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I have 132 potential positions in a wind farm layout and I have to place 66 turbines on these positions. I want to know how to make combinations to place these 66 turbines.

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Muhammad Bin
Muhammad Bin on 17 Jul 2021
Commented: David Goodmanson on 29 Jul 2021
My wind farm dimension is 11220X1360 and it is divided into grids with dimensions 340X340. There are 132 potential positions for 66 turbines in them. How to determine the ways in which they can be placed on 132 positions?
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David Goodmanson
David Goodmanson on 29 Jul 2021
Walter is correct, I forgot to add 1 when converting the gamma function to a factorial. A couple of previous comments are modified accordingly.

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Answers (1)

Jan
Jan on 17 Jul 2021
Edited: Jan on 17 Jul 2021
The notes of dpb and David mean, that the number of possible solutions is too large to be useful, if you want to test all of them. In your case testing all 132 over 66 solutions would take many years.
So you have to concentrate on a small subset. There are different ways to find "good" solutions in a huge set, e.g. randomly:
pos = randperm(1:132, 66);
Other methods of global optimizations allows to improve solutions iteratively from different starting points. This does not require to check all possible solutions, but to find a sufficiently good solution in a bearable amount of time.
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Walter Roberson
Walter Roberson on 18 Jul 2021
"I bet I could get there in one day, if I didn't sleep!"
(Will anyone else know what this refers to? Will I still know what this refers to a year from now?)

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