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A Stochastic Graph Grammar Algorithm for Interactive Search. Rahul Rai Assistant Professor Department of Mechanical Engineering California State University at Fresno Fresno, California 93740 [email protected] Tolga Kurtoglu Research Scientist Mission Critical Technologies

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a stochastic graph grammar algorithm for interactive search

A Stochastic Graph Grammar Algorithm for Interactive Search

Rahul Rai

Assistant Professor

Department of Mechanical Engineering

California State University at Fresno

Fresno, California 93740

[email protected]

Tolga Kurtoglu

Research Scientist

Mission Critical Technologies

Intelligent Systems Division

NASA Ames Research Center

Moffett Field, California 94035

[email protected]

Matthew I. Campbell

 Associate Professor

Automated Design Laboratory

Department of Mechanical Engineering

University of Texas at Austin

Austin, Texas 78712-0292

[email protected]

introduction
Introduction
  • generative grammars is a powerful approach to represent different topologies, configurations or shapes within a single search space
    • approaches the representational capacity of human designers that create and compare wildly different solutions during the conceptual design phase
    • We are interested in how grammars can be used to interactively guide human designers or even automatically find promising concepts
  • grammars merely define a space or tree of solutions
    • not a means to search this space
    • search trees -- intractably large set of solutions
    • Need some way to evaluate concepts
      • target specific areas of the tree that best meet the designer’s expectations.
  • Evaluation completely left to humans
    • Difficult on concepts when no dimensions are provided
approach
Approach
  • present a sample of solutions to the designer
  • Get feedback
  • use that information to find better solutions in the search tree
  • seeks solutions to maximize the designer’s preference
  • reflecting the user input onto the generative grammar rules
    • which rule
    • combination of rules
    • ordering of rules
    • time to execute a particular rule

…leads to the best design

seed rules for necktie knot grammar
Seed Rules for necktie knot grammar

In order to begin any tie knot a triangular basis has to be created. This beginning move creates three regions L C R (Left, Center, Right). This gives rise to seed rules. One can begin in two way Li and Lo (i denotes in plane and o denotes out plane).

continuing rules for tie knot
Continuing rules for tie knot
  • One can continue from the seed rule by implementing one of the six rules shown here
  • There are two restriction on continuing rules.
  • First, the i and o has to alternate
  • Second, next step cannot have same basis, i.e., if previous step is L then next step has to be either C or R.
terminating rules for tie knots
Terminating rules for tie knots
  • A tie knot can only terminate in one of the possible two ways shown above.
  • T denotes (termination and no more rules can be applied)
slide7
18 graph grammar rules for tie knots
  • Based on initiation, continuing, and terminating aspects of tie knot, only 18 graph grammar rules can be deduced for the tie knot problem. The rules code in graphsynth are as follows:

Rule 1

LHS Lo

RHS LoRi

Rule 2

LHS Lo

RHS LoCi

Rule 3

LHS Ri

RHS RiCo

Rule 4

LHS Ri

RHS RiLo

Rule 5

LHS Co

RHS CoLi

Rule 6

LHS Co

RHS CoRi

slide8
Rule 11

Rule 7

LHS Li

RHS LiCo

Rule 12

Rule 8

LHS Li

RHS LiRo

Rule 13

Rule 9

LHS Ro

RHS RoCi

Rule 14

Rule 10

LHS Ro

RHS RoLi

Rule 15

Rule 11

LHS Ci

RHS CiRo

Rule 16

Rule 12

LHS Ci

RHS CiLo

Rule 17 (Initiation )

Rule 13

LHS Null

RHS Li

Rule 18 (Initiation )

Rule 14

RHS Lo

LHS Null

Rule 15

Rule 19 (Termination )

RHS CoT

LHS Co

slide9
4

A green number denote that rule selected for application among applicable rules

Vertex where to apply a rule in the LHS of a step

Four in hand knot

Step 1

Li

Seed graph (Null)

Applicable Rules 13, 14

Step 2

Li

Li

Ro

Applicable Rules 7, 8

Step 3

Li

Ro

Li

Ro

Li

Applicable Rules 9, 10

Step 4

Li

Ro

Li

Li

Ro

Li

Co

Applicable Rules 7, 8

Step 5

Li

Ro

Li

Co

Li

Ro

Li

Co

T

Applicable Rules 5, 6, 15

slide10
4

A green number denote that rule selected for application among applicable rules

Vertex where to apply a rule in the LHS of a step

Step 1

Cross knot 1

Li

Seed graph (Null)

Applicable Rules 13, 14

Step 2

Li

Ro

Li

Applicable Rules 7,8

Step 3

Li

Ro

Li

Ro

Ci

Applicable Rules 9, 10

Step 4

Li

Ro

Ci

Li

Ro

Ci

Ro

Applicable Rules 11,12

Step 5

Li

Ro

Ci

Ro

Li

Ro

Ci

Ro

Applicable Rules 9,10

Li

slide11
Cross knot 2

Step 6

Li

Ro

Ci

Ro

Li

Ro

Ci

Ro

Applicable Rules 7,8

Co

Li

Li

Step 7

Li

Ro

Ci

Ro

Li

Ro

Ci

Ro

Applicable Rules 5, 6, 15

Co

Li

T

Co

Li

slide12
4

A green number denote that rule selected for application among applicable rules

Vertex where to apply a rule in the LHS of a step

Step 1

Windsor 1

Li

Seed graph (Null)

