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

Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence

Adaptation and evolution
Much of the diversity we see in the living world, results from the accumulation of mutations (in the broad sense) in proteins. If we take any protein, for instance, hemoglobin, and analyze its sequence among the individuals of one population, we will see that there are numerous protein variants, differing in one or several amino acids. Most of these variants work with equal efficiency, but some of them may exhibit slight differences in function. In certain environments some of these variants are better adapted than others and may confer some advantage to the individuals expressing them. If we continue this investigation further and analyze the hemoglobin molecules from different species, we will see that there are, in this case, considerable differences between their hemoglobins. Although these different hemoglobins play exactly the same function, they seem wonderfully adapted to the natural environment of the particular species. Indeed, the modifications that occur at the molecular level in proteins enable populations of organisms to develop new abilities, adapt to new environments, and ultimately become new species.

For populations to adapt in the long run, the individual organisms must be selected to reproduce. In terms of evolution, the survival of a particular organism is only important if this organism leaves progeny. It is the individual’s progeny that might exhibit new traits and thus be better adapted to the natural environment. And the better adapted an organism becomes, the higher the probability of being selected and leaving more offspring. The variation or genetic diversity we find in nature among organisms is, in fact, the raw material for selection as any organism in the struggle for existence exploits any advantage it may have upon others to guarantee its survival. The more successful individuals leave more progeny and these better adapted organisms (and the criterion for better adapted is that they survived) may increase in frequency in the population, altering its character with time. But, in nature, the process of adaptation never comes to a rest due to the fact that organisms not only change the same environment in which selection occurs but also because more individuals are produced than can survive. Even in stable ecosystems evolution is under way.

In evolutionary computation the term “fitness” is widely used but its meaning differs from the current meaning in evolution theory today. In evolutionary computation the term fitness has the meaning it had in Darwin’s day: a quality of organisms likely to be favored by selection. In fact, in all genetic algorithms individuals are selected according to this fitness. In evolution theory, though, fitness is a measure that incorporates both survival and reproductive success.

This shows a very important difference between adaptive computer systems and natural systems. In nature, organisms are selected against a multitude of factors and why or how a new trait is selected is not always clear. Therefore the fitness of an individual can only be measured by the progeny it leaves. But in computer systems the fitness of an individual in a certain environment is easily evaluated, and this measure can be rigorously used to determine selection. However, some scientists like to introduce a random factor in selection to mimic natural selection, and a simple way of implementing this kind of selection is by roulette-wheel sampling (Goldberg 1989). Each individual receives a slice of a circular roulette-wheel proportional to its fitness. The roulette is spun, and the bigger the slice the higher the probability of being selected. And, as it happens with all non-deterministic phenomena, sometimes the improbable happens whereas the highly probable does not happen. Nevertheless, I prefer this kind of selection because it mimics nature more faithfully and works very well in all populations (different selection schemes will be discussed in chapter 7). Indeed, this kind of selection, together with the cloning of the best individual of the previous generation (simple elitism), works very well allowing a very efficient search through the fitness landscape. 

Finally, another important difference between natural systems and computer systems is that in computer systems it is possible to measure rigorously the fitness as we know exactly what lies ahead and what we want and, therefore, only individuals more or less fit to do a predetermined job are selected. Consequently, it is fundamental the way we analyze the task at hand and choose the conditions (selection environment or fitness cases) under which individuals breed and are selected because, for once, we are bound to get what we asked for.

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