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© C. FERREIRA, 2002 (Terms of Use) ISBN: 9729589054

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

In GEP, individuals are selected according to fitness by roulette-wheel sampling (Goldberg 1989). Each individual receives a slice of the roulette-wheel proportional to its fitness. Then the roulette is spun as many times as there are individuals in the population so that the population size is maintained from generation to generation. This kind of selection, together with the simple elitism presented in section 3.1.2, was used in all the problems of this book. It is true that, with this selection scheme, some of the best individuals are sometimes lost, whereas mediocre ones are passed on to the next generation. But this is not necessarily bad as populations could be pushed into another, very distant fitness optimum. Nonetheless, due to the cloning of the best individual of each generation, the survival and reproduction of the best is guaranteed. In this way, at least the best trait is never lost and a continuous learning is also accomplished.

Other selection schemes can be found in the literature but the most popular – roulette-wheel, deterministic, and tournament selection – will be analyzed in chapter 7 (section 7.7). And we will see that, if elitism is present, no appreciable difference exists between them. All of them are very good if the rest is also good. And the rest is the essence of any evolutionary algorithm. At least for GEP, this essence does not reside in the kind of selection scheme used but in the power of the genetic operators. As we will see in the next section, the genetic operators are the real “eagles” of the fitness landscape.

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