Applicable Rules 13, 14

Step 2 and 3

Step 2

Li

Co

Li

Applicable Rules 7,8

Step 3

Li

Co

Li

Co

Li

Applicable Rules 5, 6, 15

Step 4

Li

Co

Li

Ro

Li

Co

Li

Applicable Rules 7,8

Step 5

Li

Co

Li

Ro

Li

Co

Li

Ro

Ci

Applicable Rules 9,10

slide13
Windsor 2

Step 6

Li

Co

Li

Ro

Ci

Applicable Rules 11, 12

Li

Co

Li

Ro

Ci

Ro

Step 7

Li

Co

Li

Ro

Ci

Ro

Applicable Rules 9,10

Li

Co

Li

Ro

Ci

Ro

Li

Step 8

Li

Co

Li

Ro

Ci

Ro

Li

Applicable Rules 7,8

Li

Co

Li

Ro

Ci

Ro

Li

Co

Step 9

Li

Co

Li

Ro

Ci

Ro

Li

Co

Applicable Rules 5,6,15

Li

Co

Li

Ro

Ci

Ro

Li

Co

T

slide14
4

A green number denote that rule selected for application among applicable rules

Vertex where to apply a rule in the LHS of a step

Small knot

Step 1

Lo

Seed graph (Null)

Applicable Rules 13, 14

Step 2

Lo

Lo

Ri

Applicable Rules 1, 2

Step 3

Co

Lo

Ri

Lo

Ri

Applicable Rules 3, 4

Step 4

Co

T

Lo

Ri

Co

Lo

Ri

Applicable Rules 5 ,4, 15

maximum of nine steps 85 solutions
T31

T24

Maximum of Nine Steps(85solutions)

T32

Co

T43

Co

T30

T28

Co

T33

Co

T37

Co

T9

Co

Ri

Ri

T48

Co

Ri

Co

Li

Li

T25

Co

Ri

T20

Li

Co

Li

Co

Ri

T10

Lo

Co

Co

Lo

Ro

Li

Ro

Ro

Li

Lo

T53

T3

T7

Ro

Lo

T29

Ri

Ri

Co

Ci

T40

Ro

Li

Co

Co

Li

Ri

Co

T27

Li

Co

Ci

Ro

Lo

Co

Ri

Co

Ro

Li

Ri

Co

Li

Lo

Li

Lo

Ro

Ro

Ci

T13

T39

Ci

Ri

Li

T46

Co

Co

T1

Co

Li

Ro

Ri

Ro

Li

Ro

Lo

Li

T12

Co

Ro

Co

T35

Li

Ri

Ci

Co

Co

Lo

Ri

Ri

Lo

Ri

Lo

Co

T54

Ci

Ro

Li

Ri

Lo

Ci

T19

Co

Li

Ro

Co

Ci

T51

Lo

Ri

Lo

Co

Ri

Ri

Lo

Ri

Lo

Ri

T4

T

Ri

Co

Co

Lo

Li

T23

T5

Co

Lo

Ri

Li

Co

Lo

Ri

Ro

Li

T38

Co

Lo

Co

Ci

Ri

T42

T2

Ci

Ro

Ri

Ci

Co

Co

Lo

Ro

T26

Li

T16

Ci

Ro

Ci

Ci

Lo

T11

Co

Lo

Ri

Ro

Lo

Li

Li

Ri

Ro

Ri

Ro

Li

Ri

T17

Co

Li

Ci

Lo

Ci

Co

Co

Ro

Li

Co

Lo

Co

Ri

Co

T47

T8

Lo

Co

Li

Ri

Co

Co

T41

T45

Ro

Co

Lo

Ri

Co

T6

Lo

Ro

Co

T44

T14

T55

Ri

Li

Li

Ri

Co

T52

T22

T15

Co

Co

T49

Co

Co

T50

T34

T57

T36

T58

title a stochastic graph grammar algorithm for interactive search
title: “A Stochastic Graph Grammar Algorithm for Interactive Search”
  • the tree is never explicitly represented
    • large and difficult to visualize
    • may easily contain more states than the computer can store
    • 1010 =9.3 TB if each state in only one kilobyte
  • However, the number of rules that lead to these solutions is often a small and manageable size
    • grammar rules represent heuristics or constraints provided by experts in the particular design domain
  • grammar rules make definitive changes to a particular concept and their use is often clearly discernible within the final candidate solution
    • makes sense to gather statistics on the rules used to navigate the search tree
  • In the necktie grammar, rules define shape and size of the knot.
stochastic process
Stochastic Process

rule7

rule3

rule1

rule6

  • any given state in the tree, a set of options is determined
slide18
rule7

rule3

rule1

rule6

B named for G.E.P. Box. First to coin the phrase “exploration vs. exploitation”

B = [0 1]

slide19
rule7

rule3

rule1

rule6

recreate the cross knot
Recreate the Cross-Knot
  • Go all the way to 15th level of tree (5461 candidates)
  • Calculate difference from cross-knot
results
Results

After reviewing 30 out of 5461 solutions, we find a solution in 98 percentile.

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