Evolutionary Computation Melanie Mitchell Portland State University and Santa Fe Institute Complex Systems Summer School Thursday June 19, 2008 Copyright

Evolutionary Computation

Melanie MitchellPortland State University and Santa Fe

Institute

Complex Systems Summer SchoolThursday June 19, 2008

Copyright © 2008 by Melanie Mitchell

Outline of Lectures

• Brief history of evolutionary computation

• A simple example: Evolving Robby the Robot

• EC in the real world: Case studies

• Co-evolutionary learning

Adaptive Computation• Using ideas from natural adaptive systems to build adaptive

or “life-like” computing systems.

– Neural networks

– Genetic algorithms

– Cellular automata

– Ant-colony optimization

– Swarm computing

– Artificial immune systems

– Market-inspired artificial intelligence

Evolution made simple

Essentials of Darwinian evolution:– Organisms reproduce in

proportion to their fitness in the environment

– Offspring inherit traits from parents

– Traits are inherited with some variation, via mutation and sexual recombination

Charles Darwin1809–1882

Evolution made simple

Essentials of Darwinian evolution:– Organisms reproduce in

proportion to their fitness in the environment

– Offspring inherit traits from parents

– Traits are inherited with some variation, via mutation and sexual recombination

Essentials of evolutionary algorithms:– Computer “organisms”

(e.g., programs) reproduce in proportion to their fitness in the environment (e.g., how well they perform a desired task)

– Offspring inherit traits from their parents

– Traits are inherited, with some variation, via mutation and “sexual recombination”

Appeal of ideas from evolution:

• Successful method of searching large spaces for good solutions (chromosomes / organisms)

• Massive parallelism

• Adaptation to changing environments

• Emergent complexity from simple rules

Evolutionary Computation: A Brief History

• 1940s –1950s: – “Automata theory” considered to be both an

engineering discipline and an approach to theoretical biology (e.g., von Neumann, Wiener, Turing)

• 1960s - 1970s: – Evolutionary programming (Fogel, Owens, and Walsh)

– Evolution strategies (Rechenberg and Schwefel)

– Genetic algorithms (Holland)

Evolutionary Computation: A Brief History

• 1980s –1990s:– Genetic Programming (Koza)

– “Evolutionary Computation”

EC in the real world: A few examples

• Automating parts of aircraft design (Boeing)

• Analyzing satellite images (Los Alamos)

• Automating assembly line scheduling (John Deere)

• Improving telecommunications networks (British Telecom)

• Generating realistic computer animation (The Lord of the Rings, Troy)

• Drug discovery (Daylight Chemical Information Systems)

• Detecting fraudulent stock trades (London Stock Exchange)

• Analysis of credit card data (Capital One)

• Forecasting financial markets and portfolio optimization (First Quadrant).

• Interactive evolution for graphics design (Karl Sims)

A Simple Example:Using Genetic Algorithms to Evolve Robby the

Robot

What Robby can see:

North: emptySouth: emptyEast: emptyWest: canCenter: empty

North: wallSouth: emptyEast: wallWest: emptyCenter: empty

What Robby can do:

Actions

0: Move north

1: Move south

2: Move east

3: Move west

4: Stay put

5: Pick up can

6: Random move

Example Strategy(243 possible “situations” or states)

0

1

2

3

242

Genetic Algorithm

Components of a GA:

• Population of candidate solutions to a given problem (“chromosomes”)

• Fitness function that assigns fitness to each chromosome in the population

• Selection operator that selects individuals to reproduce

• Genetic operators that take existing chromosomes and produce offspring with variation (e.g., mutation, crossover)

Evolving Robby: Details

Repeat for 1000 generations:

1. Generate initial population of 200 random strategies.

2. Calculate the fitness of each strategy in the population.

3. Apply evolution to the current population of strategies to create a new population of 200 strategies.

4. Return to step 2 with this new generation.

Example random initial population

Individual 1: 233003234216303435305460061025625151141622604356543340665115141565022064064205100664321616152165202236443336334601332650300040622050243165006111305146664232401245633345524126143441361020150630642551654043264463156164510543665346310551646005164

