finish search jim little ubc cs 322 – search 7 september 24, 2014 textbook §3.6

Finish SearchJim Little

UBC CS 322 – Search 7September 24, 2014

Textbook §3.6

Lecture Overview

• Finish MBA*• Pruning Cycles and Repeated states Examples

• Dynamic Programming• Search Recap

Heuristic value by look ahead

Memory-bounded A*

• Iterative deepening A* and B & B use a tiny amount of memory

• what if we've got more memory to use?

• keep as much of the fringe in memory as we can

• if we have to delete something:• delete the worst paths ( )• ``back them up'' to a common ancestorp

pnp1

highest f

MBA*: Compute New h(p)

Lecture Overview

• Finish MBA*• Interlude: State Space/Search Graphs

• Pruning Cycles and Repeated states Examples


Clarification: state space graph vs search tree

7

k c

b z

h

akb kc

kbz

d

fkbza kbzd

kch

k

State space graph.

If there are no cycles, the two look the same

Search tree.Nodes in this tree correspond to paths in the state space graph

kchfy

4 5

6 7 8


8

k c

b z

h

akb kc

kbz

d

fkbza kbzd

kch

k

State space graph.

Search tree.

kchf

4 5

6 7 8

8

The numbers in the search tree’s nodes mean?

Node’s name

Order in which a search algo. (here: BFS) expands nodes


9

k c

b z

h

akb kc

kbk kbz

d

f

kbkb kbkc

kbza kbzd

kch

kchf

kckb

kckc

kck

k

State space graph.

Search tree. (only first 3 levels, of BFS)• If there are cycles, the two look very different


10

k c

b z

h

akb kc

kbk kbz

d

f

kbkb kbkc

kbza kbzd

kch

kchf

kckb

kckc

kck

k

State space graph.

Search tree. (only first 3 levels, of BFS)


11

k c

b z

h

akb kc

kbk kbz

d

f

kbkb kbkc

kbza kbzd

kch

kchf

kckb

kckc

kck

k

State space graph.

Search tree. (only first 3 levels, of BFS)


12

k c

b z

h

akb kc

kbk kbz

d

z

kbkb kbkc

kbza kbzd

kch

kchz

kckb

kckc

kck

k

State space graph.

May contain cycles!


(if multiple start nodes: forest)

Cannot contain cycles!


13

k c

b z

h

akb kc

kbk kbz

d

z

kbkb kbkc

kbza kbzd

kch

kchz

kckb

kckc

kck

k

State space graph.

Why don’t we just eliminate cycles?Sometimes (but not always) we want multiple solution paths


Lecture Overview



Multiple-Path Pruning & Optimal Solutions

Problem: what if a subsequent path to n is shorter than the first path to n ?

• You can remove all paths from the frontier that use the longer path. (as these can’t be optimal)

Multiple-Path Pruning & Optimal Solutions

Problem: what if a subsequent path to n is shorter than the first path to n ?

• You can change the initial segment of the paths on the frontier to use the shorter path.

Pruning Cycles

Slide 17

Repeated States

Example

Lecture Overview



Dynamic Programming• Idea: for statically stored graphs, build a table of

dist(n):• The actual distance of the shortest path from node

n to a goal g• This is the perfect

• dist(g) = 0• dist(z) = 1• dist(c) = 3• dist(b) = 4• dist(k) = ?

• dist(h) = ?

• How could we implement that?

k c

b h

g

z

2

3

1

2

4

1

7 6

7 6

heuristic

costf function

Slide 19

This can be built backwards from the goal:

Dynamic Programming

otherwisemdistmn

ngoalisifndist

Amn )(),(costmin

),(_0)(

,

a

b

cg

2

31

3

g

b

c

a

2d

1

2

𝑑𝑖𝑠𝑡 (𝑚)

¿𝑚𝑖𝑛 [ (2+0 ) ]=2

¿𝑚𝑖𝑛 [ (3+0 ) ]=3

¿𝑚𝑖𝑛 [ (3+3 ) ,(1+2)]=3

0m

But there are at least two main problems:• You need enough space to store the graph.• The dist function needs to be recomputed for each goal

Dynamic ProgrammingThis can be used locally to determine what to do.From each node n go to its neighbor which minimizes

a

b

c

g2

3

4

3

d

3

21

3

)(m)cost(n, mdist

2

1

2

Lecture Overview



Recap SearchSelectio

nComplete Optimal Time Space

DFS LIFO N N O(bm) O(mb)

BFS FIFO Y Y O(bm) O(bm)

IDS(C) LIFO Y Y O(bm) O(mb)

LCFS min cost Y Y O(bm) O(bm)

BFS min h N N O(bm) O(bm)

A* min f Y Y O(bm) O(bm)

B&B LIFO + pruning

N Y O(bm) O(mb)

IDA* LIFO Y Y O(bm) O(mb)

MBA* min f N Y O(bm) O(bm)

Recap Search (some qualifications)

Complete Optimal Time Space

DFS N N O(bm) O(mb)

BFS Y Y O(bm) O(bm)

IDS(C) Y Y O(bm) O(mb)

LCFS Y Y ? O(bm) O(bm)

BFS N N O(bm) O(bm)

A* Y Y ? O(bm) O(bm)

B&B N Y ? O(bm) O(mb)

IDA* Y Y O(bm) O(mb)

MBA* N Y O(bm) O(bm)

C>0

h admiss.

no inf path

Search in PracticeComplete Optimal Time Space

DFS N N O(bm) O(mb)

BFS Y Y O(bm) O(bm)

IDS(C) Y Y O(bm) O(mb)

LCFS Y Y O(bm) O(bm)

BFS N N O(bm) O(bm)

A* Y Y O(bm) O(bm)

B&B N Y O(bm) O(mb)

IDA* Y Y O(bm) O(mb)

MBA* N Y O(bm) O(bm)

BDS Y Y O(bm/2) O(bm/2)

Search in Practice (cont’)

Many paths to

solution, no ∞ paths?

Informed?

Large branching factor?

F

T

approve robuddies-seminars.admin \ subscribe robuddies-seminars \Justin Hart <[email protected]>

T

approve robuddies-seminars.admin \ subscribe robuddies-seminars \Justin Hart <[email protected]>

T

F

F

IDS

B&B

MBA*

IDA*

mailto:[email protected]

mailto:[email protected]

(Adversarial) Search: ChessDeep Blue’s Results in the second tournament:

• second tournament: won 3 games, lost 2, tied 1

• 30 CPUs + 480 chess processors

• Searched 126.000.000 nodes per sec

• Generated 30 billion positions per move reaching depth 14 routinely

• Iterative Deepening with evaluation function (similar to a heuristic) based on 8000 features (e.g., sum of worth of pieces: pawn 1, rook 5, queen 10)

Modules we'll cover in this course: R&Rsys

Environment

Problem

Query

Planning

Deterministic

Stochastic

Search

Arc Consisten

cy

Search

Search Value

Iteration

Var. Elimination

Constraint Satisfacti

on

Logics

STRIPS

Belief Nets

Vars + Constrai

nts

Decision Nets

Markov Processes

Var. Elimination

Static

Sequential

RepresentationReasoningTechnique

Standard Search vs. Specific R&R systemsConstraint Satisfaction (Problems):

• State• Successor function• Goal test• Solution• Heuristic function

Planning : • State• Successor function• Goal test• Solution• Heuristic function

Inference• State• Successor function• Goal test• Solution• Heuristic function

Next class

Start Constraint Satisfaction Problems (CSPs)

Textbook 4.1-4.3

finish search jim little ubc cs 322 – search 7 september 24, 2014 textbook §3.6

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