  In multiobjective optimization, most branch and bound algorithms provide the
decision maker with the whole Pareto front, and then decision maker could
select a single solution finally. However, if the number of objectives is
large, the number of candidate solutions may be also large, and it may be
difficult for the decision maker to select the most interesting solution. As we
argue in this paper, the most interesting solutions are the ones whose
trade-offs are bounded. These solutions are usually known as the properly
Pareto optimal solutions. We propose a branch-and-bound-based algorithm to
provide the decision maker with so-called $\epsilon$-properly Pareto optimal
solutions. The discarding test of the algorithm adopts a dominance relation
induced by a convex polyhedral cone instead of the common used Pareto dominance
relation. In this way, the proposed algorithm excludes the subboxes which do
not contain $\epsilon$-properly Pareto optimal solution from further
exploration. We establish the global convergence results of the proposed
algorithm. Finally, the algorithm is applied to benchmark problems as well as
to two real-world optimization problems.
