Limits to expression in genetic programming: lattice-aggregate modeling

This paper describes a general theoretical model of size and shape evolution in genetic programming. The proposed model incorporates a mechanism that is analogous to ballistic accretion in physics. The model indicates a four-region partition of GP search space. It further suggests that two of these regions are not searchable by GP.

[1]  Terence Soule,et al.  Code growth in genetic programming , 1996 .

[2]  Riccardo Poli,et al.  The evolution of size and shape , 1999 .

[3]  William B. Langdon,et al.  Size fair and homologous tree genetic programming crossovers , 1999 .

[4]  L. Alonso,et al.  Random Generation of Trees , 1995, Springer US.

[5]  William B. Langdon,et al.  Scaling of Program Fitness Spaces , 1999, Evolutionary Computation.

[6]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[7]  Donald E. Knuth,et al.  The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition , 1997 .

[8]  John R. Koza,et al.  Genetic Programming III: Darwinian Invention & Problem Solving , 1999 .

[9]  P. Senge.  The fifth discipline : the art and practice of the learning organization/ Peter M. Senge , 1991 .

[10]  Jason M. Daida,et al.  What Makes a Problem GP-Hard? Analysis of a Tunably Difficult Problem in Genetic Programming , 1999, Genetic Programming and Evolvable Machines.

[11]  Jason M. Daida,et al.  Analysis of single-node (building) blocks in genetic programming , 1999 .

[12]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  M. D. MacLaren.  The Art of Computer Programming—Volume 1: Fundamental Algorithms (Donald E. Knuth) , 1969 .

[15]  Walter J. Savitch,et al.  Growth Functions of Stochastic Lindenmayer Systems , 1980, Inf. Control..

[16]  L. Sander,et al.  Diffusion-limited aggregation, a kinetic critical phenomenon , 1981 .

[17]  Philippe Flajolet,et al.  The Average Height of Binary Trees and Other Simple Trees , 1982, J. Comput. Syst. Sci..

[18]  William B. Langdon,et al.  Size Fair and Homologous Tree Crossovers for Tree Genetic Programming , 2000, Genetic Programming and Evolvable Machines.

[19]  Jason M. Daida,et al.  What Makes a Problem GP-Hard? , 2003 .

[20]  John R. Koza.  Genetic Programming III - Darwinian Invention and Problem Solving , 1999, Evolutionary Computation.