On a particular case of the multi-criteria unconstrained optimization problem

We consider the three-criteria unconstrained optimization problem with two binary criteria coefficients, which is a special case of the multi-criteria unconstrained optimization problem. We propose a polynomial-time greedy algorithm to find the non-dominated set. Moreover, we show that the efficient set is connected with respect to a combinatorial notion of neighborhood. This is the first positive and non-trivial result of connectedness in multi-criteria combinatorial optimization.