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(coadapted sets of alleles), making such schemata less subject to decomposition. Mutation (section 6.4) generally has a background role, supplying new alleles or new instances of lost alleles. All of this goes on without seriously disturbing the intrinsic rates of increase {µx} of most schemata instanced in  . Chapter 7 establishes the robustness and intrinsic parallelism of these type  plans for arbitrary string-representable domains  . |
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2. Generalized Genetic OperatorsCrossing-Over |
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When genetic operators are used with reproductive plans we get a surprisingly sophisticated set of adaptive plans. Like the rules of a well-constructed game (chess, go, poker), genetic operators are simply defined but subtle in their consequences. |
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Our first objective, as with reproductive plans, will be to lift genetic operators from their specific biological context to the general  framework. With the help of this framework we can then define and investigate rigorously two critical advantages (first discussed in chapter 4) conferred by genetic operators: |
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(i) intrinsic parallelism in the testing and exploitation of schemata, and |
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(ii) compact storage and use of the large amounts of information resulting from prior observations of schemata. |
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This contrasts with the common view of evolutionary processes as successive selection of the best of a sequence of variants produced by mutationa process which we will see amounts to an enumeration of structures, with its attendant disadvantages. |
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The reader should be warned that the generalized operators presented in the next three sections are idealized to varying degrees. This has been done to emphasize the basic functions of the operators, at the cost of exploring the complex (and fascinating) biological mechanism underlying their execution. Even so an attempt has been made to keep the correspondence close enough to allow ready translation of the results to the original biological context. |
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Because it serves well as a paradigm for other genetic operators, we will look first at "crossing-over." In biological systems, crossing-over is a process yielding recombination of alleles via exchange of segments between pairs of chromosomes. We can lift this process to the level of a general operator on structures by providing the structures with representations as in chapter 4. As before, for simplicity, will be taken to be the set of representations. Besides facilitating the generalization to arbitrary structures this emphasizes the effects of crossing-over on schemata. Crossing-over proceeds in three steps. |
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