Discrete integers function optimization ?
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Hi everyone,
I was wondering what is the best method or optimization tool i can use for a optimization of a function which it's variables are discrete integers ?
I already used a metaheuristic method (PSO), so i was wondering if there are other method (mathematically) can be used in such kind of optimization problems ?
The problem include constraints such as a check function to test the feasibility of the solution but it's in other file than the main objective function file.
I already saw a similar question and the answer was using GA optimization tool, but i can't use it since it falls in the same category of heuristic methods which i previously mentioned that i used one of them (PSO).
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Walter Roberson
2019-6-7
1 个投票
In the situation where all of the variables are discrete values, you can just try all of the possible combinations of values. This might take a while...
In the situation where the function is linear, then you can use https://www.mathworks.com/help/optim/ug/intlinprog.html
In some cases there are analytic approaches that can reduce the search space, if you have the Symbolic Toolbox and do a bunch of programming yourself. You find the derivative and solve for the zeros of that, which gives the locations of the extrema in continuous coordinates. You take the second derivative and substitute the locations into that and look at the sign() of that value in order to determine which kind of extrema you have. This gives you some information that can be used to partition the search space according to which extrema any given point is closest to. Now you can evaluate for all discrete points in the catch basins of the minima in order to find the local minima in discrete terms. By examining the local gradient, you could potentially also eliminate some of the searching.
6 个评论
hossam eldakroury
2019-6-14
Walter Roberson
2019-6-14
Which part do you need done step by step?
I am not going to go through the analytic approach; it would need a bit of development work, and figuring out how to partition the basins of attractions properly in the general case could be difficult. Possibly for certain kinds of functions it might not be bad.
The constraints would possibly be handled by solving each one with regards to some variable, and then substituting for that variable in the original functions, getting out a more complicated function of fewer variables that automatically satisfies the constraints (other than the integer restriction.)
https://www.mathworks.com/matlabcentral/fileexchange/35720-minlp-mixed-integer-nonlinear-programming
And an ACO based one:
hossam eldakroury
2019-6-21
Walter Roberson
2019-6-21
"So will (intlinprog) be usfel if my x variables is a string of discrete integers decisions ?"
Yes.
"and they are all unique"
That could be the tricky part to write in terms of linear constraints.
"something like travelling salesman problem."
Are the values just present / not present? Or are they ordered?
If the values are just present / not present, then uniqueness becomes trivial and exactly 15 out of 133 is easy enough to implement. But if they are ordered and also unique then I need to consider more about how that could be implemented.
hossam eldakroury
2019-6-22
Usman Bashir Tayab
2023-2-15
Hi Hossam,
Please can you share PSO codes for discrete integers variables. As I need to implement discrete integers variables using PSO for my problem.
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