Mlesd Utility Function Approach 16888 S077 Decision maker has utility function U: R2>R This function might or might not be known mathematically U maps objective vector to the real line MOP:max{(小)J=Cx,x∈S} MNP:ma(y(0)J=(x,x∈S Example 0,0 maxJ=x,+x21 (0,4) maX V2=x s. x3=(3, U=18 4x,+3x,<12 S 、U=24 x,x1≥0 Where U=2J, 12 o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics9 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Utility Function Approach Utility Function Approach Decision maker has utility function This function might or might not be known mathematically U maps objective vector to the real line : z U \ \ → MOLP: MONLP: max , {U S ( ) J J Cx x = ∈ } max , {UfS () () JJ x x = ∈ } (0,0) (0,4) (3,0) = = = 1 2 3 x x x { } { } 112 2 1 1 2 1 2 1 2 max max s.t. 4x 3 12 , 0 where 2 J x x J x x x x U JJ = + = + ≤ ≥ = x 1 x 2 c1 x 2 c 2 x 3 x1 S U=24 U=18 Example: