What Makes a Problem GP-Hard? Validating a Hypothesis of Structural Causes

This paper provides an empirical test of a hypothesis, which describes the effects of structural mechanisms in genetic programming. In doing so, the paper offers a test problem anticipated by this hypothesis. The problem is tunably difficult, but has this property because tuning is accomplished through changes in structure. Content is not involved in tuning. The results support a prediction of the hypothesis - that GP search space is significantly constrained as an outcome of structural mechanisms.

[1]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[2]  Walter Alden Tackett,et al.  Recombination, selection, and the genetic construction of computer programs , 1994 .

[3]  L. Altenberg EMERGENT PHENOMENA IN GENETIC PROGRAMMING , 1994 .

[4]  J. K. Kinnear,et al.  Advances in Genetic Programming , 1994 .

[5]  T. Soule,et al.  Using genetic programming to approximate maximum clique , 1996 .

[6]  Peter J. Angeline,et al.  The Royal Tree Problem, a Benchmark for Single and Multiple Population Genetic Programming , 1996 .

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

[8]  T. Soule,et al.  Code Size and Depth Flows in Genetic Programming , 1997 .

[9]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[10]  Terence Soule,et al.  Removal bias: a new cause of code growth in tree based evolutionary programming , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[11]  D. Goldberg How Fitness Structure Affects Subsolution Acquisition in Genetic Programming , 1998 .

[12]  David E. Goldberg,et al.  Where Does the Good Stuff Go, and Why? How Contextual Semantics Influences Program Structure in Simple Genetic Programming , 1998, EuroGP.

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

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

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

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

[17]  Rachel Harrison,et al.  Characterizing a Tunably Difficult Problem in Genetic Programming , 2000, GECCO.

[18]  Jason M. Daida,et al.  Limits to expression in genetic programming: lattice-aggregate modeling , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[19]  William B. Langdon,et al.  Combining Decision Trees and Neural Networks for Drug Discovery , 2002, EuroGP.

[20]  Riccardo Poli,et al.  Foundations of Genetic Programming , 1999, Springer Berlin Heidelberg.

[21]  Jason M. Daida,et al.  Identifying Structural Mechanisms in Standard Genetic Programming , 2003, GECCO.

[22]  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.

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