Polynomial Induction and Time Series Prediction - Gene Expression Programming - page 280

Table 7.5
The role of coefficients in polynomial evolution.
Number of runs 100

Number of generations 5000

Population size 100

Number of fitness cases 90 (Table 7.3)

Function set F1 - F16 (Table 7.2)

Terminal set a-j

Head length 21

Gene length 43

Number of genes 1

Chromosome length 43

Mutation rate 0.044

Inversion rate 0.1

IS transposition rate 0.1

RIS transposition rate 0.1

One-point recombination rate 0.3

Two-point recombination rate 0.3

Fitness function Eq. (3.5)

Average best-of-run fitness 0.02355

Average best-of-run R-square 0.3500310276

some local optimum from which it is incapable of escaping. Indeed, such local
optima are pervasive trappings of most time series prediction tasks, of which
the most common consists of using the present state for predicting the next.
Indeed, in that case, the simplistic models created have usually excellent
statistics but nil predictive power. For instance, in the particular problem of
this section, the simplistic solution y = j has already a fitness of 2.38177 and
an R-square of 0.6961811429. And as you can deduce by comparing these
values with the averaged values obtained with the GEP-OS system and in the
experiment summarized in Table 7.5, something had to have been done to
prevent the rediscovery of this solution in those systems, otherwise much
higher values for both the average best-of-run fitness and average best-of-
run R-square would have been obtained. Indeed, all the STROGANOFF ex-
periments of this chapter use a terminal control that checks the total number
of different terminals in each expression tree and selects only solutions that
use at least five different terminals, making all the solutions with less than
five arguments unviable. It is worth pointing out, though, that this kind of
measure was not implemented in the simpler GEP systems, as they are ex-
tremely flexible and can easily find ways out of all these local optima.