Can you think of your n different parameters making up an n dimensional space? It sounds like you are looking to maximize, minimize or just find some acceptable value in that n dimensional space.
This sounds like the usual maximization or search process. Those can be easy or difficult.
If your value is defined everywhere in the space and the space is relatively smooth with only one fairly clearly defined point where there is a maxima and your function to calculate the value can be done fairly quickly then you might think of using NMaximize or one of the other functions that search for a maximum.
You might also try a thousand random points in your space, keep the locations of the best few percent of those and try maximizing from each of those locations.
If thinking about your problem in this way is something that is new to you then you might see if you can find a good book on optimization and problem solving. That could give you more ideas on how to attack problems like this.