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In the context of evolutionary computation, in particular genetic algorithms, there are two stochastic operations "mutation" and "crossover". What are the differences between them?

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Mutation is an operation which is applied to a single individual in the population. It can e.g. introduce some noise in the chromosome. For example, if the chromosomes are binary, a mutation may simply be the flip of a (random) bit (gene).

Crossover is an operation which takes as input two individuals (often called the "parents") and somehow combines their chromosomes, so as to produce usually two other chromosomes (the "children"), which inherit, in a certain way, the genes of both parents.

If you're looking for a more serious comparison of both operators, have a look at the paper "Crossover versus Mutation: A Comparative Analysis of the Evolutionary Strategy of Genetic Algorithms Applied to Combinatorial Optimization Problems" by E. Osaba, R. Carballedo, F. Diaz, E. Onieva, I. de la Iglesia, and A. Perallos.

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  • $\begingroup$ Crossover usually has a stricter definition than "somehow combines their chromosomes", which might be worth mentioning as it behaves a lot like its biological inspiration. $\endgroup$ – Neil Slater Nov 20 '18 at 16:00
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    $\begingroup$ I don't know that I would agree to that limitation. Early crossover operators certainly aimed at biological inspiration, but I don't think that's a common aspect of a useful definition today. Look at something like Cycle Crossover (CX) for permutation encodings. This isn't really attempting to mimic any strict interpretation of biological crossover. They're just trying to combine information from two parents in a way that effectively generates offspring. That seems to me to be the more modern way of thinking -- operators should be useful; not necessarily biologically motivated. $\endgroup$ – deong Nov 20 '18 at 17:13
  • $\begingroup$ @s-mcgrew suggests the term "recombination operator" in their answer below. $\endgroup$ – Joachim Wagner Oct 11 at 8:20
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Evolutionary algorithms use it in a very similar way as the two terms are used in biology:

In biology, a mutation is the permanent alteration of the nucleotide sequence of the genome of an organism, virus, or extrachromosomal DNA or other genetic elements.

Source: Wikipedia

Chromosomal crossover [...] is the exchange of genetic material [...] that results in recombinant chromosomes during sexual reproduction.

Source: Wikipedia

Hence the main difference is that mutations happen within one individual while crossover is between two individuals.

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    $\begingroup$ Although we use biological definition with the same meaning, I think the OP has made it clear The OP wants it in context of Evolutionary Comp., so your answer is more suitable as a comment. $\endgroup$ – DuttaA Nov 21 '18 at 6:09
  • $\begingroup$ As a comment it would be hard to get a good, readable formatting. $\endgroup$ – Martin Thoma Nov 21 '18 at 6:13
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Mutation is secondary operator (10%) while Crossover is Primary (90%) which creates offspring while mutation can only shuffle information within the Choromsome

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I like to use the term, "recombination operator" rather than "crossover operator", because the latter term suggests a specific type of operation: constructing an offspring by switching corresponding chromosome segments between two parents. "Recombination" (to me) suggests any operation that forms an offspring from the genetic information of two parents. "Crossover" in that sense doesn't work when the individuals are, for example, permutations; but many "recombination operators" that do work are still possible, which preserve non-conflicting portions of two parent permutations.

In GA, mutation can be thought of as a relatively small random change that occurs within an individual. Mutation usually is a change of the value of one gene without making use of gene values in any other individuals, but can also be a random rearrangement of elements in a permutation, or a random change in the values of several genes. Sometimes the term is applied to a "hill climbing" procedure in which several mutations are applied to an individual and their effect on fitness is tested; then the one that produces the most fitness improvement is retained.

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