Генетикалық алгоритмдерде мутация операторының қолданылуы

Genetic operation used to add population diversity
Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of a genetic or, more generally, an evolutionary algorithm (EA). It is analogous to biological mutation. The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating point encodings or representations for combinatorial problems. The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping convergence to the global optimum. This reasoning also leads most EAs to avoid only taking the fittest of the population in generating the next generation, but rather selecting a random (or semi random) set with a weighting toward those that are fitter. The following requirements apply to all mutation operators used in an EA:
every point in the search space must be reachable by one or more mutations. there must be no preference for parts or directions in the search space (no drift). small mutations should be more probable than large ones. For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scramble, Insertion, Inversion, Swap, and so on. An overview and more operators than those presented below can be found in the introductory book by Eiben and Smith or in.

A real number can be mutated using normal distribution by adding the generated random value to the old value of the gene, resulting in the mutated value :In the case of genes with a restricted range of values, it is a good idea to choose the step size of the mutation so that it reasonably fits the range of the gene to be changed, e. g.:The step size can also be adjusted to the smaller permissible change range depending on the current value. In any case, however, it is likely that the new value of the gene will be outside the permissible range of values. Such a case must be considered a lethal mutation, since the obvious repair by using the respective violated limit as the new value of the gene would lead to a drift. This is because the limit value would then be selected with the entire probability of the values beyond the limit of the value range. The evolution strategy works with real numbers and mutation based on normal distribution. The step sizes are part of the chromosome and are subject to evolution together with the actual decision variables.

Mutations of permutations are specially designed for genomes that are themselves permutations of a set. These are often used to solve combinatorial tasks. In the two mutations presented, parts of the genome are rotated or inverted.

The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order. This can be remedied by the following modifications. The end index of the partial lists is determined as the distance to the start index :

where is determined randomly according to one of the two procedures for the mutation of real numbers from the interval and rounded. For the rotation, is determined similarly to the distance , but the value is forbidden. For the inversion, note that must hold, so for the value must be excluded.