Using integer programming to find a solution without optimizing it Oftentimes I find myself wanting to use integer programming to find a solution to a particular problem, without caring about optimizing a certain variable at all.

I've found that most packages that offer integer programming do not provide this feature.

Is it then correct to assume that maximizing/minimizing a solution is no harder than just finding any solution?

If yes, does it matter what variable you choose to optimize for (considering you really do not care either way)?

If not, why do packages almost never offer to only solve rather than optimize?
There is at most a pseudo-logarithmic gap between the complexity of optimization and simply finding a feasible solution.
We can turn any optimization problem into a feasibility problem by simply adding the optimality expression to the inequalities with some value $C$, and using binary search to find the optimal $C$.