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MITESD_77S10_lec15

MITESD_77S10_lec15 - Multidisciplinary System Design...

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1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary System Design Optimization (MSDO) Multiobjective Optimization (II) Lecture 15 Dr. Anas Alfaris

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2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics MOO 2 Lecture Outline • Direct Pareto Front (PF) Calculation Normal Boundary Intersection (NBI) • Adaptive Weighted Sum (AWS) • Multiobjective Heuristic Programming • Utility Function Optimization • n-KKT • Applications
3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Direct Pareto Front Calculation SOO: find x* MOO: find PF PF J 1 J 2 PF J 1 J 2 bad good - It must have the ability to capture all Pareto points - Scaling mismatch between objective manageable - An even distribution of the input parameters (weights) should result in an even distribution of solutions A good method is Normal-Boundary-Intersection (NBI)

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4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Normal Boundary Intersection (1) J 1 J 2 J 1 J 2 J 1 J 2 Carry out single objective optimization: Find utopia point: U – Utopia Line between anchor points, NU – normal to Utopia line Move NU from to in even increments Carry out a series of optimizations Find Pareto point for each NU setting * 1 J * 2 J * 1,2,. .., ii J J i z i* x Goal: Generate Pareto points that are well-distributed * 1 J * 2 J * 1 J * 2 J * 1 J * 2 J 12 T z J J J u 1* 2* z* J x x x
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Normal Boundary Intersection (2) Yields remarkably even distribution of Pareto points Applies for z>2, U-line becomes a Utopia- hyperplane. If boundary is sufficiently concave then the points found may not be Pareto Optimal. A Pareto filtering will be required. Reference: Das I. and Dennis J, “Normal-Boundary Intersection: A New Method for Generating Pareto Optimal Points in Multicriteria Optimization Problems”, SIAM Journal on Optimization, Vol. 8, No.3, 1998, pp. 631-657

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6 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Adaptive Weighted Sum Method for Bi-objective Optimization References: Kim I.Y. and de Weck O.L., “Adaptive weighted-sum method for bi-objective optimization: Pareto front generation”, Structural and Multidisciplinary Optimization , 29 (2), 149-158, February 2005 Kim I.Y. and de Weck, O., “Adaptive weighted sum method for multi- objective optimization: a new method for Pareto front generation”, Structural and Multidisciplinary Optimization , 31 (2), 105-116, February 2006
7 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics

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MITESD_77S10_lec15 - Multidisciplinary System Design...

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