Multiple objectives using blocking constraints

[speedfreeman]

The guidance for solving multiple lexicographically ordered objectives seems to be:

Call the solver to obtain solution s for the optimal value v of objective i
Add a constraint that objective i == v
Add s as a solution hint
Repeat for objective i+1

But what about not adding a solution hint for s but instead adding a constraint to block s? If the solver returns infeasible for anything other than the first objective, then, of the solutions obtained so far, those that are best for all objectives must also be optimal for objectives i+1 to n?

[lperron]

you can. It is just harder for the solver at each iterations as the model is bigger (less fixed variables).