Generalized Interactive Algorithm of Multicriteria Optimization*

In the interactive algorithms for multicriteria optimization the decision maker (DM) may express his/her preferences among the separate Pareto optimal solutions with the help of the values of the scalarizing problem parameters. The DM must choose the final (most preferred) solution and be responsible for this selection. The interactive methods are the best developed and wide spread methods. This is due to the following advantages:  a small part of the Pareto optimal solutions is generated and evaluated by the DM;  the DM has the possibility to learn with respect to the problem during the process of multicriteria problem solving;  the DM may change (correct) his/her preferences in the process of the multicriteria problem solving;  the DM feels more confident in his/her preferences concerning the final solution of the multicriteria problem. The interactive algorithms developed for solving multicriteria optimization problems are characterized by the following features:  each interactive method is designed for the solving of a given type of problems – linear, nonlinear, integer, etc.; each interactive method is built on the basis of a certain type of scalarizing problem and possesses the specific features of this problem, connected with the possibilities for setting DM’s preferences as well as the type and time for obtaining the currently preferred Pareto optimal solution; the larger part of the interactive algorithms are algorithms, oriented towards learning, and this means that the DM controls the process of the multicriteria problem solving;