Kauffman's NK model defines a combinatorial phase space, consisting of every string (chosen from a given alphabet) of length .
For each string in this search space, a scalar value (called the fitness) is defined.
If a distance metric is defined between strings, the resulting structure is a landscape.

Fitness values are defined according to the specific incarnation of the model, but the key feature of the NK model is that the fitness of a given string  is the sum of contributions from each locus  in the string:
and the contribution from each locus in general depends on the value of  other loci:
where  are the other loci upon which the fitness of  depends.

Hence, the fitness function  is a mapping between strings of length K + 1 and scalars, which Weinberger's later work calls "fitness contributions".
Such fitness contributions are often chosen randomly from some specified probability distribution.

In 1991, Weinberger published a detailed analysis of the case in which  and the fitness contributions are chosen randomly.
His analytical estimate of the number of local optima was later shown to be flawed.
However, numerical experiments included in Weinberger's analysis support his analytical result that the expected fitness of a string is normally distributed with a mean of approximately

and a variance of approximately
.
Kauffman's NK model defines a combinatorial phase space, consisting of every string (chosen from a given alphabet) of length . For each string in this search space, a scalar value (called the fitness) is defined. If a distance metric is defined between strings, the resulting structure is a landscape.
Fitness values are defined according to the specific incarnation of the model, but the key feature of the NK model is that the fitness of a given string  is the sum of contributions from each locus  in the string:
and the contribution from each locus in general depends on the value of  other loci:
where  are the other loci upon which the fitness of  depends.
Hence, the fitness function  is a mapping between strings of length K + 1 and scalars, which Weinberger's later work calls "fitness contributions". Such fitness contributions are often chosen randomly from some specified probability distribution.
In 1991, Weinberger published a detailed analysis of the case in which  and the fitness contributions are chosen randomly. His analytical estimate of the number of local optima was later shown to be flawed. However, numerical experiments included in Weinberger's analysis support his analytical result that the expected fitness of a string is normally distributed with a mean of approximately

and a variance of approximately
.
Stuart Kauffman