Problem Solving Agent

1. Problem Solving Agents
Blind and Informed Searches

2. Problem Solving Agent

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

5. TSM In Romania

6. Example 2: 8-Puzzel

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

11. Searching for Solutions

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)

14. Evaluation

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

17. Depth First Search

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

23. Summary