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.

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 positions 1 and 6 and a 0 at position 4. 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 $H$.

Disruption

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

See also

• Holland's schema theorem
• Propagation of schema