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this adaptive process by continually introducing new schemata for trial, while testing extant schemata in new contextsall this without much disturbing the ranking process (except for the longer schemata). Moreover, crossing-over makes it possible for the schemata represented in  to move automatically to appropriate rankings through the application of the genetic plan to individual structures from  . As a result this very large number of rankings is compactly stored in a selected, relatively small population of individuals (exploiting the possibility suggested at the end of chapter 4). |
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By extending the pressure analogy introduced just before Theorem 6.2.3 we can gain a global view of the interaction of reproduction and crossover. Whenever some schema x exhibits better-than-average performance, reproduction introduces "pressures" D > 0, disturbing the steady state which would result from the action of the crossover operator alone. The disturbances both shift the steady-state values l(x') for large numbers of schemata, because of changes in the proportions P(jx) of the alleles jx, 1 £ j £ l, and also introduce local transitory departures because P(x) > l(x). Because all schemata are being affected simultaneously, and because reproduction affects them according to observed performance, we have a diffusion "outward" from schemata currently represented in , a diffusion which proceeds rapidly in the vicinity of schemata exhibiting above-average performance. This is closely analogous to a gas diffusing from some central location through a medium of varying porosity, where above-average porosity is the analogue of above-average performance. The gas will exhibit a quickened rate of diffusion wherever it encounters a region of higher porosity, rapidly saturating the whole region. All the while it slowly but steadily infuses enclaves of low porosity. In effect, high porosity is exploited wherever it occurs, without prejudicing eventual penetration into regions of lower porosity. As a result the overall rate of penetration is much more determined by regions of high porosity and their proximity to each other than by average porosity. |
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Restated in terms of schemata, regions of higher porosity correspond to sets of schemata of above-average performance which can be produced from each other by relatively few crossovers. Thus, following the analogy, local optima in performance are thoroughly explored in an intrinsically parallel fashion. At the same time the genetic plan does not get entrapped by settling on some local optimum when further improvements are possible. Instead all observed regions of high performance are exploited without significantly slowing the overall search for better optima. Here we begin to see in a more precise context the powers of generalized genetic plans, powers first suggested in the specific context of section 1.4. |
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One final point: Plans of type  measure a schema's performance relative |
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