CSC242: Intro to AI
Lecture 5
Tuesday, February 26, 13
CSUG
Tutoring: bit.ly/csug-tutoring
League of Legends LAN Party:
Sat 2/2 @ 2PM in CSB 209
$2 to benefit Big Brothers Big Sisters
bit.ly/URLoL
Tuesday, February 26, 13
ULW
Topics due to me by tomorrow
First draft due Mar 1
Questions, more feedback, etc.?
Get in touch early!
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Project 1
Code posted on BB
Everyone should have it working
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Local Search
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States + Actions + Transition Model
=
State Space
The set of all states reachable from the
initial state by some sequence of actions
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Arad
Sibiu
Rimnicu
Vilcea
Arad
Faragas
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Timosoara
Oradea
Arad
Lugoj
Zerind
Arad
Oradea
7
2
1
6
8
3
N
7
W
7
1
7
6
2
8
6
3
4
5
3
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W
7
2
1
7
2
4
8
6
8
5
3
4
8
6
3
4
5
3
4
E
1
2
2
5
S
6
S
4
E
7
1
8
6
2
8
5
3
4
5
5
7
3
2
1
6
8
4
5
S
W
1
1
7
2
1
7
2
1
6
4
8
6
4
8
3
5
3
5
Solution graphSearch(Problem p) {
Set<Node> frontier = new Set<Node>(p.getInitialState());
Set<Node> explored = new Set<Node>();
while (true) {
if (frontier.isEmpty()) {
return null;
}
Node node = frontier.selectOne();
if (p.isGoalState(node.getState())) {
return node.getSolution();
}
explored.add(node);
for (Node n : node.expand()) {
if (!explored.contains(n)) {
frontier.add(n);
}
}
}
}
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Search Strategies
Uninformed
No additional
information about states
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Informed
(Heuristic)
Can identify
“promising” states
Search Strategies
Compl
ete?
Optima
l?
BFS
DFS
IDS
Greedy
A*
✓
✗
✓
✗
✓†
✓
✗
✓*
✗
✓†
Time
d
O(b
)
O(b
)
O(b )
O(b )
O(b )
Space
O(bd ) O(bm) O(bd) O(bm ) O(bd )
d
m
m
d
If step costs are identical
† With an admissible heuristic
*
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Systematic Search
• Enumerates paths from initial state
• Records what alternatives have been
explored at each point in the path
Good: Systematic → Exhaustive
Bad: Exponential time and/or space
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Local Search
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Initial
State
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Goal
State
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N-Queens as StateSpace Search Problem
• State
• Actions
• Transition Model
• Initial State
• Goal State(s)/Test
• Step costs
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Local Search
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Local Search
• Evaluates and modifies a small number of
current states
• Does not record history of search (paths,
explored set, etc.)
Good: Very little (constant) memory
Bad: May not explore all alternatives
=> Incomplete
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State
localSearch(Problem
p) {
Solution
graphSearch(Problem
p) {
Set<Node> frontier = new Set<Node>(p.getInitialState());
Node node explored
= new Node(p.getInitialState());
Set<Node>
= new Set<Node>();
while (true) {
if (frontier.isEmpty()) {
return null;
}
Node node = frontier.selectOne();
if (p.isGoalState(node.getState())) {
return
return node.getSolution();
node.getState();
}
explored.add(node);
for (Node n : node.expand()) {
if (!explored.contains(n)) {
frontier.add(n);
}
}
}
}
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State
localSearch(Problem
p) {
Solution
graphSearch(Problem
p) {
Set<Node> frontier = new Set<Node>(p.getInitialState());
Node node explored
= new Node(p.getInitialState());
Set<Node>
= new Set<Node>();
while (true) {
if (frontier.isEmpty()) {
return null;
}
Node node = frontier.selectOne();
if (p.isGoalState(node.getState())) {
return
return node.getSolution();
node.getState();
}
explored.add(node);
for (Node n : node.expand()) {
if (!explored.contains(n)) {
???
frontier.add(n);
}
}
}
}
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h(n)
n
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State
localSearch(Problem
p) {
Solution
graphSearch(Problem
p) {
Set<Node> frontier = new Set<Node>(p.getInitialState());
Node node explored
= new Node(p.getInitialState());
Set<Node>
= new Set<Node>();
while (true) {
if (frontier.isEmpty()) {
return null;
}
Node node = frontier.selectOne();
if (p.isGoalState(node.getState())) {
return
return node.getSolution();
node.getState();
}
explored.add(node);
for (Node n : node.expand()) {
if
{
if (!explored.contains(n))
(p.value(n) >= p.value(node))
{
frontier.add(n);
node = n;
}}
}
}
}
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State localSearch(Problem p) {
Node node = new Node(p.getInitialState());
while (true) {
if (p.isGoalState(node.getState())) {
return node.getState();
}
}
}
for (Node n : node.expand()) {
if (p.value(n) >= p.value(node)) {
node = n;
}
}
Tuesday, February 26, 13
State localSearch(Problem p) {
Node node = new Node(p.getInitialState());
while (true) {
if (p.isGoalState(node.getState())) {
return node.getState();
}
Node next = null;
for (Node n : node.expand()) {
if (p.value(n) >= p.value(node)) {
next = n;
}
}
} if (next == null) {
}
return node.getState();
} else {
node = next;
}
}
}
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State localSearch(Problem p) {
Node node = new Node(p.getInitialState());
while (true) {
Node next = null;
for (Node n : node.expand()) {
if (p.value(n) >= p.value(node)) {
next = n;
}
}
if (next == null) {
return node.getState();
} else {
node = next;
}
}
}
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Hill-climbing Search
• Move through state space in the direction
of increasing value (“uphill”)
State-space landscape
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State: [r0 , . . . , r7 ]
Action: < i, ri >
h(n) = # of pairs of queens attacking each other
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h(n) = 17
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18 12 14 13 13 12 14
14 16 13 15 12 14 12
14 12 18 13 15 12 14
15 14 14
13 16 13
14 17 15
14 16
17
16 18 15 15
18 14
15 15 14
14 14 13 17 12 14 12
h(n) = 17
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14
16
14
16
16
16
18
h(n) = 12
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State hillClimb(Problem p) {
Node node = new Node(p.getInitialState());
while (true) {
Node next = null;
for (Node n : node.expand()) {
if (p.value(n) >= p.value(node)) {
next = n;
}
}
if (next == null) {
return node.getState();
} else {
node = next;
}
}
}
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h(n) = 1
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objective function
global maximum
shoulder
local maximum
“flat” local maximum
current
state
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state space
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If at first you don’t succeed, try again.
