How can I vary a vector's element order in an optimization routine?

I am trying to set up an optimization routine which will take a vector, say, [0, 10, 20, 30, 40], and vary the element order in order to minimize a function. To illustrate, potential options could be [40, 30, 20, 10, 0] or [20, 40, 30, 10, 0]. The vector elements will be provided by myself, and to be clear, I don't want the values to change, I just want to vary the order.

The function I'm trying to minimize is nonlinear.

There may be a simple way to do this, but at the moment I'm having trouble with the implementation. If it helps, I have access to both the standard and global optimization toolboxes.

I really appreciate any ideas that you all may have on the matter.

Answer 1

[Torsten]

Use "perms" if the vector length is not that big (<=10).

Best wishes

Torsten.

[Gary]

Thank you for the tip! However, I don't think that actually helps me out here, as running through all the different permutations would defeat the point of the optimization algorithm.

Hypothetically, if my vector length was 5, I could imagine setting the optimization up with upper and lower bounds of [1,5] for each element, and then having it vary that way. I would have a separate function which assigns the element order based on the selection, and I would just need a way of ensuring they don't ever share a position. Perhaps a constraint could enforce this - I'm thinking on that at the moment.