Multiple-criteria Decision-making Support Based on the Multi-Indicator Evaluation of the Pareto-Approximation Quality

Abstract

The paper considers a problem, which is defined as multi-indicator finding the "best" algorithm to solve a multiple-criteria optimization (MCO) problem. Of a large number of known algorithms for solving the MCO, we deal with the algorithms based on the preliminary construction of its Pareto front (set) approximation and called P-algorithms. Because of a large number of P-algorithms, a problem of choosing the "best" algorithm for the given MCO problem (and / or this class of these problems) arises, i.e. a meta-optimization problem. We pose the problem of structural meta-optimization of P-algorithms, which suggests a simultaneous P-approximation construction and optimization of this approximation according to one or several P-indicators. The paper presents basic MCO-problem formulation and describes used P-approximation quality indicators. Considers several methods to choose the "best" P-algorithm such as a method based on using one or another method to visualize multi-indicator estimates of P-approximation quality, a method based on the scalar convolution of P-approximation quality indicators, chosen by a decision-maker (DM), and an author's automated method that supposes a preliminary approximation of the function of preference. Provides mathematical description, considers advantages and disadvantages, as well as shows the ways to overcome these shortcomings. The main research result involves a development of the original PREF-I method to solve the MCO problem based on identification of so-called DM’s function of preference. This method may be thought as evolution of the PREF method aimed at solving the initial MCO problem.