Searching for Pareto-Optimal Solutions

Abstract

The problem of narrowing the Pareto set is considered. The existing approaches aimed at solving the problem of finding a set of Pareto optimal solutions has been analyzed. One approach for solving multi-objective problems based on complex using methods for the construction of the Pareto optimal set and evidence theory has been proposed in this paper. The proposed technique allows to evaluate the obtained set of non-dominated alternatives by methods of the evidence theory to find the best (optimal) solution. The proposed approach allows us to obtain a more formalized procedure for narrowing the Pareto set to obtaining a single optimal solution (a single-element Pareto set). The use of the mathematical apparatus of the evidence theory makes it possible to model uncertainty in expert or decision makers judgments (the strict requirement of the “unambiguous” preference of one alternative over the other is removed). Using the proportional conflict redistribution rules for aggregating group expert assessments makes it possible to process expert evidence generated under conflicting, contradiction expert information. Numerical examples of the proposed methodology for integrated application of evidence theory and methods for Pareto set construction to find optimal solutions are given. The results obtained make it possible to improve the quality and effectiveness of finding optimal solutions.