Soviet Multi-Objective Mathematical Programming Methods: An Overview

Over the past 20--30 years multi-objective mathematical programming (MOMP) has emerged as an increasingly active area of research in the fields of management science, operations research, applied mathematics, and engineering. Despite the intensity of interest, however, earlier surveys of MOMP methods have all but ignored Soviet work in this area. Published in unfamiliar journals and often available only in Russian, the Soviet research has remained virtually unknown outside of the USSR and Eastern Europe. This has been particularly unfortunate given the extent, importance, and originality of much of the Soviet research. The current article attempts to correct this situation by providing a comprehensive, yet nontechnical, overview of Soviet MOMP methods. Using a taxonomy similar to ones that have been applied to Western MOMP techniques, the article categorizes the Soviet methods based on when they involve a decision maker in the solution process---a priori, progressively, a posteriori, or never---and what kind of information the decision maker provides. In all, 17 methods are analyzed with particular attention given to their distinctive features and to the issues of computational feasibility and burden on the decision maker. The article concludes with observations on the overall character of Soviet MOMP research, comparing the general directions in Soviet and Western research.