

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

dist(D1, D0) = 0.110 dist(D1, D0) = 0.119 dist(D2, D0) = 0.00338 dist(D2, D0) = 0.**0175**
dist(D1, D0) = 0.0937 dist(D1, D0) = 0.151 dist(D2, D0) = 0.00246 dist(D2, D0) = 0.**0693**
dist(D1, D0) = 0.0750 dist(D1, D0) = 0.**0917** dist(D2, D0) = 0.0103 dist(D2, D0) = 0.**00403**

![0_image_1.png](0_image_1.png)

defined by:

$$f_{T}(x)={\begin{cases}1.0-{\frac{d(x)}{b}}&{{\mathrm{if~}}d(x)\leq b,}\\ {\frac{r(d(x)-b)}{1.0-b}}&{{\mathrm{elsewhere}}}\end{cases}}$$

where d(x) is the Hamming distance to the global optimum, divided by N, between x and one particular solution. The problem is most deceptive as r is low and b is high. In our experiment, we will use two kinds of Trap functions with r = 0.9, one with b = 0.25 and another one with b = 0.75 (see figure 5 (a) and (b)).

To affect a fitness value to each neutral network, we first choose the optimum neutral network, denoted NNopt, (for example the one containing the solution 0 N ) and set its fitness to the maximal value 1.0. Then, for each neutral network, we compute the distance d between its centroid1and the centroid of NNopt ; finally the fit-1The centroid of a NN is the string of the frequency of appearance ness value of the NN is set according to a trap function2and the distance d. In order to ensure that all adjacent networks have different fitness values, it is possible to add a white noise to the fitness values of each NN. In the following experiments, the length of bitstring is N **= 16**. ND-landscapes are constructed with uniform neutral degree distributions. We use the distributions defined by

$$D_{p,w}[i]={\begin{cases}1/w&{\mathrm{if}}\,i\in\{p,p+w-1\},\\ 0&{\mathrm{elsewhere}}\end{cases}}$$

where p ∈ {0, 7}, w ∈ {3, 4}, and the two Trap functions defined in figure 5. For each distribution and each Trap function, 30 landscapes were generated.

of bit value 1 at each position.

2This trap function is defined for all real numbers between 0 and N