3 Experimental Investigation

Table 6.1: Experiment and problem parameters for the Binomial-3 and random polynomial experiments.

Population size	500
Functions	+,-,*,p/
Terminals	x, ERCs
Polynomial ERC range	$[-10,10]$
Binomial-3 ERC range	unity $[-1,1)$
	ten $[-10,10)$
	hundred $[-100,100)$
	control $[\textrm{no ERCs}]$
Tournament selection	size 4
Maximum tree depth	10
Ramped half-n-half tree creation	minimum depth 2
	maximum depth 4
Maximum generations	101
Other parameters same as in Chapter 4

100 independent random runs are performed for each problem instance. Experiment and problem parameters are described in Table 6.1. The fitness for both problems are calculated by summing the squared difference for each point along the problem instance's function and the function produced by the individual. All problems used here are minimisation problems with an ideal fitness of zero. However, we report the adjusted fitness $1/(1+\textrm{raw fitness})$ (with ideal value of one). For the random polynomial experiments a random seed was selected and used to generate three polynomials of degree 3, 7 and 11. The three polynomials are:

$$\begin{eqnarray*} degree 3 = (x+0.44)\times(x+0.54)\times(x+0.27) \\ degree 7... ...)\times \\ (x+0.82)\times(x+0.63)\times(x-0.75)\times(x-0.91) \end{eqnarray*}$$

The polynomials are graphically presented in Figure 6.1.