M 16888 S077 Multidisciplinary System Design Optimization(MSDO) Multiobjective Optimization () ecture 17 Apri5,2004 Prof. olivier de Weck o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary System Multidisciplinary System Design Optimization (MSDO) Design Optimization (MSDO) Multiobjective Optimization (II) Lecture 17 April 5, 2004 by Prof. Olivier de Weck
M Moo 2 Lecture Outline 16888 E5077 Lecture 2(today) Alternatives to Weighted Sum(WS) Approach Multiobjective Heuristic Programming Utility function Optimization Physical Programming(Prof Messac Application to Space System Optimization Lab preview Friday 4-9-2003- Section 1) o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics MOO 2 Lecture Outline MOO 2 Lecture Outline Lecture 2 (today) • Alternatives to Weighted Sum (WS) Approach • Multiobjective Heuristic Programming • Utility Function Optimization • Physical Programming (Prof. Messac) • Application to Space System Optimization • Lab Preview (Friday 4-9-2003 – Section 1)
Mlesd Weighted Sum(WS)Approach 50.1 Min J2) MO ∑ miss this i =1 S concave region convert back to sop LP in J-space easy to implement > Pareto scaling important front weighting determines 0 Which point along pf is J-hyperplane utopia found misses concave PF Max(J1) o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Weighted Sum (WS) Approach Weighted Sum (WS) Approach 1 z i MO i i i w J J = sf = ¦ utopia Max( J 1 ) Min( J 2 ) miss this concave region Pareto front • convert back to SOP • LP in J-space • easy to implement • scaling important ! • weighting determines which point along PF is found • misses concave PF w 2>w1 w1>w 2 J-hyperplane J*i J*i+1
MIlesd Weighted Square Sum Approach齡别 J=w1J12+w2 Obj Fun. Line Ref: messac J2 o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Weighted Square Sum Approach Weighted Square Sum Approach 2 2 11 2 2 J = + wJ wJ Obj. Fun. Line J1 J2 Ref: Messac
MIlesd Compromise Programming(CP)E5., J=W,,twJ Obj. Fun. Line This allows “ access" to the non-convex part of the pAreto front 3 5 6 55 Obiective 1 o Massachusetts istitute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Compromise Programming (CP) Compromise Programming (CP) Obj. Fun. Line 11 2 2 n n J wJ wJ = + 55 This allows “access” to the non-convex part of the Pareto front