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edition. Section 10.4 concludes the chapter with a new set of advanced questions and some new speculations. |
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There is more recent work, still in its earliest stages, that is not discussed in chapter 10. Freddy Christiannsen, Marc Feldman, and I, working through the Santa Fe Institute, have begun to introduce the effects of schemata into much-generalized versions of Fisher's equations. This work is, in part, a follow-up of work of a decade ago, by Bob Axelrod and Bill Hamilton, that began to study the relation of recombination to the prevalence of sex in spite of the two-fold genetic load it incurs. In another direction, some preliminary theoretical investigations, stimulated by the Echo models, suggest that there is a schema theorem that is relevant to any adaptive system that can be described in terms of resource flowsuch a system may involve neither reproduction nor defined fitness functions. Also in the wings is a characterization of a broad class of problems or "landscapes" that are relatively easy for genetic algorithms but difficult for both traditional optimization techniques and new weight-changing techniques such as artificial nerve nets and simulated annealing. |
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At a metalevel, the problem landscapes we've been studying may describe an essential aspect of all problems encountered by complex adaptive systems: Easy (linear, hill-climbing) problems have a short-lived influence on complex adaptive systems because they are quickly exploited and absorbed into the system's structure. Extremely difficult problems ("spikes") almost never influence the behavior because they are almost never solved. This leaves as a major continuing influence the presence of certain kinds of "bottlenecks." These bottlenecks are regions in the problem space that offer improvement but are surrounded by "valleys'' of lowered performance. The time it takes to traverse these valleys determines the trajectory, and rate of improvement, of the adaptive system. It seems likely that this rate will be determined, to a great degree, by recombination applied to "building blocks" (schemata) supplied by solutions attached to other regions of high performance. |
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It is an exciting time to study adaptation in natural and artificial systems; perhaps these studies will yield another edition sometime in the next millenium. |
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JOHN H. HOLLAND
OCTOBER 1991 |
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