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to the current average performance of the population. Thus, as time elapses, schemata must meet progressively higher criteria to attain (or retain) a high ranking. (This is, again, somewhat analogous to the slowed rate of occupation of a gas as it occupies successively larger volumes, higher porosity being required for the same occupation rate.) As a result, older schemata associated with local optima steadily lose ranking as better optima are located (unless the older schemata are components of the new schemata), so that capacity is not wasted on superseded regions. |
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The overall results of this section can be illustrated by elaborating the comment (on page 99) about f(x) of Figure 10. Using 6 bits of accuracy (l = 6), assume A1 = .001100, A2 = .000100, A3 = .101000, A4 = .110011, and A5 = .011100 have been chosen at random to form  . (The size of , M = 5, is of course much too small to be realistic even for an algorithm for artificial systems, but it is adequate to illustrate the effects of crossing-over.) Looking at Figure 10 we see that µ1 = f(A1) = f(.001100) @ ½. Similarly, µ2 = f(A2) @ 1½, µ3@ 2, µ4@ 13/4, and µ5@ ½. For these points  . Accordingly A1 will produce  offspringi.e., A1 has about 2 chances out of 5 of being reproduced. Similarly A2 will have  offspring; and so on. Figure 12 shows a typical outcome for a plan of type  using only reproduction and simple crossover on . (Thus, for the reproduction of A1, a trial was made of a random variable yielding 1 with probability 2/5 and 0 probability 3/5the outcome of the trial was 0.) The crossing- |
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Fig. 12.
Some effects of a type plan on a one-dimensional function |
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