I need to solve an optimization problem, maximizing fitness in a set of around 1 million solutions. Calculating the fitness of any solution is very time consuming, taking around 5 minutes. Therefore, I am only able to calculate the fitness of 100 solutions per run. Each solution is represented by vector in ten dimensions with real values [0..1], such that two similar vectors represent similar solutions and should have similar fitness.
Obviously I have no expectation of finding a solution that is anywhere near optimal, but is there a preferred method for AI search when you're only able to test the fitness of very few solutions? I get the feeling that I'm missing one or two keywords that would point my search in the right direction.
I'm considering calculus-based search as one option, as it's better to find a local maxima than just randomly search the space and not find any good solutions whatsoever.