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deviations above the mean in less than 600 trials (as compared to 3 standard deviations in 1000 trials). |
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Against this background Cavicchio then developed and tested a series of reproductive plans. The best of these attained a score of 75.5 in 780 trials, a score considerably beyond that attained in any of the "detector evaluation" runs. (In qualitative terms, a score of 52 would correspond to a "poor" human performance, while a score of 75.5 would correspond to a ''good" human performance. Because many characters in the "difficult task" are quite similar in form, increments in scoring are difficult to attain after the easily distinguished characters have been handled.) An important general observation of this study is that the sophistication and power of a genetic plan is lost whenever M,the size of the population (data base), is very small. It is an overwhelming handicap to use only the most recent trial (M = 1) as the basis for generating new trials (cf. Fogel et al. 1966). On the other hand, the population need not be large to give considerable scope to genetic plans (20 was a population size commonly used by Cavicchio). |
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Roy Hollstien added considerably to our detailed understanding of genetic plans by making an extensive study of genetic plans as adaptive control procedures. His emphasis is on domains wherein classical "linear" and "quadratic" approaches are unavailing, i.e., domains where the performance function exhibits discontinuities, multiple peaks, plateaus, elongated ridges, etc. To give the problems a uniform setting he transforms them to discrete function optimization problems, encoding points in the domain as strings (see p. 57). An unusual and productive aspect of Hollstien's study is his translation of breeding plans for artificial genetic selection into control policies. A breeding plan which employs inbreeding within related (akin) policies, and recurrent crossbreeding of the best policies from the best families, is found to exhibit very robust performance over a range of 14 carefully selected, difficult test functions. (The test functions include such "standards" as Rosenbrock's ridge, the sum of three Gaussian 2-dimensional density functions, and a highly discontinuous "checkerboard" pattern.) The test functions are represented on a grid of 10,000 points (100 by 100). In each case the region in which the test function exceeds 90 percent of its maximum value is small. For example, test function 7 with two false peaks (the sum of three Gaussian 2-dimensional densities) exceeds 90 percent of its maximum value on only 42 points out of the 10,000. The breeding plans are tested over 20 generations of 16 individuals each, special provisions being made to control random effects of small sample size ("genetic drift"). The breeding plan referred to above, when confronted with test function 7, placed all of its trials in the "90 percent region" after 12 generations (192 trials). A random search would be expected to take 250 trials |
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