I'm running an experiment consists in setting voltages on a set of 4 gates in an electronic device, and performing a measurement that will return a probability of success. My goal is to set the gates to a specific value that maximises the probability of success.
I can make a good initial estimate of the gate voltages I need, but I would then like to optimise over a bounded range of gate space, to maximise the probability of success.
The main issue that even though the 4D parameter space is not so large (average step in parameters is 1/10 of the bounded range), the measurement is very slow (~5 seconds), so going through the entire space by brute force will take too long.
So I am looking for an optimisation algorithm to do a more efficient walk through my gate voltage space and find the maximum success probability from my experiment.
Crude possible answer. Your "$1/10$ of the range" for step size for each parameter means a brute force search would require $10^4$ experiments. You could consider a local search algorithm that evaluates at the $3^4 = 81$ points that divide each parameter interval in quarters. Then look near the single point that offers the maximum so far. That might reduce the number of measurements from ten thousand to some hundreds.
Whether a strategy like this is likely to find a value at (or near) the maximum depends on how regular/convex the objective function is. If it actually has a single maximum at the top of a single hill you will be close. If it oscillates a lot as a function of parameter values you are out of luck.
Edit. Actually, brute force would call for $11^4$ evaluations since you want to check at the boundary points too. That makes this a fence post problem. But the essence of my suggestion is unchanged.