Individual 2: 164113431210253603403612414312011042354625253042020445164336656103532215310513144062212061463143215461025652364442202534034530502005620634026331002453416430151631210012214400664012665246351650154123113132453304433212634555005314213064423311000

Individual 3: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Individual 200: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305332661201063212455442344061365430246240160663016464641103026540006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Calculate the fitness of each strategy

Points:

Successfully picks up can: 10

Tries to pick up can in empty site: -1

Crashes in to wall: -5 (bounces back to original site)

233003234216303435305460061025625151141622604356543340665115141565022064064205100664321616152165202236443336334601332650300040622050243165006111305146664232401245633345524126143441361020150630642551654043264463156164510543665346310551646005164

Run for 200 actions per session, 100 different random sessions.

Fitness = average number of points per session

...

Calculate the fitness of each strategy

Apply evolution to the current population of strategies to create a new population of 200

strategies.Individual 1:

23300323421630343530546006102562515114162260435654334066511514 Fitness: -801565022064064205100664321616152165202236443336334601332650300040622050243165006111305146664232401245633345524126143441361020150630642551654043264463156164510543665346310551646005164

Individual 2: 16411343121025360340361241431201104235462525304202044516433665

Fitness: -1206103532215310513144062212061463143215461025652364442202534034530502005620634026331002453416430151631210012214400664012665246351650154123113132453304433212634555005314213064423311000

Individual 3: 20423344402411226132136452632464212206122122252660626144436125

Fitness: 03251266406133534015341111020616422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Individual 200: 34632525136001012225612106043301135205155320130656005322235043

Fitness: -113242506412425526553463534552305332661201063212455442344061365430246240160663016464641103026540006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Select pair of parents, crossover, and mutate

Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Parent 2: 34632525136001012225612106043301135205155320130656005322235043

3242506412425526553463534552305332661201063212455442344061365430246240160663016464641103026540006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Cross over parents


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Parent 2: 34632525136001012225612106043301135205155320130656005322235043

324250641242552655346353455230533266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Cross over parents


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Cross over parents


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Cross over parents


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551 .

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

.

Child 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Mutate: At each locus, with low probability, replace digit by random digit in [0,6]


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 1: 204233444024112261321364526324652122061221222526606261444361253251266406133534015341111022616 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102033212142402251

Child 2: 346325251360010122256121060433011352051553201306560053222350433242502412425526553463534542305 422665314552254023405115503130222020065445125062206631466135532010000400031640130154160162006134440626160505641421553133236021603355131253632642630551

Mutate: At each locus, with low probability, replace digit by random digit in [0,6]


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551 .

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 1: 204233444024112261321364526324652122061221222526606261444361253251266406133534015341111022616 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102033212142402251

Child 2: 346325251360010122256121060433011352051553201306560053222350433242502412425526553463534542305 422665314552254023405115503130222020065445125062206631466135532010000400031640130154160162006134440626160505641421553133236021603355131253632642630551

Add children to new generation


Parent 1: 204233444024112261321364526324642122061221222526606261444361253251266406133534015341111020616 422665314552254023405115503130222020065445125062206631426135532010000400031640130154160162006134440626160505641421553133236021503355131253632642630551 .

Parent 2: 346325251360010122256121060433011352051553201306560053222350433242506412425526553463534552305 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102533212142402251

Child 1: 204233444024112261321364526324652122061221222526606261444361253251266406133534015341111022616 33266120106321245544234406136543024624016066301646464110302654 0006334126150352262106063624260550616616344255124354464110023463330440102033212142402251

Child 2: 346325251360010122256121060433011352051553201306560053222350433242502412425526553463534542305 422665314552254023405115503130222020065445125062206631466135532010000400031640130154160162006134440626160505641421553133236021603355131253632642630551

Continue this process until new generation is full (200 strings)Replace current population with new generation.

