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

• Jiguan G. Lin
Chapter

## Abstract

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)

## Keywords

Differential Game Positive Weight Positive Vector Equality Constant Maximal Vector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Plenum Press, New York 1976

## Authors and Affiliations

• Jiguan G. Lin
• 1
1. 1.Department of Electrical Engineering & Comp. Sci.Columbia UniversityNew YorkUSA