M 16888 S077 Multidisciplinary System Design Optimization(MSDO) Multiobjective Optimization ( ecture 16 31 March 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 (I) Lecture 16 31 March 2004 by Prof. Olivier de Weck
M Where in Framework 16888 E077 Objective Vector Discipline A Discipline B Discipline c Coupling Multiobjective Optimization Approx Optimization Algorithms Methods Numerical Techniques Sensitivit Tradespace (direct and penalty methods Analysis Exploration Heuristic Techniques Coupling (DOE) SA, GA, Tabu Search) performance o Massachusetts Institute of Technology -Prof. de Weck and Prof. Willco 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 Where in Framework ? Where in Framework ? Discipline A Discipline B Discipline C nI put Ou pt ut Tradespace Exploration (DOE) Optimization Algorithms Numerical Techniques (direct and penalty methods) Heuristic Techniques (SA,GA, Tabu Search) 1 2 n x x x ª º « » « » « » « » « » ¬ ¼ # Coupling 1 2 z J J J ª º « » « » « » « » « » ¬ ¼ # Approximation Methods Coupling Sensitivity Analysis Multiobjective Optimization Isoperformance Objective Vector
M Lecture content 16888 E5077 Why multiobjective optimization? EXample-twin peaks optimization History of multiobjective optimization Weighted Sum Approach(Convex Combination Dominance and Pareto-Optimality Pareto Front Computation -NBI 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 Lecture Content Lecture Content • Why multiobjective optimization? • Example – twin peaks optimization • History of multiobjective optimization • Weighted Sum Approach (Convex Combination) • Dominance and Pareto-Optimality • Pareto Front Computation - NBI
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 Astronautics
4 © 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[ [
M Multiple objectives 16888 S077 The objective can be a vector j of z system responses or characteristics we are trying to maximize or minimize cost Often the objective is a scalar function but for range [km]I real systems often we attempt multi-objective J 3 weight[kg] optimization JiI-data rate [bps XHJX) Objectives are usually ROi[% conflicting o Massachusetts Institute of Technology -Prof. de Weck and Prof. Willco 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 Multiple Objectives Multiple Objectives 1 2 3 cost [$] - ran ge [km] wei ght [k g ] - data rate [bps] - ROI [%] i z J J J J J ª º ª º « » « » « » « » « » « » = = « » « » « » « » « » « » « » « » « » ¬ ¼ ¬ ¼ - # # The objective can be a vector J of z system responses or characteristics we are trying to maximize or minimize Often the objective is a scalar function, but for real systems often we attempt multi-objective optimization: [ - [ 6 Objectives are usually conflicting
M esd Why multiobjective optimization 16888 E5077 While multidisciplinary design can be associated with the traditional disciplines such as aerodynamics, propulsion structures, and controls there are also the lifecycle areas of manufacturability, supportability, and cost which require consideration After all, it is the balanced design with equal or weighted treatment of performance, cost, manufacturability and supportability which has to be the ultimate goal of multidisciplinary system design optimization Design attempts to satisfy multiple, possibly conflicting objectives at once o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
6 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Why multiobjective optimization ? Why multiobjective optimization ? While multidisciplinary design can be associated with the traditional disciplines such as aerodynamics, propulsion, structures, and controls there are also the lifecycle areas of manufacturability, supportability, and cost which require consideration. After all, it is the balanced design with equal or weighted treatment of performance, cost, manufacturability and supportability which has to be the ultimate goal of multidisciplinary system design optimization. Design attempts to satisfy multiple, possibly conflicting objectives at once
M Example FlA-18 Aircraft 16888 E5077 Design Objectives Decisions Speed Aspect Ratio Range Dihedral angle Payload Capability Vertical Tail Area Radar Cross section Engine Thrust Stall Speed Skin Thickness Stowed Volume of engines Fuselage splices Acquisition cost Suspension Points Cost/Flight hour ocation of mission MTBF Computer Engine swap time Access door Assembly hours ocations Avionics growth Potential massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
7 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Example F/A Example F/A-18 Aircraft 18 Aircraft Design Decisions Objectives Aspect Ratio Dihedral Angle Vertical Tail Area Engine Thrust Skin Thickness # of Engines Fuselage Splices Suspension Points Location of Mission Computer Access Door Locations Speed Range Payload Capability Radar Cross Section Stall Speed Stowed Volume Acquisition cost Cost/Flight hour MTBF Engine swap time Assembly hours Avionics growth Potential
M Multiobjective Examples 16888 E5077 Aircraft Design max rangel max passenger volume Design max payload massy Optimization min (specific fuel consumption] max(cruise speedy min lifecycle cost Production Planning max total net revenuel Operations max(min net revenue in any time period Research min backorders min overtime) min finished goods inventory o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
8 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multiobjective Examples Multiobjective Examples Production Planning max {total net revenue} max {min net revenue in any time period} min {backorders} min {overtime} min {finished goods inventory} Aircraft Design max {range} max {passenger volume} max {payload mass} min {specific fuel consumption} max {cruise speed} min {lifecycle cost} 1 2 z J J J ª º « » = « » « » « » ¬ ¼ - Design # Optimization Operations Research
M esd Multiobjective vs. Multidisciplinary E:D:71 Multiobjective Optimization Optimizing conflicting objectives e.g., Cost, Mass, Deformation Issues: Form Objective Function that represents designer preference! Methods used to date are largely primitive Multidisciplinary Design Optimization Optimization involves several disciplines e.g. Structures, Control, Aero, Manufacturing Issues: Human and computational infrastructure, cultural administrative, communication, software, computing time, methods All optimization is or should be) multiobjective Minimizing mass alone, as is often done, is problematic o Massachusetts Institute of Technology -Prof. de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
9 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multiobjective vs. Multidisciplinary Multiobjective vs. Multidisciplinary • Multiobjective Optimization – Optimizing conflicting objectives – e.g., Cost, Mass, Deformation – Issues: Form Objective Function that represents designer preference! Methods used to date are largely primitive. • Multidisciplinary Design Optimization – Optimization involves several disciplines – e.g. Structures, Control, Aero, Manufacturing – Issues: Human and computational infrastructure, cultural, administrative, communication, software, computing time, methods • All optimization is (or should be) multiobjective – Minimizing mass alone, as is often done, is problematic
M esd Multidisciplinary VS. Multiobjective 16888 S077 single discipline multiple dIsciplines >50 cantilever beam support bracket m F Minimize stamping o①c ,8 costs(mfg) subject to loading and geometry Minimize displacement D constraint U s t. mass and loading constraint single discipline multiple disciplines airfoil commercial aircraft fuel Maximize C,/Cn and maximize ImagetakenfromNasa'swebsitehttp://www.nasa.gov E wing fuel volume for specified a, Minimize sfc and maximize cruise speed s t fixed range and payload o Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
10 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary vs. Multiobjective Multidisciplinary vs. Multiobjective single discipline multiple disciplines single objective multiple obj. single discipline multiple disciplines Minimize displacement s.t. mass and loading constraint F l δ m cantilever beam support bracket Minimize stamping costs (mfg) subject to loading and geometry constraint F D $ airfoil α (x,y) Maximize C L/C D and maximize wing fuel volume for specified α, vo Vfuel vo Minimize SFC and maximize cruise speed s.t. fixed range and payload commercial aircraft Image taken from NASA's website. http://www.nasa.gov