Repeat algorithm for a total of 1000generations

• Strategy M (Designed by me):

• Strategy G (evolved by GA):

25435515325623525105635546115133615415103415611055015005203025625613225235032511205233305405523125505133615415066526415026650601226445360563152025643105435463240435033415325025325135235204515013015621343625235322313505126051335620152451434343212

“If there is a can in the current site, pick it up. Otherwise, if there is a can in one of the adjacent sites, move to that site. Otherwise, choose a random direction to move in.”6563536562523532526563536561513531512523532521513

53151653536562523532526563536560503530502523532520503530501513531512235325215135315105035305025235325205035305065635365625235325256353656151353151252353252151353151656353656252353252656353454

Fitness: 346(out of maximum 500)

Fitness: 483(out of maximum 500)

Strategy M in a cluster of cans

Strategy G in a cluster of cans

Dynamics from one run

Best fitness

Generation

Evolutionary Computation in the Real World:

Case Studies

Any computer program can be expressed as a “parse tree”:

(* PI (* R R))

Genetic Programming(Koza, 1990)

1. Choose a set of functions and terminals for the program, e.g.,

{+, -, *, /, sqrt, sin, cos, abs, pow, R, PI, D, C, rand()}

2. Generate an initial population of random programs (trees), each up to some maximum depth.

Koza’s genetic programming algorithm:

3. Run the GA:

– Fitness: Run each program on “training data”. Fitness is how many training cases the program gets right (or how close it gets to correct answer).

– Selection: Select parents probabilistically, based on fitness.

– Crossover: Exchange subtrees of parents.

– Mutation: Replace subtree with a random tree.

Genetic Art and Computer Graphics (Karl Sims, 1993)

• GA individuals: equations that generate a color for each pixel coordinate

• Function set: +, -, /, mod, round, min, max, abs, expt, log, and, or, xor, sin, cos, atan, if, dissolve, hsv-to-rgb, vector, transform-vector, bw-noise, color-noise, warped-bw-noise, warped-color-noise, blur, band-pass, grade-mag, grad-dir, bump, ifs, warped-ifs, warp-abs, warp-rel, warp-by-grad

• Terminal set: X, Y, rand_scalar(), rand_vector(n)

• Each function returns an image (an array of pixel colors)

Left to right, top to bottom:

a. Yb. Xc. (abs X)d. (mod X (abs Y))e. (and X Y)f. (bw-noise .2 2)g. (color-noise .1 2)h. (grad-direction

(bw-noise .15 2) 0 0)

i. (warped-color-noise (* X .2) Y .1 2)

Demo

http://www.jhlabs.com/java/art.html

http://www.jhlabs.com/java/art.html

Some Results

(round (log (+ y (color-grad (round (+ (abs (round (log (+ y (color-grad (round (+ y (log (invert y) 15.5)) x) 3.1 1.86 #(0.95 0.7 0.59) 1.35)) 0.19) x)) (log (invert y) 15.5)) x) 3.1 1.9 #(0.95 0.7 0.35) 1.35)) 0.19) x)

Evolution of Collective Computation in Cellular Automata

Jim Crutchfield Rajarshi Das Wim Hordijk

Melanie Mitchell Erik van Nimwegen

Cosma Shalizi

One-dimensional cellular automata


Rule:


Rule:


Rule:


Rule:


Rule:

Space

Time

Space-time diagram ECA 110

Cellular automata as computers:

Current renewal of interest due to: – Distributed spatial computing in sensor networks

– Reconfigurable computing (FPGAs)

– Molecular and quantum-scale computation (e.g., quantum dot cellular automata; molecular self-assembly of nanoscale electronics)

– Renewed interest in how biological systems compute (and how that can inspire new computer architectures)

– A “new kind of science”?

A computational task for cellular automata

• Design a cellular automata to decide whether or not the initial pattern has a majority of “on”cells.


• Design a cellular automata to decide whether or not the initial pattern has a majority of “on”cells.– If a majority of cells are initially on, then

after some number of iterations, all cells should turn on


• Design a cellular automata to decide whether or not the initial pattern has a majority of “on”cells.– If a majority of cells are initially on, then

after some number of iterations, all cells should turn on

– Otherwise, after some number of iterations, all cells should turn off.


majority on

initial

majority on

initial

final

majority offmajority on

initial

final


initial

final


initial

final

How to design a CA to do this?

We used cellular automata with 6 neighbors for each cell:

Rule: ... ...

..

.

