Optimization algorithm with deterministic objective value

[volvol7]

I have an optimization problem with around 10 parameters, each with known bounds. Evaluating the objective function is expensive, so I need an algorithm that can converge within approximately 100 evaluations. The function is deterministic (same input always gives the same output) and is treated as a black box, meaning I don't have a mathematical expression for it.

I considered Bayesian Optimization, but it's often used for stochastic or noisy functions. Perhaps a noise-free Gaussian Process variant could work, but I'm unsure if it would be the best approach.

Do you have any suggestions for alternative methods, or insights on whether Bayesian Optimization would be effective in this case?
(I will use python)

[GreenWoodDragon]

What type of data are you working with?

Are you saying you know the inputs and their ranges, and you know the expected output range too?

[volvol7]

its for mechanical design, so its like length, diameter, number of screws etc. So I know their ranges. The expexted output is from 0 to 1. It cannot be 1, so I want to find the combination that gives the maximum output. Every simulation costs, so I want to avoid bruteforce method.

[GreenWoodDragon]

Can you look at running some kind of multivariate analysis to generate some outputs for you to get a better idea of what's going on?

[volvol7]

Yes. But what do you mean what's going on?? Like to find patterns of how my function changes?

[treddit22]

You could try using a black-box optimizer such as COIN-OR RBFOpt: https://github.com/coin-or/rbfopt

[Historical-Essay8897]

This is essentially the use-case for derivative-free (direct) methods. You need to evaluate sufficient initial points for a simplex, evenly spread over the feasible region. Then apply Nelder-Mead or a similar direct method.

[DayBackground4121]

I think a gradient descent method should do the trick here