Trade-off rates in the hyperplane method for multiobjective optimization problems

Recently, as a generalization of the well-known scalarizing methods for characterizing Pareto optimal solutions of multiobjective optimization problems, a fully integrated scalarizing method, called the hyperplane method has been introduced by the authors. In this paper, a meaningful formula which relates the trade-off rates within the Pareto optimal solution set to the Lagrange multipliers of the hyperplane problems is derived by realizing that trade-off information is significantly useful in almost all the interactive multiobjective decision making methods. Moreover, it is shown that such a formula can be regarded as a generalized version of the trade-off rate formulae for all of the well-known scalarizing problems. Finally, various aspects of the results developed in this paper are illustrated by a numerical example.