A candidate solution that does not work: local majority voting

Evolving cellular automata with genetic algorithms

• Create a random population of candidate cellular automata rules



• The “fitness” of each cellular automaton is how well it performs the task. (Analogous to surviving in an environment.)




• The fittest cellular automata get to reproduce themselves, with mutations and crossovers.




• The fittest cellular automata get to reproduce themselves, with mutations and crossovers.

• This process continues for many generations.


The “chromosome” of a cellular automaton is an encoding of its rule table:


Rule table:

..

.


Rule table: “Chromosome”:

0

0

1

1

.

.

.

..

.

0

Create a random population of candidate cellular automata rules:

Create a random population of candidate cellular automata rules:

rule 1: 0010001100010010111100010100110111000...rule 2: 0001100110101011111111000011101001010...rule 3: 1111100010010101000000011100010010101...

.

.

.

rule 100: 0010111010000001111100000101001011111...

Calculating the Fitness of a Rule


• For each rule, create the corresponding cellular automaton. Run that cellular automaton on many initial configurations.


• For each rule, create the corresponding cellular automaton. Run that cellular automaton on many initial configurations.

• Fitness of rule = fraction of correct classifications

For each cellular automaton rule in the population:

rule 1: 0010001100010010111100010100110111000...1


rule 1: 0010001100010010111100010100110111000...1

Create rule table


rule 1: 0010001100010010111100010100110111000...1

Create rule table


..

.

rule 1 rule table:

..

.

Run corresponding cellularautomaton on many randominitial lattice configurations

rule 1 rule table:

..

.


incorrect

rule 1 rule table:

.. . .

. . .. . .

. . .

..

.

..

.


incorrect correct

rule 1 rule table:

.. . .

. . .. . .

. . .

. . .. . .

..

.

..

. .... . . . . .


incorrect correct

etc.

rule 1 rule table:

.. . .

. . .. . .

. . .

. . .. . .

..

.

..

. .... . . . . .


incorrect correct

etc.

rule 1 rule table:

.. . .

. . .. . .

. . .

. . .. . .

..

.

..

. .... . . . . .

Fitness of rule = fraction of correct classifications

GA Population:

rule 1: 0010001100010010111100010100110111000... Fitness = 0.5rule 2: 0001100110101011111111000011101001010... Fitness = 0.2rule 3: 1111100010010101000000011100010010101... Fitness = 0.4

. . .

rule 100:0010111010000001111100000101001011111... Fitness = 0.0

GA Population:

majority on

A cellular automaton evolved by the genetic algorithm (Performance 80%)

majority off

Another Task: Synchronization

Evolving image-processing algorithms

• GENIE project (GENetic Image Exploitation), Los Alamos National Laboratory

Brumby, Harvey, Perkins, Porter, Bloch, Szymanski, et al.

Consider a large library of multi-spectral photographic images from

satellites and high-flying airplanes.

• How to automatically find images containing desired features?

E.g., water, clouds, craters on Mars, forest fire damage, vegetation, urban areas, roads, airports, bridges, beaches,...

Special-purpose algorithms can (possibly) be developed for any particular feature, but goal of GENIE project is to have a general-purpose system:

Special-purpose algorithms can (possibly) be developed for any particular feature, but goal of GENIE project is to have a general-purpose system:

A user can specify any feature (via training examples), and system will quickly find images containing that feature.

Training Examples for GENIE

• Input images consist of ~10-100 spectral planes.

• User brings up training image(s) in GUI

• User paints examples of “true” and “false” pixels.

From Brumby et al., 2000


Human created training images

Green = “feature”

Red = “non-feature”

Black = “not classified”

Roads

Vegetation

Water

Data and Feature Planes

Data planes(spectral channels)

“Feature” planes

Truth plane

What GENIE Evolves

• GENIE evolves an image processing algorithm that operates on data planes to produce a new set of feature planes.

