The Use of Reference Objectives in Multiobjective Optimization

SummaryThe paper presents a survey of known results and some new developments in the use of reference objectives—that is, any reasonable or desirable point in the objective space—instead of weighting coefficients or utility (value) functions in multiobjective optimization. The main conclusions are as follows: Any point in the objective space—no matter whether it is attainable or not, ideal or not—can be used instead of weighting coefficients to derive scalarizing functions which have minima at Pareto points only. Moreover, entire basic theory of multiobjective optimization--necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, etc.—can be developed with the help of reference objectives instead of weighting coefficients or utility (value) functions. Reference objectives are very practical means for solving a number of problems such as Pareto-optimality testing, scanning the set of Pareto-optimal solutions, computer-man interactive solving of multiobjective problems, group assessment of solutions of multiobjective optimization or cooperative game problems, or solving dynamic multiobjective optimization problems.