Interactive reference direction approach using implicit parametrization for nonlinear multiobjective optimization

A method for solving nonlinear multiobjective optimization problems is presented. In this interactive method, the dialog with a decision maker takes place in terms of desirable aspiration levels forming a reference point in the objective function space. In the computation phase, a lexicographic subproblem is used to generate a desired number of nondominated solutions. Thus, the decision maker can direct the interactive solution process both by specifying reference points and by setting the number of new solutions to be generated at each iteration. The proposed method gives the decision maker a possibility to investigate any part of the whole nondominated set according to his/her preferences and emphasizes learning possibilities. The functioning of the method is illustrated with a numerical example.