Effects of phenotypic redundancy in structure optimization

Concepts from graph theory and molecular evolution are proposed for analyzing the redundancy in the genotype-phenotype mapping in structure optimization stemming from graph isomorphism. Evolutionary topology optimization of neural networks serves as an example. By means of analytical and random-walk methods, it is shown that rare and frequent structures influence the search process: operators that are unbiased in genotype space may have a remarkable bias in phenotype space. In particular, if the desired structures are rare, the probability that an evolutionary algorithm evolves them may decrease. This is verified experimentally by comparing evolutionary structure optimization algorithms with and without search operators that take the redundancy of phenotypes into account. Further, it is shown how different encodings and restrictions on the search space lead to qualitatively different distributions of rare and frequent structures