The *Interactive Evolutionary Algorithm* is looking for the minimum or
maximum solution for the differential equation respectively.
At the end of the evolutionary process
the optimal chromosome should represent the minimum/maximum function
determined by the Runge-Kutta Method.
But it is impossible to tell whether
another chromosome could have generated a better
optimum for a particular y-t-value pair during the optimizing process
or not. The overall minimum/maximum y-t-values are retrieved by
protocolling them during the
evolutionary algorithm process.
The approach introduced can be seen as a mixture
between the interacting and non interacting approach of
Bonarini and Bontempi [1] (see Section 2).

An advantage is that the *Interactive Evolutionary Algorithm*
is able to find the overall solution space. There is no spurious
behaviour introduced but it might miss out some possible behaviour.
Further it is sufficient to represent one problem set
-- initial values and parameters of the differential equation --
in a chromosome. If there is more than one problem set
necessary to represent the minimum/maximum curve the
evolutionary process jumps between these solutions back and forth
protocolling the minimum/maximum y-t-pairs.

A disadvantage is that at each generation a classical mathematical method for solving ODEs has to be performed for each chromosome which is computationally expensive.