Properties of Fitness Functions and Search Landscapes

Abstract

This tutorial is an introduction to the study of properties of fitness functions and search landscapes in the context of predicting the difficulty of search problems for genetic algorithms and, more generally, for stochastic iterative algorithms. Central to this topic is the Walsh transform, which presents a view on the fitness function in terms of the interactions between the variables of this function. The first part of this tutorial introduces the Walsh decomposition of fitness functions, and its relation to epistasis variance. Exchanging the fitness function for the fitness landscape, the second part discusses two important consequences of putting a topology on the search space: the modality and the ruggedness. Methods to estimate properties of landscapes are discussed. The last part moves away from property learning of general fitness functions and landscapes, and instead focuses on properties of classes of fitness functions originating from well-known NP-hard search problems. Important issues here are the factorization of the joint probability distribution of the fitness values and the engineering of interactions to achieve a highly multimodal, symmetric fitness landscape resembling a needle-in-a-haystack problem.