Three Methods for Determining Pareto-Optimal Solutions of Multiple-Objective Problems

Typical problems in system design, decision making, decentralized control, etc., and most multi-person games bear the following general formulation of multiple-objective (MO) optimization problems: $${\text{maximize }}{{\text{z}}_{\text{1}}} = {{\text{J}}_{\text{1}}}\left( {{{\text{x}}_1}, \ldots ,{{\text{x}}_{\text{n}}}} \right), \ldots ,\,\,{\text{and}}\,{{\text{z}}_{\text{N}}} = {{\text{J}}_{\text{N}}}\left( {{{\text{x}}_{\text{1}}}, \ldots ,{{\text{x}}_{\text{n}}}} \right)\,{\text{subject to }}\left( {{{\text{x}}_1}, \ldots ,{{\text{x}}_{\text{n}}}} \right) \in {\text{X}}{\text{.}}$$ (1)

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