Optimization through machine learning

Question

I've got a system that takes 15 points out of a 17 by 17 grid as input (order doesn't matter), and generates a single scalar as output. The system is not representable by a formal function.

The goal is to find the optimal 15 points so that the output scalar is minimum. Solving this problem exhaustively simply takes too much time to be practical as each run takes 14 seconds.

I've started taking a machine learning course online. But this problem does seem to be rather unsophisticated and I wonder if anyone can point me to the right direction. Any help is greatly appreciated!

Answer 1

Use simulated annealing. I guess this will be close to optimal here.

Therefore, start with a random distribution of the 15 points. Then, in each iteration change one and accept the new state if the resulting scalar value is lower. If it is larger, accept with a certain probability (a Boltzmann factor). Eventually you have to try this for a small number of randomly chosen initial states and afterwards accept the lowest value.