Use of Convex Cones in Interactive Multiple Objective Decision Making

One approach for solving decision problems involving multiple objectives is interactive optimization. Methods based on this approach assess the decision maker’s preference structure interactively, typically based on pairwise comparisons and tradeoffs, and guide the search process toward identifying improved solutions. A desirable feature of such approaches, that is based on minimizing the preference information requirements, is fast convergence. Toward this end, the use of convex cones as a preference structure representation has been proposed in the literature. In this work, new theory is developed that aids in further reducing preference information requirements and improving convergence. New cones termed p cones are developed. The efficiencies of solution alternatives are evaluated with respect to the p cones, and these are termed p cone efficiencies. Acceleration and Early Termination procedures that are based on these efficiencies are proposed. The procedures are presented within a solution framework for solving Multiple Objective Linear Programming (MOLP) problems along with computational results.