Schema (genetic algorithms): Difference between revisions

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In [[mathematics]], in the field of [[genetic algorithm]]s, a '''schema''', '''schemata''' or [[Holland's_schema_theorem|Holland schemata]] is a template that identifies a [[subset]] of strings with similarities at certain string positions. Schemata are a special case of [[cylinder set]]s; and so form a [[topological space]].

== Description ==

For example, consider binary strings of length 6. The schema 1**0*1 describes the set of all strings of length 6 with 1's at positions 1 and 6 and a 0 at position 4. The * is a [[Wildcard character|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]]'' <math> \delta(H) </math> 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.

==See also==

[[Holland's schema theorem]]

==References==