1. Problem Solving Agents
Blind and Informed Searches

2. Problem Solving Agent

3. Problem Types Well defined Non 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 Real-world 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 b: branching factor d: depth of the shallowest goal node
m: depth of stop
l: current depth
N: Total number of genretaed Nodes

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