Fig. 4. Typical time course of population
evolution for
the self-assembling 8-bit multiplier circuit shown in Fig. 1. a)Time course of maximum fitness
in the population: in black evaluated using its own test vector, in gray
evaluated using random test vectors. The block fitness function leads to
stepwise enhancements in fitness. Note the large jump in fitness at generation
82000, corresponding to discovery of a general solution to the problem. b)Population average of success
frequencies for individual product bits 0-15, with whiter fields indicating
more success, for each of the categories I-V of multiplication tasks (see
text). Solutions to these tasks are successively more difficult to evolve.
Additionally, the outer bits are logically less convoluted than the inner ones
and consequently are correctly multiplied first. c)Relative frequencies of
multiplications in the test vector attached to the fittest individual in the
population grouped in five categories as in b)with whiter fields indicating
higher frequencies. At generation 19000, b) indicates a jump in performance in
the class I-IV problems. Consequently, the test vectors concentrate on the final
residual category V, as shown in c). When these multiplications have been
solved, at about generation 82000, the coevolving test vectors begin to
repopulate the other categories again.

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