1 Regression Functions and Terminals

Regression problems use mathematical functions to approximate a target function. The division and logarithm function are usually ``wrapped'': division returns 1.0 if the denominator is equal to or very close to 0, while logarithm returns 0 if its argument is equal to or very close to 0. Additionally, it is common, especially for functions with coefficients such as the Rastrigin, to use ephemeral random constants (ERCs). ERCs are constants that keep their value after initialisation for the remainder of the run. In the random polynomial instances in Chapter 5, the ERCs are in the range of [-1,1] while they are varied for the Binomial-3 instances. The experiments that use the Rastrigin function in Chapter 4 do not use ERCs.

The Regression domain functions are usually a subset of the following:

• a + b, a - b, a * b : return addition, subtraction and multiplication of their arguments, respectively,
• a / b : protected division, returns 1 if denominator is $\approx$ 0, otherwise returns the quotient,
• sin(a), cos(a) : returns sine and cosine of the argument,
• log(a) : returns 0 if a $\approx$ 0, else the logarithm of the argument,
• exp(a) : returns $e^a$.

The following terminals are common in the Regression domain:

• $x$ : from the pair ($x,y$),
• ERCs.

Figure 2.3: The Quartic and Rastrigin functions.