• New feature planes are used as training data for conventional classifiers (e.g., linear discriminants, neural networks, support vector machines)

GENIE’s Gene’s

• Genes are elementary image-processing operations that read from data planes (spectral channels) or feature planes and write to feature planese.g.,

addp(d1, d2, s2)linear_comb(s2, s1, s1, 0.9)erode(s1, s1, 3, 1)

• Elementary operators include spectral, morphological, logical, and thresholding operators

GENIE’s Chromosomes• Chromosomes are algorithms made up of genes

lawd (d3, s2) ; Law’s textural operator variance (s2, s2, 3, 1) ; local variance in circular neighb. min(d1, d2, s1) ; min at each pixel locationlinear_comb (s1, d0, s1, 0.9)smooth_r5r5 (s2, s2) ; textural operator r5r5open (s2,s2, 3,1) ; erode, then dilatesubp (d1, s1, s1) ; subtract planesmin (d0, s2, s2)adds (d1, s0, 0.25) ; add scalaropcl (s1,s1, 1, 1) ; erode, dilate, dilate, erodeh_basin (s0, s0, 18) ; regional minimalinear_comb (s0, d9, s0, 0.2) linear_comb (d4, s2, s2, 0.9)addp (d6, s0, s0) ; add planes

GENIE’s Population• Initial population is a set of 20-50 randomly

generated chromosomes:

awd (d3, s2)

variance (s2, s2, 3, 1) min(d1, d2, s1)linear_comb (s1, d0, s1, 0.9)smooth_r5r5 (s2, s2)open (s2,s2, 3,1)subp (d1, s1, s1)min (d0, s2, s2)adds (d1, s0, 0.25)opcl (s1,s1, 1, 1)

erode(d3, s2,3,1)linear_comb (d2, d1, s2, 0.5)min (s1, s2, s2) open (s2,s2, 3,1)

open (s1,s2, 1,1)variance (s2, s2, 3, 1) addp (s1, s0, s2)smooth_r5r5 (d1, s3) opcl (s1,s1, 1, 3) lawd(d2, s0)subp (s1, s1, s1)

GENIE’s Fitness• Fitness:

– Run chromosome on image data to produce feature planes.

– Find linear combination of planes that maximizes spectral separation between labeled “true” and “false” pixels.

– Threshold resulting plane to get binary image (each pixel is 1 or 0):

– 1 = feature, 0= non-feature– Use threshold that will maximize fitness

GENIE’s Fitness– Fitness:

where Rd is detection rate: fraction of “feature”

pixels (green) classified correctly

Rf is false alarm rate: fraction of non-feature pixels (red) classified incorrectly

F=1000 is perfect fitness.

))1((500 fd RRF

The GA

• Selection: Selection some number of best in population

• Crossover: Recombine different genes from two different parents

• Mutation: Randomly change a chosen gene

awd (d3, s2)variance (s2, s2, 3, 1)

min(d1, d2, s1)linear_comb (s1, d0, s1, 0.9)smooth_r5r5 (s2, s2)

open (s2,s2, 3,1)subp (d1, s1, s1)min (d0, s2, s2)adds (d1, s0, 0.25)opcl (s1,s1, 1, 1)

open (s1,s2, 1,1)variance (s2, s2, 3, 1) addp (s1, s0, s2)smooth_r5r5 (d1, s3)opcl (s1,s1, 1, 3) lawd(d2, s0)subp (s1, s1, s1)

Parent 1 Parent 2







open (s2,s2, 3,1)smooth_r5r5 (d1, s3)

opcl (s1,s1, 1, 3) lawd(d2, s0)subp (s1, s1, s1)

Parent 1

Child

Parent 2







smooth_r5r5 (d1, s3)


Parent 1

Child

Parent 2







lawd(s1,s3)smooth_r5r5 (d1, s3)


Parent 1

Child

Parent 2

• The GA is run until acceptable performance on the training examples is found.

• Generalization performance is evaluated, and user then creates new training example, based on generalization performance.

Some Results



Roads and buildings

Vegetation

Water

Training Data Evolved classifier


Recent work by Ghosh & Mitchell

• Combine GENIE’s texture-learning ability with genetic shape-learning algorithm.

