Tradeoff directions in multiobjective optimization problems

Multiobjective optimization problems (MOP) typically have conflicting objectives wherein a gain in one objective is at the expense of another. Tradeoff directions, which measure the change in some objectives relative to changes in others, provide important information as to the best direction of improvement from the current solution. In this paper we present a general definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs at every Pareto optimal point of a convex MOP. This extends current definitions of tradeoffs which assume certain conditions on the feasible set and the objective functions. Two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods used to calculate them.