Tree network design with genetic algorithms an investigation in the locality of the pruefernumber en

When handling tree networks, a number of researchers have tried using the pruefernumber representation for encoding the network, but GAs often degraded or broke down when used on this encoding. This paper investigates the locality of the pruefernumber, which can be described as the relatedness of the phenotype (the tree) and the genotype (the pruefernumber) of trees. It is shown that the locality is highly irregular on the entire solution space. We demonstrate that for star and list networks small changes of the pruefernumber lead to small changes in the tree, whereas for all other networks the locality of the pruefernumber is low. Even worse, all areas of high locality are separated from each other by large areas of low locality. Using a GA with the pruefernumber can be useful when the good solutions tend to be a “star” or a “list”. As soon as the GA should find good solutions, which are more general trees, a degradation or even complete failure of the GA is inescapable.