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State randomRestart(Problem p) {
while (true) {
p.setInitialState(new random State);
State solution = hillClimb(p);
if (p.isGoal(solution)) {
return solution;
}
}
}
Does it work? Yes (but)
How well does it work?
Prob of success = p Expected # of tries = 1/p
= 0.14
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⇡7
State randomRestart(Problem p) {
while (true) {
p.setInitialState(new random State);
State solution = hillClimb(p);
if (p.isGoal(solution)) {
return solution;
}
}
}
Randomness
Stochastic hill climbing
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Randomness in Search
Pure random walk
Greedy local search
Complete,
but horribly slow
Incomplete,
but fast
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Simulated Annealing
• Follow landscape down towards global
minimum of state cost function
• Occasionally allow an upward move
(“shake”) to get out of local minima
• Don’t shake so hard that you bounce out of
global minimum
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Cost
State space
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Annealing
• A heat treatment that alters the
microstructure of a material causing
changes in properties such as strength and
hardness and ductility
• High temp => Atoms jumping around
• Low temp => Atoms settle into position
Tuesday, February 26, 13
State simulatedAnnealing(Problem p, Schedule schedule) {
Node node = new Node(p.getInitialState());
for (t=1; true; t++) {
Number T = schedule(t);
if (T == 0) {
return node;
}
Node next = randomly selected successor of node
Number deltaE = p.cost(node) - p.cost(next);
if (deltaE > 0 || Math.exp(-deltaE/T) > new Random(1)) {
node = next;
}
}
E
}
T
e
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1
0.75
y=e
0.5
E/10
0.25
y=e
0
Tuesday, February 26, 13
1
E
2
3
4
5
6
7
8
9
10
Simulated Annealing
Complete?
No.
Optimal?
No.
“But if the schedule lowers T slowly
enough, simulated annealing will find a global
minimum with probability approaching one.”
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Local Search
• Evaluates and modifies a small number of
current states
• Does not record history of search
Good: Very little (constant) memory
Bad: May not explore all alternatives
=> Incomplete
Tuesday, February 26, 13
Local Beam Search
• During hill-climbing:
• Keep track of k states rather than just
one
• At each step, generate all successors of
all k states (k*b of them)
• Keep the most promising k of them
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Local Search
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Parallel Local Search
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Parallel Local Search
-8 -5 -7 -2
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4 6 9 1
-3 3 0 -9
Local Beam Search
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Local Beam Search
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Local Beam Search
• During hill-climbing:
• Keep track of k states rather than just
one
• At each step, generate all successors of
all k states (k*b of them)
• Keep the most promising k of them
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Asexual Reproduction
Wikipedia
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Mitosis
Two diploid
cells
DNA
replication
Mitosis
Wikipedia
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Sexual Reproduction
S
N
W
F
Wikipedia
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Meiosis
Daughter
Nuclei II
Daughter
Nuclei
Interphase
Meiosis I
Homologous
Chromosomes
Meiosis II
Wikipedia
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Genetic Algorithms
• Start with k random states
• Select pairs of states and have them “mate”
to produce “offspring”
• Most fit (highest-scoring) individuals
reproduce more often
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Genetic Algorithms
• States encoded as “chromosomes” (linear
sequences, a.k.a. strings)
• During mating:
• Crossover: swap chunks of code
• Mutation: randomly change bits of code
Tuesday, February 26, 13
24748552
24 31%
32752411
32748552
32748152
32752411
23 29%
24748552
24752411
24752411
24415124
20 26%
32752411
32752124
32252124
32543213
11 14%
24415124
24415411
24415417
(a)
Initial Population
(b)
Fitness Function
(c)
Selection
(d)
Crossover
(e)
Mutation
Tuesday, February 26, 13
Genetic Algorithms
• States encoded as “chromosomes” (linear
sequences, a.k.a. strings)
• During mating:
• Crossover: swap chunks of code
• Mutation: randomly change bits of code
Tuesday, February 26, 13
GA Summary
• A version of stochastic local beam search
with a special way to generate successor
states (motivated by a naive biology
analogy)
• “Much work remains to be done to identify
the conditions under which genetic
algorithms perform well.”
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• Evaluates and modifies a small number of
current states
Does not record history of search
•Hill-climbing
Good: Very little (constant) memory
Simulated Annealing
Bad: May not explore all alternatives
24748552
24 31%
32752411
32748552
32748152
32752411
23 29%
24748552
24752411
24752411
24415124
20 26%
32752411
32752124
32252124
32543213
11 14%
24415124
24415411
24415417
(a)
Initial Population
(b)
Fitness Function
(c)
Selection
(d)
Crossover
(e)
Mutation
=> Incomplete
Local Beam Search
Tuesday, February 26, 13
Genetic Algorithms
For next time:
AIMA 5.0–5.2.2
Quiz?
Project 1: Get Going!
Tuesday, February 26, 13