Hyperplane ranking, nonlinearity and the simple genetic algorithm

We examine the role of hyperplane ranking during genetic search by developing a metric for measuring the degree of ranking that exists with respect to static hyperplane averages taken directly from the function, as well as the dynamic ranking of hyperplanes during genetic search. We show that the degree of dynamic ranking induced by a simple genetic algorithm is highly correlated with the degree of static ranking that is inherent in the function, especially during the initial generations of search. The φ 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. Correlations between the φ metric and convergence behavior of a simple genetic algorithm are studied over large sets of functions with varying degrees of nonlinearity.

[1]  L. Darrell Whitley,et al.  A Walsh Analysis of NK-Landscapes , 1997, ICGA.

[2]  John J. Grefenstette,et al.  Deception Considered Harmful , 1992, FOGA.

[3]  David E. Goldberg,et al.  Genetic Algorithms and Walsh Functions: Part II, Deception and Its Analysis , 1989, Complex Syst..

[4]  L. Darrell Whitley,et al.  Predicting Epistasis from Mathematical Models , 1999, Evolutionary Computation.

[5]  Keith E. Mathias,et al.  Hyperplane Ranking in Simple Genetic Algorithms , 1995, ICGA.

[6]  David B. Fogel,et al.  Schema processing under proportional selection in the presence of random effects , 1997, IEEE Trans. Evol. Comput..

[7]  L. Darrell Whitley,et al.  An Executable Model of a Simple Genetic Algorithm , 1992, FOGA.

[8]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[9]  John J. Grefenstette,et al.  How Genetic Algorithms Work: A Critical Look at Implicit Parallelism , 1989, ICGA.

[10]  David E. Goldberg,et al.  Genetic Algorithms and Walsh Functions: Part I, A Gentle Introduction , 1989, Complex Syst..

[11]  L. Darrell Whitley,et al.  Fundamental Principles of Deception in Genetic Search , 1990, FOGA.

[12]  John H. Holland,et al.  Building Blocks, Cohort Genetic Algorithms, and Hyperplane-Defined Functions , 2000, Evolutionary Computation.

[13]  Hillol Kargupta,et al.  Gene Expression and Fast Construction of Distributed Evolutionary Representation , 2001, Evolutionary Computation.

[14]  John J. Grefenstette,et al.  Conditions for Implicit Parallelism , 1990, FOGA.

[15]  A. Wright,et al.  Form Invariance and Implicit Parallelism , 2001, Evolutionary Computation.

[16]  Riccardo Poli,et al.  Exact Schema Theorem and Effective Fitness for GP with One-Point Crossover , 2000, GECCO.

[17]  Colin R. Reeves,et al.  An Experimental Design Perspective on Genetic Algorithms , 1994, FOGA.

[18]  Colin R. Reeves,et al.  Epistasis in Genetic Algorithms: An Experimental Design Perspective , 1995, ICGA.

[19]  Gunar E. Liepins,et al.  Punctuated Equilibria in Genetic Search , 1991, Complex Syst..