Pruefer Numbers and Genetic Algorithms: A Lesson on How the Low Locality of an Encoding Can Harm the Performance of GAs

When handling tree networks, researchers have sometimes tried using the Pruefer number representation for encoding networks, however GAs often degraded when used on this encoding. This paper investigates the locality of the Pruefer number and its affect on the performance of a Genetic Algorithm (GA). The locality describes how the neighborhood of the genotype is preserved when constructing the phenotype (the tree) from the genotype (the Pruefer number). It is shown that the locality of the Pruefer number is highly irregular on the entire solution space, and that the performance of a GA depends on the structure of the optimal solution. A GA is able to perform well only for networks that have a high locality (stars). For all other types of networks (lists, trees) the locality is low and a GA fails to find the best list or tree. Using a GA with the Pruefer number encoding can be useful, when the best solution tends to be a star. The locality of an encoding could have a strong influence on the performance of a GA. When choosing encodings for optimization problems, researchers should be aware of this and be careful with low locality encodings. If the locality of the encoding is low, a failure of the GA is often unavoidable.