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This talk gives an overview of multi-objective optimization problems(MOPs)and their applications.We then review the methods for MOPs and point out the need for efficient methods for global solutions of moderate to high dimensional MOPs.The cell mapping methods,originally developed by C.S.Hsu of UC Berkeley for global analysis of nonlinear dynamical systems,are introduced for MOPs.Concepts of cell mappings are discussed.Several implementations of cell mapping methods are discussed for obtaining global optimal solutions of MOPs.Examples are presented including benchmark mathematical optimization problems,and optimal designs of feedback controls and fractional damping.