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Hi. Just my thoughts. Solver using a "Not Equal to" is not usually implemented due to limits.
If you have such a constraint, it usually indicates your model can be implemented differently.
For Example, x <> 5.
This means that a value of 4.999 is acceptable.
So is 4.9999999... etc
These are all valid, but for all practical purposes, it is close to 5.
So, in general, it's not really feasible to use <> in a optimization problem without resorting to other techniques.