Genetic Programming, Probabilistic Incremental Program Evolution, and Scalability

This paper discusses scalability of standard genetic programming (GP) and the probabilistic incremental program evolution (PIPE). To investigate the need for both effective mixing and linkage learning, two test problems are considered: ORDER problem, which is rather easy for any recombination-based GP, and TRAP or the deceptive trap problem, which requires the algorithm to learn interactions among subsets of terminals. The scalability results show that both GP and PIPE scale up polynomially with problem size on the simple ORDER problem, but they both scale up exponentially on the deceptive problem. This indicates that while standard recombination is sufficient when no interactions need to be considered, for some problems linkage learning is necessary. These results are in agreement with the lessons learned in the domain of binary-string genetic algorithms (GAs). Furthermore, the paper investigates the effects of introducing unnecessary and irrelevant primitives on the performance of GP and PIPE.

[1]  David E. Goldberg,et al.  Scalability of the Bayesian optimization algorithm , 2002, Int. J. Approx. Reason..

[2]  D. Goldberg,et al.  Probabilistic Model Building and Competent Genetic Programming , 2003 .

[3]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[4]  Peter A. N. Bosman,et al.  Learning Probabilistic Tree Grammars for Genetic Programming , 2004, PPSN.

[5]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

[6]  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.

[7]  David E. Goldberg Design of Competent Genetic Algorithms , 2002 .

[8]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[9]  Rafal Salustowicz,et al.  Probabilistic Incremental Program Evolution , 1997, Evolutionary Computation.

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

[11]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[12]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[13]  Kalyanmoy Deb,et al.  Analyzing Deception in Trap Functions , 1992, FOGA.

[14]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.