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6. Reproductive Plans and Genetic Operators |
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In the earlier informal discussion of genetics (sections 1.4 and 3.1) reproductive plans were introduced as the fundamental procedure of genetic adaptation. The present chapter lifts reproductive plans from the specific context of genetics to the general framework of chapter 2. This, at one stroke, makes reproductive plans suitable objects for rigorous study and yields a class of plans applicable to the full range of adaptive systems. Genetic plans, i.e., reproductive plans using generalized genetic operators, will be the prime focus; emphasis will be laid upon the operators' retention and use of relevant history as they exploit opportunities for improved performance. |
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Genetic plans can be applied to any domain of structures  represented by strings (l-tuples). (To build a better intuition for this flexibility the reader may find it useful to consistently interpret the properties and theorems advanced here in the most familiar of the nongenetic illustrations of chapter 3.) We will see that each structure generated and tested by a genetic plan in effect tests a multitude of schemata and that the plan actually preserves and exploits this information. Genetic plans do this by generating sequences of structures in such a way that, once a few instances of any given schema x occur, one can count on the cumulative number of instances of x increasing at a rate closely related to µx. The generalized genetic operators act so as to test old schemata in new contexts, generate instances of schemata not previously tested, and so on (see sections 7.2-7.5), without disturbing the rates of increase. Genetic plans thus exhibit the intrinsic parallelism discussed at the ends of chapters 4 and 5. |
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Interpreted in genetics, the results of the next two chapters indicate that adaptation proceeds largely in terms of pools of coadapted sets of alleles rather than gene pools. As one important offshoot, this approach yields an extension of Fisher's (1930) classical result (on the rates of increase of alleles) to coadapted sets of alleles with epistatic interaction (see section 7.4). A typical interpretation for artificial systems can be obtained by looking again at the function f(x) of Figure 10. |
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