Жыныс клеткаларының араласуы: генетикалық алгоритмдердегі кроссовер операторы

Operator used to vary the programming of chromosomes from one generation to the next

In genetic algorithms and evolutionary computation, crossover, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. Solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions may be mutated before being added to the population. Different algorithms in evolutionary computation may use different data structures to store genetic information, and each genetic representation can be recombined with different crossover operators. Typical data structures that can be recombined with crossover are bit arrays, vectors of real numbers, or trees. The list of operators presented below is by no means complete and serves mainly as an exemplary illustration of this dyadic genetic operator type. More operators and more details can be found in the literature.

Traditional genetic algorithms store genetic information in a chromosome represented by a bit array. Crossover methods for bit arrays are popular and an illustrative example of genetic recombination.

A point on both parents' chromosomes is picked randomly, and designated a 'crossover point'. Bits to the right of that point are swapped between the two parent chromosomes. This results in two offspring, each carrying some genetic information from both parents.

In two point crossover, two crossover points are picked randomly from the parent chromosomes. The bits in between the two points are swapped between the parent organisms. Two point crossover is equivalent to performing two single point crossovers with different crossover points. This strategy can be generalized to k point crossover for any positive integer k, picking k crossover points.

In uniform crossover, typically, each bit is chosen from either parent with equal probability. Other mixing ratios are sometimes used, resulting in offspring which inherit more genetic information from one parent than the other. In a uniform crossover, we don’t divide the chromosome into segments, rather we treat each gene separately. In this, we essentially flip a coin for each chromosome to decide whether or not it will be included in the off spring.

For the crossover operators presented above and for most other crossover operators for bit strings, it holds that they can also be applied accordingly to integer or real valued genomes whose genes each consist of an integer or real valued number. Instead of individual bits, integer or real valued numbers are then simply copied into the child genome. The offspring lie on the remaining corners of the hyperbody spanned by the two parents and , as exemplified in the accompanying image for the three dimensional case.

If the rules of the uniform crossover for bit strings are applied during the generation of the offspring, this is also called discrete recombination.

For combinatorial tasks, permutations are usually used that are specifically designed for genomes that are themselves permutations of a set. The underlying set is usually a subset of or If 1 or n point or uniform crossover for integer genomes is used for such genomes, a child genome may contain some values twice and others may be missing. This can be remedied by genetic repair, e. g. by replacing the redundant genes in positional fidelity for missing ones from the other child genome. In order to avoid the generation of invalid offspring, special crossover operators for permutations have been developed which fulfill the basic requirements of such operators for permutations, namely that all elements of the initial permutation are also present in the new one and only the order is changed. It can be distinguished between combinatorial tasks, where all sequences are admissible, and those where there are constraints in the form of inadmissible partial sequences. A well known representative of the first task type is the traveling salesman problem (TSP), where the goal is to visit a set of cities exactly once on the shortest tour. An example of the constrained task type is the scheduling of multiple workflows. Workflows involve sequence constraints on some of the individual work steps. For example, a thread cannot be cut until the corresponding hole has been drilled in a workpiece. Such problems are also called order based permutations. In the following, two crossover operators are presented as examples, the partially mapped crossover (PMX) motivated by the TSP and the order crossover (OX1) designed for order based permutations. A second offspring can be produced in each case by exchanging the parent chromosomes.

The PMX operator was designed as a recombination operator for TSP like Problems. The explanation of the procedure is illustrated by an example:
Procedure   Example   Example Chromosome     Let be given two permutations of the same set. and Randomly select two crossover points forming a gene segment in   Here from gene position 4 to 6. The selected section is copied to the child chromosome in the same position. The open positions are indicated by question marks. Look for genes that have not been copied in the corresponding segment of starting at the first crossover point. For each gene found (called ), look up in the offspring which element (called ) was copied in its place from Copy to the position held by in if it is not occupied. Otherwise, continue with the next step. Gene is the first uncopied gene in the corresponding segment of : Gene was copied from in its place in     The position of in is the furthest right position and will be placed there in   If the place taken by in is already occupied by an element in the descendant, is put in the place taken by in   The next gene in is and this has already been copied into the child chromosome. Thus, the next gene to be handled is Its position in the offspring would be the position of in However, this place is already occupied by gene So is copied to the position of in   After processing the genes from the selected segment in , the remaining positions in the offspring are filled with the genes from that have not yet been copied, in the order of their appearance. This results in the finished child genome. The genes copied from are and .