Objective Function

The chromosomes are evaluated using a classical mathematical method for solving differential equations like, Euler Method, etc. The result of this method is a curve represented by pairs of y-t-values. To select the fittest chromosome for each population a quality value has to be determined, defined as following:

Given pairs of (x_i,y_i) with i=0, 1, 2, ..., n where n is the maximum number of steps used to approximate the result of the differential equation by the Runge-Kutta method. Then the objective function is defined:

$Q=\sum_{i=0}^{n} y_i \ \text{with} \ i=0,1,2,...,n$

The sum of all y-values is the objective function that determines the evaluation value for each chromosome.