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Multidisciplinary System Design Optimization >> Content Detail



Lecture Notes



Lecture Notes

Special software is required to use some of the files in this section: .xls.


SES #TOPICSLECTURE NOTES
Module 1: Problem Formulation and Setup
1Introduction to Multidisciplinary System Design Optimization

Course Administration, Learning Objectives, Importance of MSDO for Engineering Systems, "Dairy Farm" Sample Problems
(PDF - 1.8 MB)
2Open Lab
3Problem Formulation

Definitions, Mathematical Notation, Introduction of Design Variables, Parameters, Constraints, Objectives

Formal Optimal Design Problem Definition

Distinction between Simulation Model and Optimizer

Active Learning Exercise: In Class Role Play (Student Groups) to Find Problem Formulation for a Range of Complex Systems/Products
(PDF)
4Modeling and Simulation (iSIGHT CD-ROM handed out)

Design Variable -> Objective Mapping, Simulation Module Identification, Physics-based Modeling (Governing Equations) vs. Empirical Modeling, N2 Diagrams and Design Structure-Matrices (DSM), Model Fidelity and Benchmarking, Modeling Environments, Runtime Reduction Strategies

Active Learning: Find N2 Diagram for Communication Satellite
(PDF)
5Lab 1: Introduction to Optimization
6Decomposition and Coupling

Task Sequencing, Parallelization, Simcode-optimizer Coupling, Process Integration and Design Optimization (PIDO) Environments, Formal MDO Approaches: Collaborative Optimization (CO), Concurrent Subspace Optimization (CSSO), Bi-level Integrated System Synthesis (BLISS)
(PDF - 1.1 MB)
7Design Space Exploration

Design of Experiments (DoE): Full Factorial, Monte Carlo, Parameter Study (Univariate Search), one-at-a-time, Orthogonal Arrays (Taguchi), Latin Hypercubes

Active Learning Exercise: Paper Airplane
(PDF)

Associated file

MSDO_L5_MSDOAirplaneData2004.xls (XLS)
8Lab 1: Introduction to Optimization (cont.)
Module 2: Optimization and Search Methods
9Numerical Optimization I

Existence and Uniqueness of an Optimum Solution, Karush-Kuhn-Tucker Conditions, Convex and Non-convex Spaces, Unconstrained Problems, Linear Programming

Active Learning Exercise
(PDF)
10Numerical Optimization II

Constrained Problems, Reduced Gradient and Gradient Projection Methods, Penalty and Barrier Methods, Augmented Lagrangian Methods, Projected Lagrangian Methods, Convergence and Termination Criteria, Mixed-integer Programming, Examples

Active Learning Exercise
(PDF)
11Open Lab
12Sensitivity Analysis

Jacobian, Hessian Matrix Properties, Sensitivity Analysis w.r.t Design Variables, Fixed Parameters and Constraints, Normalization, Finite Difference Approximation, Automatic Differentiation, ANOVA, Adjoint Methods, Examples

Active Learning Exercise
(PDF)
13Guest Lecture 1

Overview of MDO, Issues in Optimization
(PDF - 2.6 MB) (Courtesy of Jaroslaw Sobieski. Used with permission.)

Biography (PDF)
14Simulated Annealing (SA)

Statistical Mechanics Analogy, Simulated Annealing Algorithm, Metropolis Step, System Temperature Cooling Schedule Tuning, Strengths and Weaknesses Relative to GA, Multiobjective SA, Tabu Search, Examples
(PDF 1) (Courtesy of Cyrus Jilla. Used with permission.)

