|
|
|
|
|
|
|
restatements are full-fledged research problems with the discrete results serving only as guidelines. In any case, the instants of time can be freely reinterpreted in different applicationsthey may be nanoseconds in one application (e.g., artificial intelligence), centuries in another (e.g., evolutionary theory). The properties and relations established with the formalism remain valid, only their durations will vary. Thus, at the outset, we come upon a major advantage of the formalism: Features or procedures easily observed in one process can be abstracted, set within the framework, and analyzed so that they can be interpreted in other processes where duration of occurrence, or other detail, obscures their role. |
|
|
|
|
|
|
|
|
As our starting point for constructing the formalism let us take the domain of action of the adaptive plan, the set of structures  . At the most abstract level will simply be an arbitrary, nonempty set; when the theory is applied, will designate the set of structures appropriate to the field of interest. Because the more general parts of the theory are valid for any nonempty set , we have great latitude in interpreting or applying the notion of structure in particular cases. Stated the other way around, the diversity of objects which can serve as elements of assures flexibility in applying the theory. In practice, the elements of can be the formal counterparts of objects much more complex than the basic structures (chromosomes, mixes of goods, etc.) of the preliminary survey. They may be sets, sequences, or probability distributions over the basic structures; moreover, portions of the adaptive system's past history may be explicitly represented as part of the structure. Often the basic structures themselves will exhibit additional properties, being presented as compositions of interacting components (chromosomes composed of alleles, programs composed of sets of instructions, etc.). Thus (referring to section 1.4), if the elements of are to represent chromosomes with  specified genes, where the ith gene has a set of ki alleles Ai = {ai1, . . ., aiki}, then the set of structures becomes the set of all combinations of alleles, |
|
|
|
|
|
|
|
|
 |
|
|
|
|
|
|
|
|
Finally, the set will usually be potential rather than actual. That is, elements become available to the plan only by successive modification (e.g., by rearrangement of components or construction from primitive elements), rather than by selection from an extant set. We will examine all of these possibilities as we go along, noting that relevant elaborations of the elements of provide a way of specializing the general parts of the theory for particular applications. |
|
|
|
|
|
|
|
|
The adaptive plan t produces a sequence of structures, i.e., a trajectory through , by making successive selections from a set of operators W. The particular |
|
|
|
|
|