• Application: Find prostate in CAT scans of pelvic region

Training image, contour drawn by radiologist

From Ghosh & Mitchell, 2006

Results from our hybrid algorithm

Test image, with hand-segmentation by a radiologist

Results from GENIE alone

Examples of Advanced EC topics

• Multi-objective optimization

• Self-adapting evolutionary algorithms

• Stochastic process theory of EC

• More realistic analogies with evolution:– Diploid chromosomes– Development of phenotype– Ecological interactions (e.g., co-evolution, spatial

proximity)

Examples of Advanced EC topics

• Multi-objective optimization

• Self-adapting evolutionary algorithms

• Stochastic process theory of EC

• More realistic analogies with evolution:– Diploid chromosomes– Development of phenotype– Ecological interactions (e.g., co-evolution, spatial

proximity)

Co-evolutionary Learning

Melanie Mitchell (Portland State U.)Ludo Pagie (U. Utrecht)

Mick Thomure (Portland State U.)Jennifer Meneghin (Portland State U.)

Martin Cenek (Portland State U.)

Problem for GAs (and other machine learning methods):

How to select training examples appropriate to different stages of learning?

One solution: Co-evolve training examples, using inspiration from host-

parasite co-evolution in nature.

Host-parasite co-evolution in nature

• Hosts evolve defenses against parasites

• Parasites find ways to overcome defenses

• Hosts evolve new defenses

• Continual “biological arms race”

Heliconius-egg mimicry in Passiflora

http://www.ucl.ac.uk/~ucbhdjm/courses/b242/Coevol/Coevol.html

• Darwin recognized the importance of co-evolution in driving evolution

• Darwin recognized the importance of co-evolution in driving evolution

• Co-evolution was later hypothesized to be major factor in evolution of sexual reproduction



Candidate solutions and training examples co-evolve.



– Fitness of candidate solution (host): how well it performs on training examples.




– Fitness of training example (parasite): how well it defeats candidate solutions.




– Fitness of training example (parasite): how well it defeats candidate solutions.

Co evolutionary learning originally proposed by Hillis (1990).

Why should we expect co-evolution to work?


Hypotheses:


Hypotheses: 1. Allows arms races to emerge, with the

evolution of training examples targeted to weaknesses in learners, and subsequent adaptation of learners to those training examples, and so on.


Hypotheses: 1. Allows arms races to emerge, with the

evolution of training examples targeted to weaknesses in learners, and subsequent adaptation of learners to those training examples, and so on.

2. Helps maintain diversity in the population


Hypotheses: 1. Allows arms races to emerge, with the evolution of

training examples targeted to weaknesses in learners, and subsequent adaptation of learners to those training examples, and so on.


Effect: Increases success of learning while reducing the amount of training data needed


Hypotheses: 1. Allows arms races to emerge, with the evolution of

training examples targeted to weaknesses in learners, and subsequent adaptation of learners to those training examples, and so on.


Effect: Increases success of learning while reducing the amount of training data needed

These hypotheses are plausible but have been largely untested in work on co-evolution.

Results

Cellular Automata Function Induction

Spatial Coev. 64% (32/50) 78% (39/50)

Non-Spatial Coev. 0% (0/50) 0% (0/50)

Spatial Evol. 0% (0/50) 14% (7/50)

Non-Spatial Evol. 0% (0/50) 6% (3/50)

Non-Spatial Boosting

0% (0/10) —

Percentage of successful runs(mutation only)

Spatial Co-evolution


• 2D toroidal lattice with one host (h) and one parasite (p) per site



hp

hp

hp

. ...

.

.

hphp



hp

hp

hp

. ...

.

.

hphp

correctly answered

9 offraction )(fitness

p

g neighborinh



hp

hp

hp

. ...

.

.

hphp

correctly answered


p

g neighborinh

correct not is )( if 0

correct is (p) if 0)(fitness

ph

hp



hp

hp

hp

. ...

.

.

hphp

correctly answered


p

gneighborinh

Each h is replaced by mutated copy of winner of tournament among itself and 8 neighboring hosts.



ph

hp



hp

hp

hp

. ...

.

.

hphp

correctly answered


p

gneighborinh

Each h is replaced by mutated copy of winner of tournament among itself and 8 neighboring hosts.

