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What is Neutral?Neutral Changes and
Resiliency
Terence SouleDepartment of Computer Science
University of Idaho
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
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?
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
Mutation – Constant Crossover
Probability P of changing a gene to another value: 1 to 0, etc.More genes (including 0s) greater chance of mutations.
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?
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.