In genetic algorithms and

evolutionary computation In computer science, evolutionary computation is a family of algorithms for global optimization inspired by biological evolution, and the subfield of artificial intelligence and soft computing studying these algorithms. In technical terms, th ...

, crossover, also called recombination, is a genetic operator used to combine the

genetic information A nucleic acid sequence is a succession of bases signified by a series of a set of five different letters that indicate the order of nucleotides forming alleles within a DNA (using GACT) or RNA (GACU) molecule. By convention, sequences are u ...

of two parents to generate new offspring. It is one way to

stochastically Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...

generate new

solutions Solution may refer to: * Solution (chemistry), a mixture where one substance is dissolved in another * Solution (equation), in mathematics ** Numerical solution, in numerical analysis, approximate solutions within specified error bounds * Soluti ...

from an existing population, and is analogous to the

crossover Crossover may refer to: Entertainment Albums and songs * ''Cross Over'' (Dan Peek album) * ''Crossover'' (Dirty Rotten Imbeciles album), 1987 * ''Crossover'' (Intrigue album) * ''Crossover'' (Hitomi Shimatani album) * ''Crossover'' (Yoshino ...

that happens during

sexual reproduction Sexual reproduction is a type of reproduction that involves a complex life cycle in which a gamete ( haploid reproductive cells, such as a sperm or egg cell) with a single set of chromosomes combines with another gamete to produce a zygote th ...

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...

. Solutions can also be generated by

cloning Cloning is the process of producing individual organisms with identical or virtually identical DNA, either by natural or artificial means. In nature, some organisms produce clones through asexual reproduction. In the field of biotechnology, c ...

an existing solution, which is analogous to

asexual reproduction Asexual reproduction is a type of reproduction that does not involve the fusion of gametes or change in the number of chromosomes. The offspring that arise by asexual reproduction from either unicellular or multicellular organisms inherit the ...

. Newly generated solutions are typically 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 In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, ...

that can be recombined with crossover are bit arrays, vectors of real numbers, or

trees In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are u ...

Examples

Traditional genetic algorithms store genetic information in a

chromosome A chromosome is a long DNA molecule with part or all of the genetic material of an organism. In most chromosomes the very long thin DNA fibers are coated with packaging proteins; in eukaryotic cells the most important of these proteins ar ...

represented by a bit array. Crossover methods for bit arrays are popular and an illustrative example of

genetic recombination Genetic recombination (also known as genetic reshuffling) is the exchange of genetic material between different organisms which leads to production of offspring with combinations of traits that differ from those found in either parent. In eukaryo ...

One-point crossover

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.

Two-point and k-point crossover

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.

Uniform crossover

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’ll be included in the off-spring. We can also bias the coin to one parent, to have more genetic material in the child from that parent.

Crossover for ordered lists

In some genetic algorithms, not all possible chromosomes represent valid solutions. In some cases, it is possible to use specialized crossover and mutation operators that are designed to avoid violating the constraints of the problem. For example, a genetic algorithm solving the travelling salesman problem may use an ordered list of cities to represent a solution path. Such a chromosome only represents a valid solution if the list contains all the cities that the salesman must visit. Using the above crossovers will often result in chromosomes that violate that constraint. Genetic algorithms optimizing the ordering of a given list thus require different crossover operators that will avoid generating invalid solutions. Many such crossovers have been published: # partially mapped crossover (PMX) # cycle crossover (CX) # order crossover operator (OX1) # order-based crossover operator (OX2) # position-based crossover operator (POS) # voting recombination crossover operator (VR) # alternating-position crossover operator (AP) # sequential constructive crossover operator (SCX) # simulated binary crossover operator (SBX) Other possible methods include the

edge recombination operator The edge recombination operator (ERO) is an operator that creates a path that is similar to a set of existing paths (parents) by looking at the edges rather than the vertices. The main application of this is for crossover in genetic algorithms wh ...

. Alternatively, to overcome the mentioned issue, double chromosomes can be used.

References

* John Holland, ''Adaptation in Natural and Artificial Systems'',

University of Michigan Press The University of Michigan Press is part of Michigan Publishing at the University of Michigan Library. It publishes 170 new titles each year in the humanities and social sciences. Titles from the press have earned numerous awards, including ...

, Ann Arbor, Michigan. 1975. . * Larry J. Eshelman, ''The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination'', in Gregory J. E. Rawlins editor, Proceedings of the First Workshop on Foundations of Genetic Algorithms. pages 265-283. Morgan Kaufmann, 1991. . * Tomasz D. Gwiazda, ''Genetic Algorithms Reference Vol.1 Crossover for single-objective numerical optimization problems'', Tomasz Gwiazda, Lomianki, 2006. .

External links

Newsgroup: comp.ai.genetic FAQ
- see section on crossover (also known as recombination). {{DEFAULTSORT:Crossover (Genetic Algorithm) Genetic algorithms