Evolving programs with parameters and loops

At the current state of the art, genetic programs do not contain two constructs that commonly occur in programs written by humans, that is, loops and functions with parameters. In this paper we describe an investigation into the evolution of programs for a problem that can only be solved by evolving a parameterised program with one or more loops. We provide training examples of the desired program behaviour for a number of problem sizes and require the evolution of a program P(n) that will give the correct output for any value of n. We have chosen a problem, that of reproducing a binary string to a given number of bits, that can be made harder or easier by adjusting various aspects of the formulation. We are interested seeing in which formulations lead to success and which do not. We conclude that programs with parameters and loops can be successfully evolved if the search space is appropriately restricted by (1) grammars which restrict the possible program structures, (2) limits on program depth and (3) limits on the range of random constants.