**4. Fitness function**

The fitness function is used to provide the measure of how individuals performed. In this instance, the problem domain was that the PSS parameters should stabilize the system simultaneously over a certain range of specified operating conditions. The PSS which parameters are to be optimized has a structure similar to the conventional PSS (CPSS) as shown in Fig. A. 3. of Appendix 8.2.3. There are three parameters *KS*, *T*1 and *T*<sup>2</sup> that are to be optimized, where *Ks* is the PSS gain and *T*1 and *T*2 are lead-lag time constants. *Tw* is the washout time constant which is not critical and therefore has not been optimized.

The fitness function that was used is to maximize the lowest damping ratio. Mathematically the objective function is formulated as follows:

$$val = \max(\min(\zeta\_{ij}))\tag{4}$$

where

*i* = 1,2, … n , *j* =1, 2, ….m

$$\mathcal{L}\_{\overline{\psi}} = \frac{-\sigma\_{\overline{\psi}}}{\sqrt{\sigma\_{\overline{\psi}}^2 + a\_{\overline{\psi}}^2}}$$

ζ*<sup>i</sup>* j is the damping ratio of the ݅th eigenvalue of the jth operating conditions. The number of the eigenvalues is *n*, and *m* is the number of operating conditions.

σ*ij* and *ωij* are the real part and the imaginary part (frequency) of the eigenvalue, respectively.