Each p is replaced by mutated copy of winner tournament among itself and 8 neighboring parasites.



ph

hp

Non-Spatial Co-evolution


• No spatial distribution of host and parasite populations



hosts

parasites



correctly answered

)population parasite fromchosen (randomly

9 offraction )(fitness ph

hosts

parasites



correctly answered



population

host fromchosen randomly host for



h

ph

hp

hosts

parasites



correctly answered



Each h is replaced by mutated copy of winner of tournament among itself and 8 randomly chosen hosts.

population




h

ph

hp

hosts

parasites



correctly answered



Each h is replaced by mutated copy of winner of tournament among itself and 8 randomly chosen hosts.

Each p is replaced by mutated copy of winner tournament among itself and 8 randomly chosen parasites.

population




h

ph

hp

hosts

parasites

• Spatial Evolution: – Same as spatial co-evolution, except

parasites don’t evolve.

– A new population of random parasites is generated at each generation.

• Spatial Evolution: – Same as spatial co-evolution, except parasites don’t evolve.

– A new population of random parasites is generated at each generation.

• Non-Spatial Evolution: – Same as non-spatial co-evolution, except parasites don’t evolve.

– A new sample of 100 random parasites is generated at each generation.

– Fitness of a host is classification accuracy on these 100 randomly generated parasites

Results

Cellular Automata Function Induction

Spatial Coev. 64% (32/50) 78% (39/50)

Non-Spatial Coev. 0% (0/50) 0% (0/50)

Spatial Evol. 0% (0/50) 14% (7/50)

Non-Spatial Evol. 0% (0/50) 6% (3/50)

Non-Spatial Boosting

0% (0/10) —

Percentage of successful runs(mutation only)

In short: Spatial co-evolution significantly out-performs other methods on both problems

Analysis

Why was spatial co-evolution successful?

Hypotheses:1. Maintains diversity over long period of time

2. Creates extended “arms race” between hosts and parasite populations

Here we examine these hypotheses for the CA task.

• The GA evolves four types of strategies:

– Random

– Default

– Block Expanding

– Particle

“Default” strategy(performance 0.5)

“Block-expanding” strategy (0.55 performance < 0.72)

“Particle” strategy(performance 0.72)

Measuring diversity in host population

• Plot distribution of host strategies in typical CA runs

Random Very low performance

Default Low performance

Block expanding Medium performance

Particle High performance

Spatial Co-evolution(typical run)

Non-Spatial Co-evolution (typical run)

Spatial Evolution (typical run)

173173

Non-Spatial Evolution (typical run)

174174

Summary of diversity results


• Spatial co-evolution seems to preserve more diversity in the host population than the other methods.


• Spatial co-evolution seems to preserve more diversity in the host population than the other methods.

• In the other methods:– Spatial methods: One strategy quickly

comes to dominate the population

– Nonspatial methods: Population oscillates between two different strategies

Arms races between the host and parasite populations


• Hypothesis: Initial configurations are evolving “deceptive blocks”:



– Occurrence of a block of seven or more adjacent 0s or 1s in the 149-bit IC

– Probability of such an occurrence in a randomly generated string of the same density is less than 0.01.



– Occurrence of a block of seven or more adjacent 0s or 1s in the 149-bit IC

– Probability of such an occurrence in a randomly generated string of the same density is less than 0.01.

• For a typical run of spatial co-evolution, we plotted the fraction of parasites with deceptive blocks

generations

Summary: Why does spatial co-evolution

improve performance?



• Maintains diversity in population




• Produces “arms race” with ICs targeting weaknesses in CAs (e.g., block expanding) and CAs adapting to overcome weaknesses (e.g., particle strategies)




• Produces “arms race” with ICs targeting weaknesses in CAs (e.g., block expanding) and CAs adapting to overcome weaknesses (e.g., particle strategies)

• Note that spatial co-evolution requires significantly fewer training examples for successful learning

But why, precisely, does putting population on a spatial lattice improve performance?

But why, precisely, does putting population on a spatial lattice improve performance?

Still an open question.

Possible applications to real-world problems


– Drug design to foil evolving viruses/bacteria



– Coevolving software/hardware with test cases




– Evolving game-playing programs




– Evolving game-playing programs

– Coevolving computer security systems with possible threats

Documents

Evolutionary Computation Melanie Mitchell Portland State University and Santa Fe Institute Complex Systems Summer School Thursday June 19, 2008 Copyright