Initial population **For 'Olympus' and 'Neutral' based GAs, the initial population is randomly chosen in the Olympus. For cGA, the initial population**
is generated according to the centroid: probability to have '1' at a given bit position is given by C
′
**value at the same position. In the same way, if one bit**
is mutated, its new value is generated according to C
′
.

Selection schema **oGA and cGA both use the same selection scheme as**
in Mitchell et al.**. The top of 20 % of the rules in the population, so-called** elite rules**, are copied without modification to the next generation and the** remaining 80 % for the next generation were formed by random choice in the elite rules. The selection scheme is similar to the (µ+λ**) selection method. The**
nGA uses tournament selection of size 2. It takes into account the **neutrality**
of the landscape: if the fitnesses of two solutions are not statistically different using the t-test of 95 % of confidence, we consider that they are equal and choose the individual which is the more distant from the centroid C
′
**; this**
choice allows to spread the population over the neutral network. Otherwise the best individual is chosen. nGA uses elitism where the top 10 % of different rules in the population are copied without modification.

Performance Each GA run lasts 103 **generations and 50 independent runs**
were performed. For each run, we have performed post-processing. At each generation, the best individuals are evaluated on new sample of 104**ICs and**
the average distance between all pairs of individuals is computed. Best and average performances with standard deviation are reported in table 8. We also computed the percentage of runs which are able to reach a given fitness level and the average number of generations to reach this threshold (see figure 19).

Table 8

GA performances computed on sample of size 104.

GA Average Std Deviation Best

| GA   | Average   | Std Deviation   | Best   |
|------|-----------|-----------------|--------|
| oGA  | 0.8315    | 0.01928         | 0.8450 |
| cGA  | 0.8309    | 0.00575         | 0.8432 |
| nGA  | 0.8323    | 0.00556         | 0.8472 |

All GAs have on average **better performances than the optima find by human or by genetic programming. As expected, searching in the Olympus is**
useful to find good rules. All the GAs have nearly the same average **performances. However, standard deviation of 'Olympus' is four times larger than**
standard deviation of 'Centroid'. As it is confirmed by the mean distance between individuals, the cGA quickly looses diversity (see fig. 20). On the other hand, 'Neutral' GA keep genetic diversity during runs. Figure 19 shows that for the most interesting threshold over 0.**845, 'Neutral' have more runs able**