Nonlinearity, Walsh Coefficients, Hyperplane Ranking
and the Simple Genetic Algorithm
R. B. Heckendorn
D. Whitley
S. Rana
Department of Computer Science
Colorado State University
Fort Collins, Colorado 80523 USA
{heckendo,whitley,rana}@cs.colostate.edu
ABSTRACT
Several metrics are used in empirical studies to explore the mechanisms
of convergence of genetic algorithms. The 0 metric is designed to
measure the consistency of an arbitrary ranking of hyperplanes in a
partition with respect to a target string. Walsh coefficients can be
calculated for small functions in order to characterize sources of linear
and nonlinear interactions. A simple deception measure is also developed
to look closely at the effects of increasing nonlinearity of functions.
Correlations between the 0 metric and deception measure are discussed
and relationships between 0 and convergence behavior of a simple genetic
algorithm are studied over large sets of functions with varying degrees of
nonlinearity.