1. CSE 473 Artificial Intelligence Oren Etzioni
Search
CSE 473
Artificial Intelligence
Oren Etzioni
What are the fundamental Scientific Questions?
How did the Universe start?
Genome AI
Theory for each, except AI..
GO OVER SYLLABUS
HAND OUT SEATING CHART

2. What is Search?
Search is a class of techniques for systematically finding or constructing solutions to problems.
Example technique: generate-and-test.
Example problem: Combination lock.
Generate a possible solution.
Test the solution.
If solution found THEN done ELSE return to step 1.
© Daniel S. Weld

3. Why is search interesting?
Many (all?) AI problems can be formulated as search problems!
Examples:
Path planning
Games
Natural Language Processing
Machine learning
Genetic algorithms
© Daniel S. Weld

4. Weak Methods “In the knowledge lies the power…” [Feigenbaum]
But what if no knowledge????
© Daniel S. Weld

5. Search Tree Example: Fragment of 8-Puzzle Problem Space
© Daniel S. Weld

6. Problem Space / State Space
Search thru a
Problem Space / State Space
Input:
Set of states
Operators [and costs]
Start state
Goal state [test]
Output:
Path: start  a state satisfying goal test
[May require shortest path]
State Space Search is basically a GRAPH SEARCH PROBLEM
STATES are whatever you like!
OPERATORS are a compact DESCRIPTION of possible STATE TRANSITIONS – the EDGES of the GRAPH
May have different COSTS or all be UNIT cost
OUTPUT may be specified either as ANY PATH (REACHABILITY), or a SHORTEST PATH
© Daniel S. Weld

7. Example: Route Planning
Input:
Set of states
Operators [and costs]
Start state
Goal state (test)
Output:
States = cities
Start state = starting city
Goal state test = is state the destination city?
Operators = move to an adjacent city; cost = distance
Output: a shortest path from start state to goal state
SUPPOSE WE REVERSE START AND GOAL STATES?
© Daniel S. Weld

8. Example: N Queens Q Input: Set of states Operators [and costs]
Start state
Goal state (test)
Output
© Daniel S. Weld

9. Classifying Search GUESSING (“Tree Search”) SIMPLIFYING (“Inference”)
Guess how to extend a partial solution to a problem.
Generates a tree of (partial) solutions.
The leafs of the tree are either “failures” or represent complete solutions
SIMPLIFYING (“Inference”)
Infer new, stronger constraints by combining one or more constraints (without any “guessing”)
Example: X+2Y = 3
X+Y =1
therefore Y = 2
WANDERING (“Markov chain”)
Perform a (biased) random walk through the space of (partial or total) solutions
HERE ARE THE THREE BASIC PRINCIPLES
Guessing – guess how to EXTEND A PARTIAL SOLUTION one step at a time
Simplifying – make inferences about how the PROBLEM CONSTRAINTS interact
X + 2Y = 3
X + Y = 1
Y = 2
3. Wandering – RANDOMLY step through the space of POSSIBILITIES
© Daniel S. Weld

10. Constraint Satisfaction
Roadmap
Guessing – State Space Search
BFS
DFS
Iterative Deepening
Bidirectional
Best-first search A*
Game tree
Davis-Putnam (logic)
Cutset conditioning (probability)
Simplification – Constraint Propagation
Forward Checking
Path Consistency (Waltz labeling, temporal algebra)
Resolution
“Bucket Algorithm”
Wandering – Randomized Search
Hillclimbing
Simulated annealing
Walksat
Monte-Carlo Methods
Constraint Satisfaction
© Daniel S. Weld

11. Search Strategies v2 Blind Search Informed Search
Constraint Satisfaction
Adversary Search
Depth first search
Breadth first search
Iterative deepening search
Iterative broadening search
© Daniel S. Weld

12. Depth First Search Maintain stack of nodes to visit Evaluation
Complete?
Time Complexity?
Space Complexity?
Not for infinite spaces a
O(b^d) b e
O(d) g h c d f
© Daniel S. Weld

13. Breadth First Search Maintain queue of nodes to visit Evaluation
Complete?
Time Complexity?
Space Complexity?
Yes a
O(b^d) b c
O(b^d) g h d e f
© Daniel S. Weld

14. Memory a Limitation? Suppose: 2 GHz CPU 1 GB main memory
100 instructions / expansion
5 bytes / node
200,000 expansions / sec
Memory filled in 100 sec … < 2 minutes
© Daniel S. Weld

15. Iterative Deepening Search
DFS with limit; incrementally grow limit
Evaluation
Complete?
Time Complexity?
Space Complexity?
Yes a b e
O(b^d) c f d i
O(d) g h j k L
© Daniel S. Weld

16. Cost of Iterative Deepeningb
ratio ID to DFS 2 3 5
1.5 10
1.2 25
1.08
100
1.02
© Daniel S. Weld

17. Forwards vs. Backwards
start
end
© Daniel S. Weld

18. vs. Bidirectional
© Daniel S. Weld

19. Problem All these methods are slow (blind)
Solution  add guidance (“heurstic estimate”)
 “informed search”
© Daniel S. Weld