1. CS 540 - Fall 2016 (Shavlik©), Lecture 8, Week 5
11/18/2018
Today’s Topics
FREE Code that will Write Your PhD Thesis, a Best-Selling Novel, or Your Next
Methods for Intelligently/Efficiently Searching a Space of Possible Solutions
Depth, Breadth, Best-first Search
Casting a Task as a Search Problem
An Infinite Space
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5

2. Generating Great Text is Easy, Discarding the Junk is Hard
WriteMyThesis(int expectedLengthInChars) let text = “” while (random() > 1.0 / expectedLengthInChars) text += getRandomASCIIcharacter() if (acceptable(text)) return text else return WriteMyThesis(expectedLengthInChars)
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5

3. Visualizing AI Search as Discrete Graphs
Nodes: an importance aspect of the problem Directed Arcs: legal transitions between nodes Weights (optional): cost of traversing an arc
Note: nodes usually a complex data structure (eg, a tree)
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5

4. Recall: Aspects of an AI Search Algorithm
Search Space
Where we are looking; for now this will be a DISCRETE SPACE
Operators
Legal ways to move from one node to another
Search Strategy
How we decide which move to make next
Heuristic Function
Some search methods score nodes to help guide search strategy (optional)
Start Node(s)
Where we start (usually a single node, but could be a set)
Goal Node(s)
How we know we are done (sometimes we’ll have an end test, ie code that says ‘DONE!’)
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

5. The KEY Question of AI Search
Given a set of search-space nodes, which one should we ‘consider’ next?
The youngest (most recently created)? This is DEPTH-FIRST SEARCH (DFS)
The oldest (least recently created)? This is BREATH-FIRST SEARCH (BFS)
A random choice? SIMULATED ANNEALING (SA) does this
The best (need some scoring function)? This is BEST-FIRST SEARCH (BEST)
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

6. Another Task Viewed as AI Search – the ‘8 Puzzle’
Possible heuristic (for scoring nodes)? 1 3 5 6 7 2 4 8
Start State
i) Count of #’s in wrong cell
ii) Sum of moves if ‘collisions’ allowed
Legal moves: slide number into empty cell
(‘state space’ drawn on blackboard)
In AI we build the state space as we go, and rarely generate the whole space. In HWs and textbooks, we often are given the WHOLE space, but that is misleading. 1 2 3 4 5 6 7 8
Goal State
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

7. CS 540 - Fall 2016 (Shavlik©), Lecture 8, Week 5
Designing Heuristics
One good method is to think of a ‘relaxed’ (ie, simplified version) of the task
This guides the search algo, while the search algo works out the details of the unrelaxed version
Eg, in ROUTE PLANNING, assume one can ‘drive as the crow flies’ directly to the goal state (aka, ‘straight-line’ or Euclidean distance)
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5

8. General Pseudocode for Searching
The following is the basic outline for the various search algorithms (some steps need to be modified depending on the specifics of the search being used).
OPEN = { startNode } // Nodes under consideration.
CLOSED = { } // Nodes that have been expanded.
While OPEN is not empty
Remove the first item from OPEN. Call this item X.
If goalState?(X) return the solution found.
// Expand node X if it isn’t a goal state.
Add X to CLOSED. // Prevents infinite loops.
Generate the immediate neighbors (i.e., children) of X.
Eliminate those children already in OPEN or CLOSED.
Based on the search strategy, insert the remaining
children into OPEN.
Return FAILURE // Failed if OPEN exhausted w/o a goal found.
Called ‘expanding’ a node
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

9. Variations of “Return Solution”
CS 540 Fall 2015 (Shavlik)
11/18/2018
Variations of “Return Solution”
Might simply return SUCCESS
Or return the GOAL node (this is what ID3 does)
Or return PATH found from START to GOAL eg, if planning a route to travel in a GPS
Proper choice is problem specific
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

10. Data Structures for OPEN
Breadth-first
Use a ‘queue’ (first in, first out; FIFO)
OPEN  OPEN + RemainingChildren
Depth-first
Use a ‘stack’ (last in, first out; LIFO)
OPEN  RemainingChildren + OPEN
Best-first
Use a ‘priority queue’
OPEN  sort(OPEN + RemainingChildren)
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

11. Example (via blackboard) - assume LOWER scores are better
Start score = 9
B score = 11
C score = 8
D score = 4
Use these headers for HW2, Problem 2
Goal score = 0
E score = 3
Step# OPEN CLOSED X CHILDREN RemainingCHILDREN
(this part done on blackboard for BFS, DFS, and BEST)
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

12. CS 540 - Fall 2016 (Shavlik©), Lecture 8, Week 5
BFS - remember we fill out line n+1 while working on line n Step# OPEN CLOSED X CHILDREN RemainingCHILDREN 1 { S } { } S { S, B, C} { B, C } 2 { B, C } { S } B { D } { D } 3 { C, D } { S, B } C { G } { G } 4 { D, G } { S, B, C} D { C, E } { E } 5 { G, E} { S, B, C, D} G DONE - note we check for GOALS upon removal from OPEN in order to get SHORTEST PATHS in later algo’s BEST - we now need to record the heuristic score and sort OPEN 1 { S9 } { } S9 { S9, B11, C8} { B11, C8 } 2 { C8, B11 } { S9 } C8 { G0 } { G0 } 3 { G0, B11 } { S9, C8} G0 DONE
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

13. CS 540 - Fall 2016 (Shavlik©), Lecture 8, Week 5
DFS - remember we fill out line n+1 while working on line n Step# OPEN CLOSED X CHILDREN RemainingCHILDREN 1 { S } { } S { SS, BS, CS} { BS, CS } 2 { BS, CS } { S } BS { DB } { DB } 3 { DB, CS } { S, BS } DB { CD, ED } { ED } 4 { ED, CS } { S, BS, DB} ED { GE } { GE } 5 { GE, CS } {S,BS,DB,ED} GE DONE Notice we did not get the shortest path here (BFS did, though) We might want to also record the PARENT of each node reached, so we can easily extract the path from START to GOAL. This was done in the above using SUPERSCRIPTs
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

14. Think before you compute!
LOWER Better or Worse?
Need to carefully check if lower scores are better or worse
Our default is lower is better, because often the score is ‘estimated distance to goal’
For algo’s where HIGHER is better (hill climbing, simulated annealing), use
scoretoUse = - scoreoriginal
Think before you compute!
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5

15. A ‘Blocks World’ Example
Initial State
Goal State A B A B C C
‘Preconditions’ of a legal move(?x, ?y) action:
clearTop(?x) ˄ clearTop(?y) ˄ ?x ≠ ?y
Heuristic?
One possibility: # blocks in correct final position
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

16. CS 540 - Fall 2016 (Shavlik©), Lecture 8, Week 5
An INFINITE Space
Legal actions:
A) add TWO blocks (from an infinite bin) to an existing tower
B) add ONE block to an existing tower
Initial state: ONE block on the table (ie, a tower of height 1)
Goal state: a tower of height TWO
What might go wrong?
might produce tower of height 3, of height 5, …
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CS Fall 2016 (Shavlik©), Lecture 8, Week 5

17. A (Hollywood) Famous AI Puzzle
Task: put exactly 4 gallons of water in a 5 gallon jug, given
a hose and an infinite supply of water
a 3 gallon jug (no ‘depth’ markings on the jug)
a 5 gallon jug
Operators
Can fully empty or fill either jug
Can pour Jug ?A into Jug ?B until ?A empty or ?B full
From the movie ‘Die Hard’
10/4/16
CS Fall 2016 (Shavlik©), Lecture 8, Week 5