The Breeder Genetic Algorithm-a provable optimal search algorithm and its application

Evolution of natural organisms is based on three major components-reproduction, variation and selection. Some reproductions of natural organisms occur with ´failures´ called mutations. A more systematic variation of the genetic material happens in sexual reproduction. Each parent contributes half of its genetic material to the offspring. This method of variation is called recombination. The offspring will be identical to the parents if the parents are genetically equal. Variation is necessary to allow selection to work. Selection in nature is very difficult to define precisely. The term was introduced by Darwin (1859) very informally. ´The preservation of favourable variations and the rejection of injurious variations, I call Natural Selection´. But how can an observer predict which are the favorable variations? The favorable variations are the variations which are preserved! The variations can only be judged after they have competed in the ´struggle for life´. Natural selection is no independent force of nature, it is the result of the competition of natural organisms for resources. In contrast, in the science of breeding the above problem does not exist. The selection is done by human breeders. Their strategies are based on the assumption that mating two individuals with high fitness more likely produces an offspring of high fitness than two randomly mating individuals. The Breeder Genetic Algorithm (BGA) introduced by the author previously (1993) is based on the science of breeding. The science is part of applied statistics. A major component is the parent-offspring correlation and the heritability coefficient.