Parent Selection Pressure Auto-Tuning for Tournament Selection in Genetic Programming

Selection pressure restrains the selection of individuals from the current population to produce a new population in the next generation. It gives individuals of higher quality a higher probability of being used to create the next generation so that evolutionary algorithms (EAs) can focus on promising regions in the search space. An evolutionary learning process is dynamic and requires different selection pressures at different learning stages in order to speed up convergence or avoid local optima. Therefore, it is desirable for selection mechanisms to be able to automatically tune selection pressure during evolution. Tournament selection is a popular selection method in EAs, especially genetic algorithms and genetic programming (GP). This paper focuses on tournament selection and shows that the standard tournament selection scheme is unaware of the dynamics in the evolutionary process and that the standard tournament selection scheme is unable to tune selection pressure automatically. This paper then presents a novel approach which integrates the knowledge of the fitness rank distribution (FRD) of a population into tournament selection. Through mathematical modeling, simulations, and experimental study in GP, this paper shows that the new approach is effective and using the knowledge of FRD is a promising way to modify the standard tournament selection method for tuning the selection pressure dynamically and automatically along evolution.

[1]  Cláudio F. Lima,et al.  Adaptive Population Sizing Schemes in Genetic Algorithms , 2007, Parameter Setting in Evolutionary Algorithms.

[2]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[3]  Kalyanmoy Deb,et al.  A Comparative Analysis of Selection Schemes Used in Genetic Algorithms , 1990, FOGA.

[4]  Reinhold Huber-Mörk,et al.  Mixed size tournament selection , 2002, Soft Comput..

[5]  Sean Luke,et al.  Fighting Bloat with Nonparametric Parsimony Pressure , 2002, PPSN.

[6]  Kenneth A. De Jong,et al.  Understanding EA Dynamics via Population Fitness Distributions , 2003, GECCO.

[7]  Chang-Yong Lee,et al.  Entropy-Boltzmann selection in the genetic algorithms , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[8]  L. Darrell Whitley,et al.  Unbiased tournament selection , 2005, GECCO '05.

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

[10]  Marcus Hutter,et al.  Equivalence of probabilistic tournament and polynomial ranking selection , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[11]  Lothar Thiele,et al.  A Comparison of Selection Schemes Used in Evolutionary Algorithms , 1996, Evolutionary Computation.

[12]  Mengjie Zhang,et al.  Automatic Selection Pressure Control in Genetic Programming , 2006, Sixth International Conference on Intelligent Systems Design and Applications.

[13]  Mengjie Zhang,et al.  An analysis of constructive crossover and selection pressure in genetic programming , 2007, GECCO '07.

[14]  Steven M. Gustafson An analysis of diversity in genetic programming , 2004 .

[15]  J. Kratica,et al.  Fine Grained Tournament Selection for the Simple Plant Location Problem , 2002 .

[16]  Kenneth DeJong,et al.  Parameter Setting in EAs: a 30 Year Perspective , 2007, Parameter Setting in Evolutionary Algorithms.

[17]  David E. Goldberg,et al.  Genetic Algorithms, Tournament Selection, and the Effects of Noise , 1995, Complex Syst..

[18]  Riccardo Poli,et al.  Backward-chaining genetic programming , 2005, GECCO '05.

[19]  T. Stewart Extrema selection: accelerated evolution on neutral networks , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[20]  Lothar Thiele,et al.  A Mathematical Analysis of Tournament Selection , 1995, ICGA.

[21]  Mark Johnston,et al.  Is the not-sampled issue in tournament selection critical? , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[22]  Georges R. Harik,et al.  Finding Multimodal Solutions Using Restricted Tournament Selection , 1995, ICGA.

[23]  Mengjie Zhang,et al.  Another investigation on tournament selection: modelling and visualisation , 2007, GECCO '07.

[24]  Riccardo Poli,et al.  Elitism reduces bloat in genetic programming , 2008, GECCO '08.

[25]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

[26]  Shu-Yuen Hwang,et al.  A Genetic Algorithm with Disruptive Selection , 1993, ICGA.

[27]  Mark Johnston,et al.  An analysis of multi-sampled issue and no-replacement tournament selection , 2008, GECCO '08.

[28]  K. Matsui New selection method to improve the population diversity in genetic algorithms , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[29]  Leon Poladian,et al.  Excluding the best and worst individuals from parent selection , 2007, 2007 IEEE Congress on Evolutionary Computation.

[30]  Tatsuya Motoki,et al.  Calculating the Expected Loss of Diversity of Selection Schemes , 2002, Evolutionary Computation.

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

[32]  Stephan M. Winkler,et al.  GA-Selection Revisited from an ES-Driven Point of View , 2005, IWINAC.

[33]  Anne Brindle,et al.  Genetic algorithms for function optimization , 1980 .

[34]  J. Hammersley SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[35]  Mengjie Zhang,et al.  Population Clustering in Genetic Programming , 2006, EuroGP.

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

[37]  H. C. Andersen,et al.  Global Selection Methods for Simd Computers , 2007 .

[38]  David E. Goldberg,et al.  Genetic Algorithms, Selection Schemes, and the Varying Effects of Noise , 1996, Evolutionary Computation.

[39]  Yuren Zhou,et al.  Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Prügel-Bennett,et al.  Analysis of genetic algorithms using statistical mechanics. , 1994, Physical review letters.

[41]  D. H. Robinson,et al.  Simulating exponential normalization with weighted k-tournaments , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).