What is Neutral?Neutral Changes and

Resiliency

Terence SouleDepartment of Computer Science

University of Idaho

The experiments

Gene/exon selectionIntrons and exon selectionEffects of operators

Experiment 1Tree based, generational GPFunctions {+}Terminals/Genes {0.5, 1.0}Fitness: difference from 10

Both terminals are exons. Is one selected?

+

+

0.5

1.0

1.0

Gene/Exon Choice

0

0.25

0.5

0 20 40 60 80 100Generation

Per

cent

of c

ode

by

gene

1.00.5+

Average Fitness

2.4

2.6

2.8

3

0 20 40 60 80 100

Generation

Av

erg

e F

itn

es

s

Average fitness improves – after crossover.

Resiliency

A measure of expected fitness change as a function of genotype change.Resilient individuals are less likely to change fitness or have a smaller average fitness change in response to genotype changes (crossover and mutation).Similar to the idea of effective fitness, but more general.

Experiment 2Tree based, generational GPFunctions {+}Terminals/Genes {0, 1, 4}Fitness: difference from 40

Now there are two exons and an intron. What is selected?

Number of Genes

020406080

100120140160180

0 500 1000 1500 2000

Num

ber

of

Generation

0s1s4s

Resiliency

-6

-5

-4

-3

-2

-1

0

1

0 250 500 750

Fit

ness

Cha

nge

CrossoverMutation

Ratio of 1s to 4s

Results – Experiment 2Changes don’t affect current fitness – Are they Neutral?Changes affect expected fitness of the next generation – increase (average) resiliency

Experiment 3Variable length, linear encoding, generationalGenes {0, 1, 4}Sample individual: 010041014Fitness: difference of sum of genes from 54

Experiment 3 - Crossover

Proportional crossover – select two random points per parent.Constant crossover – length of crossed region is:

2 50% of the time4 25% of the time8 12.5% of the time…

00 104 04

440 01011 0401

00 01011 04

440 104 0401

Genes – Constant Crossover

0

50

100

150

200

0 200 400 600 800 1000Generation

Nu

mb

er

of

0s

1s

4s

Genes – Proportional Crossover

9

10

11

12

13

0 200 400 600 800 1000Generation

Nu

mb

er

of

0s

1s

4s

Mutation – Constant Crossover

Probability P of changing a gene to another value: 1 to 0, etc.More genes (including 0s) greater chance of mutations.

Growth – constant crossover

ConclusionsMany ‘neutral’ changes can be explained in terms of resiliency

1.0 two 0.5s (selecting exons)4s four 1s and four 1s one 4sIncreasing 0s (increasing introns)

Operator choice significantly affects these changes

Proportional versus constant crossoverMutations

Per node versus per individual rates are significant.

DiscussionTypes of changes

1st order – affect fitness2nd order – affect expected fitness of offspring (resiliency)3rd order? - affect expected fitness of Nth generation? Affect ability to respond to ‘environmental’ changes?

Any consistent pattern of change has an evolutionary explanation(?)It’s possible to predict some changes by using the idea of resiliency.Do these changes affect search?

Thank You

Questions?

Bibliography“Exons and Code Growth in GP” Genetic Programming 5th European Conference, EuroGP-2002, Springer LNCS2278, 2002 .“Solution Stability in Evolutionary Computation” Proceedings of the 17th International Symposium on Computer and Information Sciences, CRC Press, 2002.“Operator Choice and the Evolution of Robust Solutions” Genetic Programming Theory and Practice, Kluwer, 2003.