(PDF 2) (Courtesy of Cyrus Jilla. Used with permission.)
15Genetic Algorithms I

Combinatorial Optimization Problems, Overview of Heuristic (Stochastic) Search Methods, Evolutionary Computing, Basic Genetic Algorithm, Chromosome Encoding/Decoding, Selection, Crossover, Mutation Operators, Population Strategies

Active Learning Exercise: The binary GA game
(PDF)
16Genetic Algorithms II

Specialty Variants of GA's: Parallel GA's, Diffusion GA, Micro-GA and Cellular automata

Constraint Resolution, Application of GA's in Multiobjective Optimization, Mating Restrictions, Pareto Fitness Ranking, Speciation
(PDF)
17Lab 2: Optimization Algoritms
18Particle Swarm Optimization (PDF - 1.0 MB) (Courtesy of Rania Hassan. Used with permission.)
19Post-optimality Analysis

Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory
(PDF)
20Lab 2: Optimization Algoritms
Module 3: Multiobjective and Stochastic Challenges
21Goal Programming

Objectives Versus Constraints

Performance Targets as Equality Constraints, Isoperformance, Contour following Algorithms, Singular Value Decomposition of Jacobian, Goal Programming, Satisficing Design Philosophy, Target Cascading
(PDF - 3.0 MB)
22Multiobjective Optimization I

Scalar versus Vector Optimization, The Vector Maximum Problem, Edgeworth-Pareto Optimality, Generalized Karush-Kuhn-Tucker Conditions, Strong and Weak Dominance, Domination Matrix, Multiobjective Linear Programming (MOLP), Preference Weightings and Aggregation Methods (1st Generation Methods)
(PDF)
23Open Lab
24Multiobjective Optimization II

Generation of Pareto frontier (2D) and Surface (Multidimensional), Normal-boundary-intersection (NBI), Multiobjective Evolutionary (2nd Generation) Algorithms, Review of Pareto Based Fitness Ranking Schemes

Research and Industrial Examples, Tradeoff Resolution/Design Selection, Relationship with Utility and Game Theory
 (PDF)
25Design Space Optimization

Multi-level Optimization Problems, Design Space Optimization - Number of Design Variables as a Design Variable, Conceptual Design Optimization, S-pareto Approach to Concept Selection, Applications from Structural Topology Optimization and MEMS
(PDF) (Courtesy of Il Yong Kim. Used with permission.)
26Lab 3: Multiobjective Optimization
27Approximation Methods

Design Variable Linking, Reduced-basis Methods, Response Surface Approximations, Kriging, Neural Networks as Multivariable Function Approximators, Variable-fidelity Models
(PDF)
28Guest Lecture 2

MDO at General Motors (IFAD/CDQM)
(PDF 1 of 3 - 2.8 MB) (PDF 2 of 3 - 2.5 MB) (PDF 3 of 3 - 2.1 MB) (Courtesy of Peter A. Fenyes. Used with permission.)
29Lab 3: Multiobjective Optimization (cont.)
Module 4: Implementation Issues and Real World Applications
30Robust Design

Review of Probability and Statistics, Probability Density Functions, Reliability Analysis, Taguchi Robust Design Method, Computational Issues in Robust Design Optimization
(PDF) (Courtesy of Prof. Dan Frey. Used with permission.)
31Open Lab
32Visualization Techniques

Convergence, Objective Vector and Active Constraint Set Monitoring during Optimization Execution, Multivariable Plotting Techniques: Radar Plots, Carpet Plots and Glyphs

Linking of Optimization to Dynamic (Geometric) Design Representation
33Computational Strategies

Parallel Computing, Grid Computing, Compiled versus Interpretive Languages
(PDF 1)

(PDF 2)
34Open Lab
35Project Presentations I
36Project Presentations II
37Project Presentations III
38Design for Value Net Present Value, What is Value and How do we Quantify it? How do we Design for Value? A Value Framework

Cost Models, Revenue Models, Examples from Aircraft, Spacecraft and Automotive Engineering
(PDF)
39Course Summary

Provide Summary and Highlights of Course, Classify Materials Learned as either Principles, Methods or Tools, Give Pointers to Resources for Further Individual Learning after the Course, Give Time for Student Feedback, Course Critique
(PDF)

 








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