Presentation Overview

 

  1. History of EC
  2. What is IEC
  3. Motivation for human component
  4. Overview of IEC field
  5. Towards a Theory of IGA
  6. Problems in IEC
  7. Solutions?
  8. Applications and Results of IEC

History of EC

What is IEC?

Interactive Evolutionary Computation

Human user is involved in evolutionary computation in some way

Two definitions:

Narrow -

User aids fitness function

Broad -

User aids entire search

What is IEC?

Human input can also be benficial in

  • Evolution Strategies (IES)
  • Genetic Programming (IGP)
  • Human-Based Genetic Algorithms (HBGA)

"Human in the loop" is not restricted only to interactive GA (IGA)

IGA vs HBGA

IGA comes in narrow and broad flavors as defined

  • Fitness
  • Search

HBGA has human involvement at every step

  • Fitness
  • Search (Selection)
  • Initialization of Population
  • Recombinant Crossover
  • Mutation

Motivation

We know how to do this with non-interactive GA

Note - Stochastic hill climber used here

http://rogeralsing.com/2008/12/07/genetic-programming-evolution-of-mona-lisa/

Motivation

What if we don't know the target?

Maybe we're not

great artists?

Aoki, K. and Tagaki, H.: 3D CG Lighting with Interactive GA

Motivation

IEC can assist in human creativity

Used in many creative domains:

  • Visual art
    • 3D lighting
    • 3D/2D image creation 
  • Music
    • Melody generation
    • Rhythm Generation
    • Synthesizer optimization
  • Industrial design 
  • etc

Overview of Field

Towards a Theory

One major attempt to create theoretical model of IEC

Rudolph:

  • Can IEC be modeled in a probabilistic framework?
  • If so, is there any utility?

Towards a Theory

Classic EAs can be modeled by Markov Chains

Too restricted for IEA

Rudolph attempts to model IEA using stochastic automata

Towards a Theory

Stochastic Automata

\langle{S, X, Y, P(s', y|s, x)}\rangle
⟨S,X,Y,P(s​′​​,y∣s,x)⟩
S=States
S=States
Y=Output\ Symbols
Y=Output Symbols
X = Input\ Symbols
X=Input Symbols
P:S \times Y \times S \times X \to [0,1]
P:S×Y×S×X→[0,1]
\displaystyle\sum_{(s^{\prime} ,y)\in S\times Y} P(s^{\prime}, y|s, x)=1, forall\ (s,x)\in S\times X
​(s​′​​,y)∈S×Y​∑​​P(s​′​​,y∣s,x)=1,forall (s,x)∈S×X

Towards a Theory

Special Cases of stochastic automata

Markov Chains:

\langle{S, \emptyset, \emptyset, P(s'|s x)}\rangle
⟨S,∅,∅,P(s​′​​∣sx)⟩

Towards a Theory

Special Cases of stochastic automata

Stochastic Mealy Automata:

\langle{S, X, Y, P(s', y|s, x)}\rangle
⟨S,X,Y,P(s​′​​,y∣s,x)⟩
P(s', y | s, x) = P(s' | s, x) \cdot P(y | s, x)
P(s​′​​,y∣s,x)=P(s​′​​∣s,x)⋅P(y∣s,x)
P(s'|s,x)= \displaystyle\sum_{y \in Y}P(s', y|s, x)
P(s​′​​∣s,x)=​y∈Y​∑​​P(s​′​​,y∣s,x)
P(y|s,x)= \displaystyle\sum_{s^{\prime} \in S} P(s', y|s, x)
P(y∣s,x)=​s​′​​∈S​∑​​P(s​′​​,y∣s,x)

Where,

Towards a Theory

Special Cases of stochastic automata

Stochastic Automata with Deterministic Output:

\langle{S, X, Y, P(s', y|s, x)}\rangle
⟨S,X,Y,P(s​′​​,y∣s,x)⟩

TODO

Towards a Theory

To model IEC as SMA, need:

  • State space
  • Input set
  • Output set
  • Transition matrices
\langle{S, X, Y, P(s', y|s, x)}\rangle
⟨S,X,Y,P(s​′​​,y∣s,x)⟩

S = Set of all possible populations

Y = Function of current state - can be        ignored

X = User selection

 

 

A(x) = transition matrices

{N(2N-1)}\over (N!)^2
​(N!)​2​​​​N(2N−1)​​

#selection operations = 

Problems...

Solutions?

Applications and Results

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