Editing Gene expression programming (section)

===Reproduction with modification===
The reproduction of programs involves first the selection and then the reproduction of their genomes. Genome modification is not required for reproduction, but without it adaptation and evolution won't take place.

====Replication and selection====
The selection operator selects the programs for the replication operator to copy. Depending on the selection scheme, the number of copies one program originates may vary, with some programs getting copied more than once while others are copied just once or not at all. In addition, selection is usually set up so that the population size remains constant from one generation to another.

The replication of genomes in nature is very complex and it took scientists a long time to discover the [[DNA double helix]] and propose a mechanism for its replication. But the replication of strings is trivial in artificial evolutionary systems, where only an instruction to copy strings is required to pass all the information in the genome from generation to generation.

The replication of the selected programs is a fundamental piece of all artificial evolutionary systems, but for evolution to occur it needs to be implemented not with the usual precision of a copy instruction, but rather with a few errors thrown in. Indeed, genetic diversity is created with [[genetic operator]]s such as [[Mutation (genetic algorithm)|mutation]], [[Crossover (genetic algorithm)|recombination]], [[Transposition (genetics)|transposition]], inversion, and many others.

====Mutation====
In gene expression programming mutation is the most important genetic operator.<ref>{{cite web|last=Ferreira|first=C.|year=2002|title=Mutation, Transposition, and Recombination: An Analysis of the Evolutionary Dynamics|url= http://www.gene-expression-programming.com/webpapers/ferreira-fea02.pdf|publisher=  In H. J. Caulfield, S.-H. Chen, H.-D. Cheng, R. Duro, V. Honavar, E. E. Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang, Y. Yang, eds., Proceedings of the 6th Joint Conference on Information Sciences, 4th International Workshop on Frontiers in Evolutionary Algorithms, pages 614–617, Research Triangle Park, North Carolina, USA}}</ref> It changes genomes by changing an element by another. The accumulation of many small changes over time can create great diversity.

In gene expression programming mutation is totally unconstrained, which means that in each gene domain any domain symbol can be replaced by another. For example, in the heads of genes any function can be replaced by a terminal or another function, regardless of the number of arguments in this new function; and a terminal can be replaced by a function or another terminal.

====Recombination====
[[Crossover (genetic algorithm)|Recombination]] usually involves two parent chromosomes to create two new chromosomes by combining different parts from the parent chromosomes. And as long as the parent chromosomes are aligned and the exchanged fragments are homologous (that is, occupy the same position in the chromosome), the new chromosomes created by recombination will always encode syntactically correct programs.

Different kinds of crossover are easily implemented either by changing the number of parents involved (there's no reason for choosing only two); the number of split points; or the way one chooses to exchange the fragments, for example, either randomly or in some orderly fashion. For example, gene recombination, which is a special case of recombination, can be done by exchanging homologous genes (genes that occupy the same position in the chromosome) or by exchanging genes chosen at random from any position in the chromosome.

====Transposition====
[[Transposition (genetics)|Transposition]] involves the introduction of an insertion sequence somewhere in a chromosome. In gene expression programming insertion sequences might appear anywhere in the chromosome, but they are only inserted in the heads of genes. This method guarantees that even insertion sequences from the tails result in error-free programs.

For transposition to work properly, it must preserve chromosome length and gene structure. So, in gene expression programming transposition can be implemented using two different methods: the first creates a shift at the insertion site, followed by a deletion at the end of the head; the second overwrites the local sequence at the target site and therefore is easier to implement. Both methods can be implemented to operate between chromosomes or within a chromosome or even within a single gene.

====Inversion====
Inversion is an interesting operator, especially powerful for [[combinatorial optimization]].<ref>{{cite web|last=Ferreira|first=C.|year=2002|title=Combinatorial Optimization by Gene Expression Programming: Inversion Revisited|url= http://www.gene-expression-programming.com/webpapers/Ferreira-ASAI02.pdf|publisher= In J. M. Santos and A. Zapico, eds., Proceedings of the Argentine Symposium on Artificial Intelligence, pages 160–174, Santa Fe, Argentina}}</ref> It consists of inverting a small sequence within a chromosome.

In gene expression programming it can be easily implemented in all gene domains and, in all cases, the offspring produced is always syntactically correct. For any gene domain, a sequence (ranging from at least two elements to as big as the domain itself) is chosen at random within that domain and then inverted.

====Other genetic operators====
Several other genetic operators exist and in gene expression programming, with its different genes and gene domains, the possibilities are endless. For example, genetic operators such as one-point recombination, two-point recombination, gene recombination, uniform recombination, gene transposition, root transposition, domain-specific mutation, domain-specific inversion, domain-specific transposition, and so on, are easily implemented and widely used.