Lecture 1, Slide 1

Today’s Topics

• FREE Code that will Write Your PhD Thesis, a Best-Selling Novel, or Your Next Email

• 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

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

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)

9/29/15 2

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

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

9/29/15 3

Note: nodes usually a complex data structure (eg, a tree)

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 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!’)9/29/15 4

Another Task Viewed as AI Search – the ‘8 Puzzle’

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 5

1 3 5

6 7

2 4 8

Start State

1 2 3

4 5 6

7 8

Goal State

Legal moves: slide number into empty cell(‘state space’ drawn on paper using document camera)

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.

Possible heuristic (for scoring nodes)?i) Count of #’s in wrong cell

ii) Sum of moves if ‘collisions’ allowed

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)

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 6

The KEY Question of AI Search

Given a set of search-space nodes, which one should we ‘consider’ next?1. The youngest (most recently created)?

This is DEPTH-FIRST SEARCH (DFS)

2. The oldest (least recently created)?This is BREATH-FIRST SEARCH (BFS)

3. A random choice? SIMULATED ANNEALING (SA) does this

4. The best (need some scoring function)?This is BEST-FIRST SEARCH (BEST)

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 7

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.9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 8

Called ‘expanding’ a node

Lecture 1, Slide 9

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 GOALeg, if planning a route to travel in a GPS

• Proper choice is problem specific

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

Data Structures for OPEN

Breadth-firstUse a ‘queue’ (first in, first out; FIFO)

OPEN OPEN + RemainingChildren

Depth-firstUse a ‘stack’ (last in, first out; LIFO)

OPEN RemainingChildren + OPEN

Best-firstUse a ‘priority queue’

OPEN sort(OPEN + RemainingChildren)9/29/15 10

Example (via Doc Camera)- assume LOWER scores are better

9/29/15 CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 11

Startscore = 9

Bscore = 11

Cscore = 8

Dscore = 4

Escore = 3

Goalscore = 0

Step# OPEN CLOSED X CHILDREN RemainingCHILDREN

(this part done on doc camera for BFS, DFS, and BEST)

Use these headers for HW2,

Problem 2

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

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 { 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

Step# OPEN CLOSED X CHILDREN RemainingCHILDREN

1 { S9 } { } S9 { S9, B11, C8} { B11, C8 }

2 { C8, B11 } { S9 } C8 { G0 } { G0 }

3 { G0, B11 } { S9, C8} G0 DONE

9/29/15 Lecture 1, Slide 12

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

LOWER Better or Worse?

• Need to carefully check if lowerscores 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!9/29/15 13

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4 Lecture 1, Slide 14

A ‘Blocks World’ Example

‘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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CBA

Initial State

C

B

AGoal State

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

An INFINITE Space

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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, …

CS 540 - Fall 2015 (Shavlik©), Lecture 9, Week 4

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 full9/29/15 16

From the movie

‘Die Hard’