elected P-protein and feed it to the cart model. As the interval of update for the cart model is 0.02s**, the interval of measurement of the P-gene was set to** 2000 time steps. This is however arbitrary, and could become a parameter to optimise, as it could be set differently for different genomes (some genomes have slower reactions, others have faster ones).

## 3.2 The Evolutionary Algorithm

The evolutionary algorithm used to evolve the binary genomes was an evolutionary strategy (250+250)−ES**: 250 parents give birth to 250 offspring, and the best**
250 of all 500 are used as the new parent population; a maximum of 50 **iterations**
were allowed. The only variation operator used was a simple bit-flip mutation, set to 1% and adapted by the well-known 1/**5 rule of Evolution Strategies [12]:** when the rate of successful mutations is higher than 1/**5 (i.e. when more than** 20% mutation events result in a reduction of the error measure), the mutation rate is doubled; it is halved in the opposite case. However, to avoid stagnation of evolution, if the number of mutation events (i.e. the number of bits flipped per generation) drops below 250, the mutation rate is doubled.

## 4 Results And Analysis

Fig. 2 shows the average fitness evolution for 50 independent runs, for both

![0_image_0.png](0_image_0.png) expression measurement approaches. Both approaches solve the problem quite fast, but it is obvious that using product tendency gives faster convergence to an optimal solution. This is an expected result: when using P-protein **absolute** values, the concentration of a P-protein has to be fairly close to 50%, in order to provide a solution. However, when using P-protein tendency, the starting concentration of the P-protein has no influence on the behaviour of the cart.