find out the best combination within all possible combinations using optimization technique

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Kim NamHoon
Kim NamHoon 2020-8-11
Dear all.
In general optimization problem, we just try to find out the best solution in accordance with the initial condition.
But, some problems face to consider all possible combinations and find out the best combination among them.
My question is that when I use the genetic algorithm (ga) or other optimization technique, is there any chance to find the optimal solution within the candidate solutions?
Actually, I solved this kind of problem using "nchoosek" and find the optimal solution with min(mse). *mse: mean square error
But, when n is too large (large search space), it's very hard to reflect all the possible solutions.
For example, I have 25 uniform points and find out the best 10 points combinations (see attached below figure).
In this case, I have to consider all possible combination using nchoosek(1:25,10). But, I have 3,268,760 possible combinations and it has heavy computation cost....
So, I try to solve such problem using some kind of optimization technique like below example:
ex) find the best 10 points combination within 25 points array
obj_fun = @(x) objective_function
[x_opt,fval] = ga(obj_fun,10,[],[],[],[],lb,ub,[],[],[]);
I think that we can do optimization with all possible combinations as inputs using above very simple code.
If there is any technical solution to solve such kind of problem reflecting above code or other things, please give some comments.
Thank you for your help in advance.
Best regard.

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