Find parameters to maximise output score
In this kind of optimization problem a genetic algorithm is often a good approach, assuming computing the value of  f() is not too costly.
The idea is to represent the 6 parameters as &quot;genes&quot;. In the first generation their values are assigned randomly, then each &quot;individual&quot; in the generation (combination of parameters) is evaluated (i.e. calculate f), and the top performing &quot;individuals&quot; are selected. The next generation is obtained by cross-over and random mutation, and the process is repeated until f converges to a maximum.