Investigating the role of diploidy in simulated populations of evolving individuals

In most work applying genetic algorithms to populations of neural networks there is no real distinction between genotype and phenotype. In nature both the information contained in the genotype and the mapping of the genetic information into the phenotype are usually much more complex. The genotypes of many organisms exhibit diploidy, i.e., they include two copies of each gene: if the two copies are not identical in their sequences and therefore have a functional difference in their products (usually proteins), the expressed phenotypic feature is termed the dominant one, the other one recessive (not expressed). In this paper we review the literature on the use of diploidy and dominance operators in genetic algorithms; we present the new results we obtained with our own simulations in changing environments; finally, we discuss some results of our simulations that parallel biological findings. 1 Genotypes for neural networks Genetic algorithms are computational models of evolution that may be applied to populations of neural networks to study the evolution of organisms whose behavior is controlled by a neural network. Imagine a population of such organisms living in an environment and reproducing as a function of some performance criterion. The initial population of neural networks is randomly generated. Hence, each individual organism will be assigned a neural network that is different from the neural network of other individuals and, as a consequence, will tend to behave differently from any other individual. The individuals that behave more efficiently according to the performance criterion will reproduce while less fit individuals are more likely to die without leaving offspring. Reproduction consists in generating one or more copies of the reproducing individual's neural network (we are assuming non-sexual reproduction) with the addition of some random changes to some of the network's traits (genetic mutations). Hence, an offspring's behavior will tend to be similar but not identical to its parent's behavior. Genetic mutations will result in most cases in offspring that perform less well than their parents but in some rare cases an offspring will outperform its parent. It is these luckier individuals that will tend to reproduce rather than their less lucky siblings. Selective reproduction and the constant addition of variability to the "genetic pool" will cause an increase in the population's level of performance across a certain number of generations. In most work applying genetic algorithms to populations of neural networks there is no real distinction between genotype and phenotype. The inherited genetic information maps one to one into the phenotypic neural network. For example, in populations with fixed network architecture the genetically inherited trait tends to be the matrix of connection weights. The inherited genotype directly encodes the matrix of weights and the genetic mutations directly change the value of some of the weights. Therefore, the genotype and the phenotype are virtually identical. In nature both the information contained in the genotype and the mapping of the genetic information into the phenotype are usually much more complex. The mapping from genetic to phenotypical traits is not one to one, but one single genetic trait can enter into the determination of many different phenotypical traits