  Many existing branch and bound algorithms for multiobjective optimization
problems require a significant computational cost to approximate the entire
Pareto optimal solution set. In this paper, we propose a new branch and bound
algorithm that approximates a part of the Pareto optimal solution set by
introducing the additional preference information in the form of ordering
cones. The basic idea is to replace the Pareto dominance induced by the
nonnegative orthant with the cone dominance induced by a larger ordering cone
in the discarding test. In particular, we consider both polyhedral and
non-polyhedral cones, and propose the corresponding cone dominance-based
discarding tests, respectively. In this way, the subboxes that do not contain
efficient solutions with respect to the ordering cone will be removed, even
though they may contain Pareto optimal solutions. We prove the global
convergence of the proposed algorithm. Finally, the proposed algorithm is
applied to a number of test instances as well as to 2- to 5-objective
real-world constrained problems.
