I've created a R model that estimates the admixture of 220 populations. I let the simulations run for randomly chosen parameters and recorded the parameter values as well as the residual sum of squares (RSS). Now I'd like to estimate under which parameter values the residual sum of squares may be minimal.
My model is based on 4 parameters and takes about 40 seconds for one run. In order to generate a reliable data set for the optimization I already generated 15,000 runs. But unfortunately I don't know how the response surface function, RSS = f(p1,p2,p3,p4), may look like. Thus, I either need to estimate it first or need to use other optimization procedures.
An example data set of what I have may look like this:
params <- cbind(runif(1000, 0, 0.8), runif(1000, 0, 0.8), runif(1000, -0.5, 0.5), runif(1000, -0.5, 0.5))
data <- cbind(params, (params[,1]*params[,2] + params[,3] + params[,4])^2)
colnames(data) <- c("parameter 1", "parameter 2", "parameter 3", "parameter 4", "RSS")
However, remember that I don't know the relation between the response variable and the 4 parameters (although I've assumed a linear relationship in the example data above).
To summarize my request: I'm looking for a method that estimates optimal values for the 4 parameters which minimize the residual sum of square of the model.
Thanks a lot in advance!
