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Evolutionary Robotics

Genetic Algorithm

• Let’s evolve a pancake recipe

• Need:• representation/encoding• mutation• fitness function• selection

Genetic Algorithm

• Representation/Encoding• binary

- 0001110101010101010111010101010

• real- 3.4, 0.2, -5.6, ....

• What do we need to represent?

Genetic Algorithm

• Mutation• binary

- per site vs. per genome rate

• real:- uniform/gaussian/other

- gaussian: variance?

• note: mutations usually “deleterious”• good rule of thumb: 1 genomic

Genetic Algorithm

• Fitness Function• options?

Genetic Algorithm

• Selection• options?

Concepts

• Many terms and concepts you should learn

• Mostly applies to all optimization, AI, machine learning

• Tend to use biological language

• Equip your conceptual toolbox

Fitness Landscapes

• Sewall Wright (1932)

• Terms• Higher= better

- Peaks, Valleys, Plateaus, Global/Local Optima

• Lower= better- Minima, Basins, Global/Local Minima

Genotype

Fitn

ess

Fitness Landscape

•Sewall Wright (1932)

•Walk around (via mutation/permutation)

•neighboring solutions have similar values

fitness valley

fitness peak

note: often inverted

Smooth Rugged More Rugged

Fitness Landscapes

Very Rugged

Needle In Haystack

Fitness Landscapes

Selection Options

Selection: • Truncation• Fitness Proportional• Tournament• Random

Selection: • Truncation• Fitness Proportional• Tournament• Random

Selection Options

Selection: • Truncation• Fitness Proportional• Tournament• Random

Selection Options

Selection: • Truncation• Fitness Proportional• Tournament• Random

Selection Options

Fitness Landscapes & Selection

Selection: • Truncation• Fitness Proportional• Tournament• Random

!

Note: they all have parameters

Epistasis

• aka “Interaction Effects”

geneA, geneB, geneC

geneA, geneX, geneY

geneA increases fitness

geneA decreases fitness

Pleiotropy

geneA

Pale Skin

Red Hair

Freckles

Crossover

• Exchanging DNA between organisms• Note: Horizontal Gene Transfer is another means of exchange

Crossover

Can combine good “building blocks”

geneA, geneB, geneC, geneD, geneE, geneF, geneG

geneA’, geneB, geneC’, geneD, geneE’, geneF, geneG’

Mom

Dad

geneA’, geneB, geneC’, geneD, geneE, geneF, geneG

geneA’, geneB, geneC’, geneD, geneE’, geneF, geneG

Mom

Dad

Crossover

Can reduce “genetic load”: deleterious mutations

geneA, geneB, geneC, geneD, geneE, geneF, geneG

geneA’, geneB, geneC’, geneD, geneE’, geneF, geneG’

Mom

Dad

geneA’, geneB, geneC’, geneD, geneE, geneF, geneG

geneA, geneB, geneC, geneD, geneE’, geneF, geneG’

Mom

Dad

Crossover

• Kinds• One-point• Two-point• Uniform

Building Blocks

• How are they affected by crossover?• one point• two point• uniform

geneA’, geneB, geneC’, geneD, geneE , geneF, geneG

geneA , geneB, geneC , geneD, geneE’, geneF, geneG’

sub-solution

sub-solution

Crossover

Misevic et al. Proc. Royal Society. 2006

Nature’s Encoding

Evolutionary Algorithms (EAs)

Encode Problem

Generate Population

Score PopulationSelect Parents

mutation and/or recombination

1 2 3 4 W L.2 .1 .5 .2 1 .9

genome

Encodings

how information is stored in a genome + process that produces phenotype

gattaca ccatgat tggacct

Direct vs. Generative Encodings

Direct Encoding: each genotypic element specifies an independent phenotypic element

Genotype Phenotype leg 1: 2’ leg 2: 2’ leg 3: 2’ leg 4: 2’

Genotype Phenotype leg 1: 2’ leg 2: 2’ leg 3: 2’ leg 4: 2’

Genotype' Phenotype' leg 1: 2’ leg 2: 2’ leg 3: 1’ leg 4: .5’

Direct vs. Generative Encodings

Direct Encoding: each genotypic element specifies an independent phenotypic element

Genotype Phenotype leg 1: 2’ leg 2: 2’ leg 3: 2’ leg 4: 2’

Genotype' Phenotype' leg 1: 2’ leg 2: 2’ leg 3: 1’ leg 4: .5’

X

Direct vs. Generative Encodings

Direct Encoding: each genotypic element specifies an independent phenotypic element

Genotype Phenotype leg 1: 2’ leg 2: 2’ leg 3: 2’ leg 4: 2’

Genotype Phenotype

4x leg: 2’

Genotype' Phenotype' leg 1: 2’ leg 2: 2’ leg 3: 1’ leg 4: .5’

Direct vs. Generative Encodings

X

Direct Encoding: each genotypic element specifies an independent phenotypic element

Generative Encoding: genotypic elements can influence many phenotypic elements

Genotype Phenotype leg 1: 2’ leg 2: 2’ leg 3: 2’ leg 4: 2’

Genotype' Phenotype' leg 1: 2’ leg 2: 2’ leg 3: 1’ leg 4: .5’

Genotype Phenotype

4x leg: 2’

Genotype' Phenotype'

4x leg: 1’

Direct vs. Generative Encodings

X

Direct Encoding: each genotypic element specifies an independent phenotypic element

Generative Encoding: genotypic elements can influence many phenotypic elements

Desirable properties

• Coordinated mutational effects

• Scalability

• Low dimensional search, highly complex phenotype

• Structural Organization

• Regularity...with and without variation

• Modularity

• Hierarchy

Generative Encodings

Regularityreuse of information

compressibility

Lipson (2007)

irregular

less compressible

irregularity

less compressible

Regularity

multiple regularities

Generative EncodingDirect Encoding

Hornby (2005)

Examples of Regularity in Generative Encodings

Previous Work

• Generative outperforms direct on regular problems

• No tests across a continuum of problem regularity

Game Plan

• Case-study: generative encoding vs. direct encoding • as problem regularity varies

• HyperNEAT • Has a good direct encoding control

• Based on an important concept from developmental biology

2011

• Generative encoding...

• ...where cell fate is a function of geometric position

How nature builds complexity

Development involves producing complex coordinate frames

Sean Carroll: Endless Forms Most Beautiful (2005)

How nature builds complexity

How nature builds complexity

encodes phenotypic elements as a function of their geometric location

Compositional Pattern Producing Networks (CPPNs) Stanley 2007

Adapted from: Stanley (2007)

x y

value at x,y

y

x... for all x,y coordinates

genome f(x,y) = fate

Compositional Pattern Producing Networks (CPPNs) Stanley 2007

Adapted from: Stanley (2007)

asymmetry • f(x) left-right • f(y) anterior-posterior symmetry • gaussian(x) proximal-distal repetition • within segment symmetric anterior-posterior

x y

value at x,y

y

x

gaussian(x)

sine(y)

... for all x,y coordinates

Compositional Pattern Producing Networks (CPPNs) Stanley 2007

picbreeder.org

Compositional Pattern Producing Networks (CPPNs) Stanley 2007

Previous Generative Encodings

Sims 1994

Dawkins 1986Hornby & Pollack 2002