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which is approximately equal to l0(x)·1PM when 1PM is small relative to 1/l. Thus, adding mutation to the list of operators in Theorem 6.2.3, we get |
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COROLLARY 6.4.1: Under a reproductive plan of type  using the simple crossover operator and mutation, the expected proportion of each schema represented in  changes in one generation from P(x, t) to |
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Unlike the case for crossing-over, mutation is a constant source of loss for a schema x, with 1PM fixed, even when P(x, t) = 1. In effect it is a "disturbance" introduced to prevent entrapment on a false peak. |
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Summing up: Mutation is a "background" operator, assuring that the crossover operator has a full range of alleles so that the adaptive plan is not trapped on local optima. (Of course if there are many possible allelese.g., if we consider a great many variants of the nucleotide sequences defining a given genethen even a large population will not contain all variants. Then mutation serves an enumerative function, producing alleles not previously tried.) |
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5. Further Increases in Power |
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The next chapter will establish that the three genetic operators just described are adequate for a robust and general purpose set of adaptive plans, with one important reservation which will be discussed at the end of this section. However, there are additional operators which can make significant contributions to efficiency in more complex situations. Chief among these is the dominance-change operator which (among other things) helps to control losses resulting from mutation. Because losses resulting from mutation, for given 1PM, do not diminish as schema x gains high rank, a constant "load" is placed on the adaptive plan by the random movements away from optimal configurations. For this reason it is desirable to keep the mutation rate 1PM as low as possible consistent with mutation's role of supplying missing alleles. In particular, if the rate of disappearance of alleles can be lowered without affecting the efficiency of the adaptive plan, then the mutation rate can be proportionally lower. Since the main cause of disappearance of alleles is sustained below-average performance, the rate of loss can be reduced by shielding such |
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