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I'm confused with the following topic.

I have a simulator with 3 real parameters as input and 1 real parameter as output. I don't have a function representing the relation between the parameters and the output, and I want to find out the best combination of the three parameters that give the maximum output.

The objective is to do it with few simulations, so my first idea was to use the Genetic Algorithm: Create a population, obtain output and stick with the highest outputs while doing crossover and mutation until X iterations.

The other option is to create a training set and approximate the function (probably by Bayesian Optimization). Then, find the optima. The point is that I don't want to create a lot of training since the simulation is time consuming.

Does it make sense to do GA even though I don't have an explicit objective function?

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In this case the simulator is your function. It is a complicated, noisy, black-box function that you want to optimize. Yes, you can use genetic algorithms, Bayesian optimization, or a number of other derivative-free optimization algorithms to seek for it's optimum. The only problem is how efficient (in terms of speed and precision) would be the algorithm you choose for this particular problem, but I am afraid that the choice of algorithm may be problem-specific. Some algorithms may work better for some cases and worse for others, so you should either look for a literature on problems similar to yours for suggestions, or just check it by trial and error.

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