal sequence of actions as defined by operators  The search can be performed on  On a search tree derived from expanding the current state using the possible operators Tree-Search algorithm  A graph representing the state space Graph-Search algorithm
  • 12. Uninformed search strategies  Uninformed strategies use only the information available in the problem definition  Breadth-first search  Uniform-cost search  Depth-first search  Depth-limited search  Iterative deepening search  Bidirectional Search
  • 13. BFS  Expand shallowest unexpanded node (shortest path in the frontier)
  • 15. Evaluation  Complete?? Yes (if b is finite)  Optimal?? Yes (if cost = 1 per step); not optimal in general  Time?? b^d  Number of nodes generated: 1 + b + b^2 + … + b^d  Space?? b^d Space is the big problem; can easily generate nodes at 100MB/sec so 24hrs = 8640GB.
  • 16. Uniform-cost search  Expand first least-cost path (Equivalent to breadth-first if step costs all equal)  Implementation: fringe = priority queue ordered by path cost, lowest first
  • 18. DFS  Depth first search is another way of traversing graphs, which is closely related to preorder traversal of a tree. Recall that preorder traversal simply visits each node before its children. It is most easy to program as a recursive routine.  Complete?? No  Optimal?? No  Time?? b^d  Space?? b*d
  • 19. Depth limited search  A version of DFS in which l is defined by an expert  There is a chance of converging to local optima  Complete?? Yes(if l>d)  Optimal?? Yes  Time?? b^l  Space?? b*l
  • 20. Iterative Deeping Search(IDS) This search strategy always expands one node to the deepest level of the tree. Only when a dead-end is encountered does the search backup and expand nodes at shallower levels. N=(d+1)1+(d)b+(d-1)b2+...+(3)bd-2+(2)bd-1+bd
  • 21. IDS Evaluation  Complete?? Yes  Optimal?? Yes  Time?? b^d  Space?? b.d
  • 22. Bidirectional search  Idea: Run two simultaneous searches.  One Forward from initial state  One Backward from goal state  Until two fingers met