The Influence Of Binary Representations Of Integers On The Performance Of Selectorecombinative Genetic Algorithms

When using representations for genetic algorithms (GAs) every optimization problem can be separated into a genotype-phenotype and a phenotype-fitness mapping. The genotypephenotype mapping is the used representation and the phenotype-fitness mapping is the problem that should be solved. This paper investigates how the use of different binary representations of integers influences the performance of selectorecombinative GAs using only crossover and no mutation. It is shown that the used representation strongly influences the performance of GAs. The binary and gray encoding are two different, well known possibilities to assign bitstring genotypes to integer phenotypes. Focusing our investigation on these two encodings reveals that for the easy integer one-max problem selectorecombinative GAs perform better using binary encoding than using gray encoding. This is surprising as binary encoding is affected with problems due to the Hamming cliff and because there is evidence that shows the superiority of gray encoding. However, the performance of selectorecombinative GAs is determined by the structure of the building blocks (BBs) and not by the structure of the search space. Therefore, the performance difference between the encodings can be explained by analyzing the fitness of the resulting schemata. It reveals for the easy integer one-max problem that binary encoding results in BBs of lower order than gray encoding. Therefore, the integer one-max problem is more difficult and the performance of selectorecombinative GAs is lower when using gray encoding.