Epistasis as a Basic Concept in Formal Landscape Analysis

In this note we measure the interdependency of bits in the encoding of a fitness function using two different invariants. The first invariant, normalized epistasis, features a strong correlation with GA-hardness, as we illustrate here with generalized Royal Road functions. The second one, bit decidability, imitates epistasis, but has the avantage of being less difficult to calculate and approximate. Although it seems less powerful than epistasis, it is equally able to rank fitness functions according to their GA-hardness. We prove that the function class E3, which is similar to the class of NK( ; 2) landscapes, is NPequivalent. This class is based on a generalization of the concept of epistasis, and, because of the latter theorem, its structure is believed to be important in landscape analysis.