

![0_image_0.png](0_image_0.png)

Altenberg defined evolvability as the ability to produce fitter variants [43]. The idea is to analyze the variation in fitness between one solution and its neighbors. Evolvability is said positive if neighbor solutions are fitter than the solution and negative otherwise. In this section, we define the **evolvability** horizon **(EH) as the sequence of solutions, ordered by fitness values, which can** be reached with one bitflip from the given solution. We obtain a graph with fitness values in ordinates and the corresponding neighbors in abscissa sorted by fitnesses (see figure 10).

Figure 10 shows the evolvability horizon of the blok**. There is no neighbor with**
a better fitness value than the initial rule; so, all the best known rules are local optima. The fitness landscape has two important neutral networks at fitness 0 (NN0) and fitness 0.5 (NN0.5**) (see section 4.3). No local optimum is nearby** NN0**; but a large part of neighbors of local optima (around 25% on average)**
are in NN0.5. As a consequence a neutral local search on NN0.5 **can potentially**
find a portal toward the **blok**.

For each EH, there is an abscissa r **from which the fitness value is roughly**
linear. Let fr **be this fitness value,** f128 **the fitness of the less sensible bit, and**
m the slope of the curve between abscissa r and 128. Thus, the smaller m and r, the better the neighbors. On the contrary, higher slope and r **values mean** that the neighbor fitness values decay faster. For example evolvability is slightly negative from GLK, as it has a low slope and a small r**. At the opposite, the Coe2 rule has a high slope ; this optimum** is thus isolated and evolvability is strongly negative. We can imagine the **space** "view from GLK" flatter than the one from Coe2.