and the second is the more difficult test sequence:

where n consists of the nonnegative integers.

These problems were chosen for three reasons: first, although not trivial, they can be exactly solved by the algorithm and therefore provide an accurate measure of performance in terms of success rate; second, they require relatively small populations and relatively short evolutionary times, making the task feasible; and third, they can be exactly solved using both unigenic and multigenic systems and therefore provide two different approaches for the analysis of genetic neutrality.

For the test function (3.1), a set of 10 random fitness cases chosen from the interval [-10, 10] was used; the fitness function was based on the relative error with a selection range of 25% and a precision error of 0.01%, giving maximum fitness f_max = 250 [7]; and population sizes P of 30 and evolutionary times G of 50 generations were chosen.

For the sequence induction problem, the first 10 positive integers n and their corresponding an term were used as fitness cases; the fitness function was also based on the relative error with a selection range of 25% and maximum precision (0% error), giving f_max = 250; the population size and the evolutionary time were increased, respectively, to 50 and 100 as this problem is slightly more difficult than the function finding one.

In all the experiments, the function set F = {+, -, *, /} and the terminal set T consisted only of the independent variable which was represented by a, giving T = {a}; genetic modification was introduced using a mutation rate of 0.03, an IS and RIS transposition rates of 0.1 using three transposons of lengths 1, 2, and 3, and two-point and one-point recombination rates of 0.3; in multigenic systems gene recombination and gene transposition were also used as sources of genetic modification, both at rates of 0.1 and the linking was made by addition; the selection was made by roulette-wheel sampling coupled with simple elitism and the success rate was evaluated over 100 independent runs.