The Impact of External Dependency in Genetic Programming Primitives

Both control and data dependencies among primitives impact the behavioural consistency of subprograms in genetic programming solutions. Behavioural consistency in turn impacts the ability of genetic programming to identify and promote appropriate subprograms. We present the results of modelling dependency through a parameter-ized problem in which a subprogram exhibits internal and external dependency levels that change as the subprogram is successively incorporated into larger subsolutions. We nd that the key diierence between non-existent and \full" external dependency is a longer time to solution identiication and a lower likelihood of success as shown by increased diiculty in identifying and promoting correct subprograms. 1 Motivation One reason our understanding of genetic programming Koza, 1992] is imprecise is the lack of an adequate account of how program dependencies impact the eeectiveness of selection and crossover. Program dependencies can be decomposed into two classes: control and data. A control dependency between two program statements means that they must be executed in speciic order so that the program proceeds correctly. A data dependency between two statements means that one statement sets up a data state (e.g. variable) which the other one subsequently needs to reference. We and others contend O'Reilly and Oppacher, 1995, Luke and Spector, 1997] that program dependency is a key issue in GP. In our view a subprogram has both internal dependencies and external dependencies. Internal dependencies are data and control relationships that stay within the subprogram. External dependencies denote a data or control relationship between the subprogram and code that either precedes it in execution or follows it in execution. Regardless of how code surrounding a subprogram changes, the part of its behaviour that depends on internal dependencies never changes. In the case of external dependencies, quite the opposite is true. The code which surrounds a subprogram innuences the eeectiveness of its externally dependent behaviour. This has the following consequences: The subprogram tnesses the algorithm estimates and then uses to guide promotion of subprograms are inaccurate. Assume that, as per versions of the