## Dynamic Royal Road Function

Used in: [FMRR08][PCR08][YWW+08][YT08]

Royal road functions (Mitchell, Forrest, and Holland, 1992) constitute a class of fitness landscapes. A royal road function is defined in terms of various landscape features; for this purpose, a schema tree is typically used, where a block size and a block length must be defined. The difficulty of these functions rely on the formation of plateaus in the fitness landscape.

The fitness of a binary string **x** is defined as:

ƒ(*x*) = ∑_{s ∈ S} c_{s}σ_{s}(*x*)

where **c _{s}** is the value assigned to schema

**s**and

**σ**is 1 if

_{s}(x)**x**is an instance of schema

**s**, 0 otherwise.

The dynamic problem can be defined as a generalization of the static one, where the schemas change over time.

ƒ(*x*, *t*) = ∑_{s ∈ S} c_{s}σ_{s}(*x*, *t*)

The severity can be controlled with the degree of changed bits in each schema.