## A.3 Scaling Method

If the normal selection ruler is used during the GA computation (pselecti = fi/f ) in later generations, when the population average fitness gets close to the population best fitness, the above-average members are overwhelmed by average members and under-average ones. The computation becomes more a random walk. In this case fitness scaling can help. The linear scaling looks like this :

f' = af + b.

Problems:

• TFit is intended to be a number from the interval <0,1>
• The linearity must be preseved.

As a solution the following alternative was chosen.

All genes under favg are degraded by the Deg value. The Deg is a multiplicator between <0,1> specified by user.

The possible implementation:

```
void CalculateScaling (TPopulation &pop, double deg, double &avg,
double &a, double &b)
{
double total=0;

for (uint i=0; i<pop.GetSize(); i++)
total+=pop[i].GetFit();
if (pop.GetSize()) avg = total / pop.getSize();
else avg = 0;
if (avg<1) a = (deg*avg - 1) / (avg - 1);
else a=1;
b = 1 - a;
return;
}```

```TFit ScaleFit (TFit from, double deg, double avg, double a, double b)
{
if (from <= avg) return (deg*from);
return (a*from)+b;
}
```