I have the following problem, there is an objective function f() depending on 7 variables x=(x1,x2,...x7), so f(x)=f((x1,x2,...x7)) and I want to find the combination of variables that minimize the objective function (x* for which f(x*) is minimum). The formula of the objective function is unknown. The problem is that the evaluation of objective function for a given point x, f(x), is difficult and requires running of a simulation software that can take time and computational resources so I want to do as few estimations of f() as possible. Which method/algorithm do you think would be most suitable here? What about Monte Carlo stochastic optimization?
I will add here more details about the objective function - this is a result of a simulation software called MIKE11 that models flow of water in rivers. The model of the river is 1D and the user's manual says that the equations used for the hydrodynamic part are Saint Venant equations. Now the objective function represents the maximum flow (in cubic meters per second) on a point on the river. And I want to minimize the objetive function (so I want the minimum of the maximum flow values). So to estimate the objetive function for the x vector of parameters I have to run one MIKE simulation.