What is Neutral? Neutral Changes and Resiliency Terence Soule Department of Computer Science University of Idaho

The experiments Gene/exon selection Introns and exon selection Effects of operators

Experiment 1 Tree based, generational GP Functions {+} Terminals/Genes {0.5, 1.0} Fitness: difference from 10 Both terminals are exons. Is one selected?

Gene/Exon Choice

Average Fitness 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 2 Tree based, generational GP Functions {+} Terminals/Genes {0, 1, 4} Fitness: difference from 40 Now there are two exons and an intron. What is selected?

Number of Genes Number of Generation 0s 1s 4s

Resiliency Fitness Change Crossover Mutation

Ratio of 1s to 4s

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

Experiment 3 Variable length, linear encoding, generational Genes {0, 1, 4} Sample individual: Fitness: 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 time 4 25% of the time % of the time …

Genes – Constant Crossover

Genes – Proportional Crossover

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

Conclusions Many ‘neutral’ changes can be explained in terms of resiliency 1.0  two 0.5s (selecting exons) 4s  four 1s and four 1s  one 4s Increasing 0s (increasing introns) Operator choice significantly affects these changes Proportional versus constant crossover Mutations Per node versus per individual rates are significant.

Discussion Types of changes 1 st order – affect fitness 2 nd order – affect expected fitness of offspring (resiliency) 3 rd 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 5 th European Conference, EuroGP-2002, Springer LNCS2278, “Solution Stability in Evolutionary Computation” Proceedings of the 17 th International Symposium on Computer and Information Sciences, CRC Press, “Operator Choice and the Evolution of Robust Solutions” Genetic Programming Theory and Practice, Kluwer, 2003.