Modification of the interactive multicriterial optimization procedure

Abstract

Based on an analysis of existing approaches to finding a compromise in solving multicriteria optimization problems in which alternatives are not explicitly formulated, an iterative procedure was proposed that should facilitate the process of understanding which course of action in certain specific conditions should be chosen to coordinate local goals, and ensure that upon reaching a compromise solution it will be Pareto-optimal. However, the use of this procedure showed that although awareness of the lines of action that create the prerequisites for obtaining a subjectively better solution does not cause difficulties, it is not without some drawbacks. This is, firstly, determined by the complexity of the choice at each iteration of the specific values of the scale coefficients of matching local criteria and, secondly, the lack of effectiveness of the standard way to eliminate the heterogeneity of individual criteria. The proposed modification of this procedure makes it possible to simplify man-machine interaction aimed at interactively developing one or more compromise solutions acceptable from the point of view of the decision maker by increasing the transparency of the model redeployment method to obtain a new solution and thus ensuring faster progress to a compromise that the decision creator would consider satisfactory enough. This is achieved by using to obtain a new Pareto-optimal solution of a scalar function of the form:

F(x) = ((z*1 – z1)/(z*1 – v*1))p + (ß2(z*2 – z2)/(z*2 – v*2))p +…+ ((z*k – zk)/(z*k – v*k))p,

where z*і is the extreme value of the i-th local criterion (which cannot be achieved if all the subjective requirements are satisfied), zi is the current value of the i-th local criterion, v*i is the desired value of the i-th local criterion, p is a positive integer. In this case, the main way to reconfigure the model in order to obtain a new Pareto optimal solution is to correct one or more values of the vector v* before the subsequent minimization of the function F (x).