Can we improve solution time when integer variables are determined by continuous variables?
AnsweredIf we have a mixed integer linear program over continuous variables X and discrete (say, binary) variables Y, where we know that for almost all fixed X there exists at most one feasible Y, can we tell that to Gurobi somehow? Would it improve optimization time? What about if we only want to solve the feasibility problem?
Thank you!

Hello Daniel,
I do not think that in general one can exploit this information the uniqueness of continuous portion of the solution as a function of discrete variables' values to speed up the solution process. If possible, I would rather experiment with several alternative model formulations instead, to see if one formulation could be computationally superior to another.
Regards,
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One more quick addition to the above, Daniel.
It may also be the case that placing more emphasis on branching during the solve could be beneficial here. So, you may consider adding branchPriorities for some (important) binary variables, https://www.gurobi.com/documentation/9.0/refman/branchpriority.html
and reducing the importance off cuts, https://www.gurobi.com/documentation/9.0/refman/cuts.html
but without experimenting it is really impossible to predict the outcome.
Regards.
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