The Use of Reference Objectives in Multiobjective Optimization - Theoretical Implications and Practical Experience

Abstract

The 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 in multiobjective optimization. The main conclusions are as follows: 
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\n(1) 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 functions. 
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\n(2) 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.