Schema (genetic algorithms)

A schema is a template in computer science used in the field of genetic algorithms that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets; and so form a topological space.^[1]

Description

For example, consider binary strings of length 6. The schema 1**0*1 describes the set of all words of length 6 with 1's at the first and sixth positions and a 0 at the fourth position. The * is a wildcard symbol, which means that positions 2, 3 and 5 can have a value of either 1 or 0. The order of a schema is defined as the number of fixed positions in the template, while the defining length $\delta (H)$ is the distance between the first and last specific positions. The order of 1**0*1 is 3 and its defining length is 5. The fitness of a schema is the average fitness of all strings matching the schema. The fitness of a string is a measure of the value of the encoded problem solution, as computed by a problem-specific evaluation function.

Length

The length of a schema $H$ , called $N(H)$ , is defined as the total number of nodes in the schema. $N(H)$ is also equal to the number of nodes in the programs matching $H$ .^[2]

Disruption

If the child of an individual that matches schema H does not itself match H, the schema is said to have been disrupted.^[2]

Propagation of schema

In evolutionary computing such as genetic algorithms and genetic programming, propagation refers to the inheritance of characteristics of one generation by the next. For example, a schema is propagated if individuals in the current generation match it and so do those in the next generation. Those in the next generation may be (but don't have to be) children of parents who matched it.

The Schematic Completion

In <ref name = "Fletcher"> Jack Flethcher (2017). "A natural approach to studying schema processing" (PDF). arXiv preprint arXiv:1705.04536. {{cite journal}}: Unknown parameter |month= ignored (help) schema are study using Order Theory and Lattice Theory

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References

^ Holland, John Henry (1992). Adaptation in Natural and Artificial Systems (reprint ed.). The MIT Press. ISBN 9780472084609. Retrieved 22 April 2014. {{cite book}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
^ ^a ^b "Foundations of Genetic Programming". UCL UK. Retrieved 13 July 2010.

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[Holland1-1] Holland, John Henry (1992). Adaptation in Natural and Artificial Systems (reprint ed.). The MIT Press. ISBN 9780472084609. Retrieved 22 April 2014. {{cite book}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)

[UCL1-2] "Foundations of Genetic Programming". UCL UK. Retrieved 13 July 2010.

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