Suppose a MILP model includes the following constraint:
$ \begin{gather*} B_{1} + B_{2} + B_{3} \le 100 \end{gather*} $, where $B_{1},B_{2},B_{3}$ are nonnegative reals.
Suppose that
$\begin{gather*} (B_{1},B_{2},B_{3}) = (10,30,60) \\ (B_{1},B_{2},B_{3}) = (20,60,20)\\ (B_{1},B_{2},B_{3}) = (80,10,10) \\ (B_{1},B_{2},B_{3}) = (60,10,10) \\ \cdots \end{gather*} $
are optimal solution vectors.
Is there a way to tell the solver to prefer one of these solution vectors over the others? For example, is it possible to formulate a constraint that tells the solver to prefer an optimal solution with increasing values (if it exists?)?
Edit
I think I need to clarify the purpose of the approach I am looking for. The purpose is not really to find a "preferred" solution but to help the B&B to get faster to the optimal solution by cutting off solutions that have the same value as the "preferred". So I don't want to determine all alternative solutions and then choose one, I want to get as fast as possible to a solution.
Adding constraints $B_{1} \le B_{2} \le B_{3} ... $ would help if I knew that there exists an optimal solution that satisfies these constraints, but I don't know this.