| 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 | |