5.1 Introduction
نویسنده
چکیده
This chapter uses three differently sized versions of an illustrative problem that has considerable regularity, symmetry, and homogeneity in its problem environment to compare genetic programming with and without the newly developed mechanism of automatic function definition. Genetic programming with automatic function definition can automatically decompose a problem into simpler subproblems, solve the subproblems, and assemble the solutions to the subproblems into a solution to the original overall problem. The solutions to the problem produced by genetic programming with automatic function definition are more parsimonious than those produced without it. Genetic programming requires fewer fitness evaluations to yield a solution to the problem with 99% probability with automatic function definition than without it. When we consider the three differently sized versions of the problem we find that the size of the solutions produced without automatic function definition can be expressed as a direct multiple of problem size. In contrast, the average size of solutions with automatic function definition is expressed as a certain minimum size representing the overhead associated with automatic function definition; however, there is only a very slight increase in the average size of the solutions with problem size. Moreover, the number of fitness evaluations required to yield a solution to the problem with a 99% probability grows very rapidly with problem size without automatic function definition, but this same measure grows only linearly with problem size with automatic function definition.
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