M esd History (3)-Extension to Engineering 16888 S077 After the translation of Pareto's Manual of political Economy into english Prof Wolfram Stadler of San Francisco state University begins to apply the notion of pareto optimality to the fields of engineering and science in the middle 1970s The applications of multi-objective optimization in engineering design grew over the following decades · References: Stadler, W, "A Survey of Multicriteria Optimization, or the Vector Maximum Problem, Journal of Optimization Theory and Applications, Vol. 29, pp. 1-52, 1979 Stadler, W."Applications of Multicriteria Optimization in Engineering and the Sciences(A Survey), "Multiple Criteria Decision Making Past Decade and Future Trends, ed M. Zeleny, JAl Press Greenwich. Connecticut. 1984 Ralph E. Steuer, " Multicriteria Optimization Theory, Computation and application, 1985 o Massachusetts Institute of Technology-Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
16 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics History (3) History (3) – Extension to Engineering Extension to Engineering • After the translation of Pareto’s Manual of Political Economy into English, Prof. Wolfram Stadler of San Francisco State University begins to apply the notion of Pareto Optimality to the fields of engineering and science in the middle 1970’s. • The applications of multi-objective optimization in engineering design grew over the following decades. • References: – Stadler, W., “A Survey of Multicriteria Optimization, or the Vector Maximum Problem,” Journal of Optimization Theory and Applications, Vol. 29, pp. 1-52, 1979. – Stadler, W. “Applications of Multicriteria Optimization in Engineering and the Sciences (A Survey),” Multiple Criteria Decision Making – Past Decade and Future Trends, ed. M. Zeleny, JAI Press, Greenwich, Connecticut, 1984. – Ralph E. Steuer, “Multicriteria Optimization - Theory, Computation and Application”, 1985
M ed Notation and classification 16888 E5077 Traditionally-single objective constrained optimization maxJ=f(x) f(x)bJ objective function St.X∈S SH feasible region If f(x)linear constraints linear single objective= LP If f(x)linear constraints linear multiple obj = MOLP If f(x and/or constraints nonlinear single obj=NLP If f(x and/or constraints nonlinear& multiple obj =MONLP Ref. Ralph E. Steuer, " Multicriteria Optimization- Theory, Computation and Application, 1985 o Massachusetts Institute of Technology-Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
17 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Notation and Classification Notation and Classification Ref: Ralph E. Steuer, “Multicriteria Optimization - Theory, Computation and Application”, 1985 Traditionally - single objective constrained optimization: max ( ) . . f st S = ∈ - [ [ ( ) objective function feasible region f J S [ 6 6 If f(x) linear & constraints linear & single objective = LP If f(x) linear & constraints linear & multiple obj. = MOLP If f(x) and/or constraints nonlinear & single obj.= NLP If f(x) and/or constraints nonlinear & multiple obj.= MONLP