Abstract
During the last few years, numerous methods related to multiobjective optimization and decision-making have been proposed. Among them interactive techniques assume that the decision maker (DM) is able to assess his preference on a local level to a particular solution. In order to help the DM express his degree of preference, the trade-off rates information between two objectives is very useful. On the other hand, one of the most powerful methods of generating Pareto optimal solutions is the weighted Tchebycheff norm method. It can be applicable to multiobjective optimization problems involving nonconvexities, but the trade-off rates between the objectives have not been given explicitly. In this paper, we develop the meaningful results which relate the trade-off rates within the Pareto optimal solution set to the Lagrange multipliers and the weighting vectors of the weighted Tchebycheff norm problem. Furthermore, various aspects of the results obtained are illustrated by the numerical example.
