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In observing what happens to small sets of genes under its action, we have seen one way in which the plan t1 preserves the history of its interactions with the environment. It also retains certain kinds of advances thereby, favoring structural components which have proved their worth by augmenting fitness. At the same time, since these components are continually tried in new contexts and combinations, stagnation is avoided. In brief, sets of alleles engendering above-average performance provide comparative success in reproduction for the chromosomes carrying them. This in turn assures that these alleles become predominant components of later generations of chromosomes. Though this description is sketchy, it does indicate that reproductive plans using genetic operators proceed in a way which is neither enumeration nor simple duplication of fit structures. The full story is both more intricate and more sophisticated. Because reproductive plans are provably efficient over a broad range of conditions, we will spend considerable time later unraveling the skeins of this story. |
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5. Some General Observations |
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One point which comes through clearly from the examples is the enormous size of  , even for a very modest system. This size has a fatal bearing on what is at first sight a candidate for a "universal" adaptive plan. The candidate, called t0 in the first example, and henceforth designated an enumerative plan, exhaustively tests the structures in . Enumerative plans are characterized by the fact that the order in which they test structures is unaffected by the outcome of previous tests. For example, the plan first generates and tests all structures attainable (from an initially given structure) by single applications of the basic operators, then all structures attainable by two applications of the operators, etc. The plan preserves the fittest structure it has encountered up to any given point in the process, replacing that structure immediately upon generating a structure which is still more fit. Thus, given enough time (and enough stability of the environment so that the fitness of structures does not change during the process) an enumerative plan is guaranteed to discover the structure most fit for any environment confronting it. The simplicity of this plan, together with the guarantee of discovering the most fit structure, would seem to make it a very important adaptive plan. Indeed enumerative plans have been repeatedly proposed and studied in most of the areas mentioned in section 1.1. They are often set forth in a form not obviously enumerative, particularly in evolutionary studies (mutation in the absence of other genetic operators), learning (simple trial-and-error), and artificial intelligence (random search). |
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