Lecture Notes

SES #	TOPICS	LECTURE NOTES
Module 1: Problem Formulation and Setup
1	Introduction to Multidisciplinary System Design Optimization Course Administration, Learning Objectives, Importance of MSDO for Engineering Systems, "Dairy Farm" Sample Problems	(PDF - 1.8 MB)
2	Open Lab
3	Problem 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)
4	Modeling 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)
5	Lab 1: Introduction to Optimization
6	Decomposition 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)
7	Design 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)
8	Lab 1: Introduction to Optimization (cont.)
Module 2: Optimization and Search Methods
9	Numerical 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)
10	Numerical 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)
11	Open Lab
12	Sensitivity 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)
13	Guest Lecture 1 Overview of MDO, Issues in Optimization	(PDF - 2.6 MB) (Courtesy of Jaroslaw Sobieski. Used with permission.) Biography (PDF)
14	Simulated 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.)
15	Genetic 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)
16	Genetic 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)
17	Lab 2: Optimization Algoritms
18	Particle Swarm Optimization	(PDF - 1.0 MB) (Courtesy of Rania Hassan. Used with permission.)
19	Post-optimality Analysis Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory	(PDF)
20	Lab 2: Optimization Algoritms
Module 3: Multiobjective and Stochastic Challenges
21	Goal 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)
22	Multiobjective 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)
23	Open Lab
24	Multiobjective 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)
25	Design 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.)
26	Lab 3: Multiobjective Optimization
27	Approximation Methods Design Variable Linking, Reduced-basis Methods, Response Surface Approximations, Kriging, Neural Networks as Multivariable Function Approximators, Variable-fidelity Models	(PDF)
28	Guest 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.)
29	Lab 3: Multiobjective Optimization (cont.)
Module 4: Implementation Issues and Real World Applications
30	Robust 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.)
31	Open Lab
32	Visualization 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
33	Computational Strategies Parallel Computing, Grid Computing, Compiled versus Interpretive Languages	(PDF 1) (PDF 2)
34	Open Lab
35	Project Presentations I
36	Project Presentations II
37	Project Presentations III
38	Design 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)
39	Course 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)