Calendar

SES #	TOPICS	LECTURERS	KEY DATES
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	de Weck, and Willcox
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	Willcox	Assignment 1 handed out
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	de Weck
5	Lab 1: Introduction to Optimization	Kim
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)	de Weck
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	Willcox
8	Lab 1: Introduction to Optimization (cont.)	Kim
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	Willcox	Assignment 1 due Assignment 2 handed out
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	Willcox
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	Willcox
13	Guest Lecture 1 Overview of MDO, Issues in Optimization	Dr. Jaroslaw Sobieski - NASA LaRC
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	de Weck, and Dr. Cyrus Jilla
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	de Weck	Assignment 2 due Assignment 3 handed out
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	de Weck
17	Lab 2: Optimization Algoritms	Kim
18	Particle Swarm Optimization	Dr. Rania Hassan
19	Post-optimality Analysis Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory	Willcox, and de Weck
20	Lab 2: Optimization Algoritms	Kim
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	de Weck	Assignment 3 due Assignment 4 handed out
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)	de Weck
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	de Weck
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	Il Yong Kim
26	Lab 3: Multiobjective Optimization	Kim
27	Approximation Methods Design Variable Linking, Reduced-basis Methods, Response Surface Approximations, Kriging, Neural Networks as Multivariable Function Approximators, Variable-fidelity Models	Willcox	Assignment 4 due Assignment 5 handed out
28	Guest Lecture 2 MDO at General Motors (IFAD/CDQM)	Dr. Peter Fenyes, GM Research Center
29	Lab 3: Multiobjective Optimization (cont.)	Kim
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	Prof. Dan Frey
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	Willcox	Assignment 5 due Final Report Assignment handed out
33	Computational Strategies Parallel Computing, Grid Computing, Compiled versus Interpretive Languages	de Weck
34	Open Lab
35	Project Presentations I	Students
36	Project Presentations II	Students
37	Project Presentations III	Students
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	Willcox	Final report (journal article paper format) due
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	Willcox, and de Weck