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amount by which x's average performance µx exceeds the average performance µ of the whole population. At the same time the rankings are stored compactly in the way suggested at the end of chapter 4, at least 2l schemata being ranked in a population which may consist of only a few dozen elements from  . Moreover, genetic plans automatically access this information, update it, and use it to generate new structures, each of which efficiently tests large numbers of schemata. |
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In detail: Schemata of above-average performance are combined and tested in new contexts by crossing-over outside their defining locations. Because (the instances of) schemata increase or decrease exponentially in terms of observed performance (Lemma 7.3), the overall average performance is close to the best observed. Because a wide range of promising variants is generated and tested (section 6.2) entrapment on "false peaks" (local optima) is prevented. Even for moderate sizes of population and representation, say M = 100 and l = 20, if the initial population  is varied, a crossover probability Pc > ½ will make it almost certain that every structure A generated during the initial stages of adaptation is new. Nevertheless, this high value of Pc does not disturb the rankings of schemata which are consistently above average. Thus, sampling efficiency remains high, while ranking information is preserved and used. In conjunction with these processes, inversion by changes in linkage assures that schemata consistently associated with above-average performance are steadily shortened (l/(x) is decreased), thereby reducing operator losses (section 6.4 and the definition of  in Lemma 7.2). |
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Overall, genetic plans, by simple operations on the current "data base"  ,produce sophisticated, intrinsically parallel tests of the space of schemata X. Large numbers of local optima, instead of diverting the plan from further improvement, are exploited to improve performance on an interim basis while the search for more global optima goes on. High dimensionality (such as a multitude of factors affecting fitness or play of a game) creates no difficulties for genetic plans, in contrast to its effect on classical procedures, because of the intrinsic parallelism (the r' factor of Theorem 7.4). |
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