Multiple-objective problems: Pareto-optimal solutions by method of proper equality constraints

The method of proper equality constraints for obtaining the set
P
of all Pareto-optimal solutions of a general multiple-objective problem and the set
M
of all performance index vectors attainable by the Pareto-optimal solutions is presented in this paper. These sets are very useful for those designers, performance analyzers, control agents, and decision makers who are faced with multiple objectives to make appropriate compromises, tradeoffs or choices. That this method is effective for general applications is clearly demonstrated by examples with various kinds of complexity. New necessary and sufficient conditions for Pareto optimality, local Pareto optimality, and local maximal index vectors are also presented. These conditions and the method are useful for both computation and analysis. New observations on a generalized classical Pareto-optimum problem are thereby obtained.