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.

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 ${\displaystyle \delta (H)}$ 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.

The length of a schema ${\displaystyle H}$, called ${\displaystyle N(H)}$, is defined as the total number of nodes in the schema. ${\displaystyle N(H)}$ is also equal to the number of nodes in the programs matching ${\displaystyle H}$.

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