M Multiobjective Optimization Problem.888 S077 Formal Definition Design problem may be formulated as a problem of Nonlinear programming(NLP). When Multiple objectives(criteria) are present we have a MONLP minJ(x, P) wheJ=[(x)…J:( s.g(x,p)≤0 X h(x, p) g =g1(x)…gn(x) m1 i LB UB X o Massachusetts Institute of Technology -Prof. de Weck and Prof. Willco Engineering Systems Division and Dept of Aeronautics and Astronautics4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multiobjective Optimization Problem Multiobjective Optimization Problem Formal Definition Formal Definition ( ) , , 1, ..., ) min , s.t. , 0 , =0 ( i LB i i UB x xx i n = ≤ ≤ ≤ - [S J[ S K[ S Design problem may be formulated as a problem of Nonlinear Programming (NLP). When Multiple objectives (criteria) are present we have a MONLP () () [ ] 1 2 1 1 1 1 where () () () () = ª º ¬ ¼ = = ª º ¬ ¼ = ª º ¬ ¼ " " " " " T z T i n T m T m J J x x x g g h h -[ [ [ J[ [ K[ [