Linear selection

In most forms of selection, when multiple individuals are needed for an operation, these are drawn independently from the population. So, for example, in the case of crossover, the probability of a particular pair of parents being selected is given by the product of the selection probabilities of each parent. In this paper we investigate a form of selection where pairs of parents are not selected independently. We show that a particular form of dependent selection, linear selection, leads a genetic algorithm with homologous crossover to become very similar to a genetic algorithm with standard (independent) selection and headless chicken crossover, i.e., it turns crossover into a type of mutation. In the paper we analyse this form of selection theoretically, and we compare it to ordinary selection with crossover and headless chicken crossover in real runs.

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

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

[3]  Michael D. Vose,et al.  The simple genetic algorithm - foundations and theory , 1999, Complex adaptive systems.

[4]  Terry Jones,et al.  Crossover, Macromutationand, and Population-Based Search , 1995, ICGA.

[5]  R. Poli,et al.  Exact GP schema theory for headless chicken crossover and subtree mutation , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[6]  Riccardo Poli,et al.  Tournament Selection, Iterated Coupon-Collection Problem, and Backward-Chaining Evolutionary Algorithms , 2005, FOGA.

[7]  D. Goldberg,et al.  Modeling tournament selection with replacement using apparent added noise , 2001 .

[8]  ThieleLothar,et al.  A comparison of selection schemes used in evolutionary algorithms , 1996 .

[9]  Colin R. Reeves,et al.  Genetic Algorithms—Principles and Perspectives , 2002, Operations Research/Computer Science Interfaces Series.

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

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

[12]  Alden H. Wright,et al.  Emergent Behaviour, Population-based Search and Low-pass Filtering , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[13]  Riccardo Poli,et al.  Backward-chaining evolutionary algorithms , 2006, Artif. Intell..

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

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