Table of Contents
Study Materials
Readings
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Textbooks and Readings
Due to the fact that multidisciplinary system design optimization is a relatively young field, we know of no single textbook that would capture all the material of this course and be suitable as a classroom text. There are, however, a number of references that could potentially be useful:
Papalambros, Panos Y., and Douglass J. Wilde. Principles of Optimal Design – Modeling and Computation. 2nd ed. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521627273. (Paperback)
Vanderplaats, Garret N. Numerical Optimization Techniques for Engineering Design. 3rd ed. Colorado Springs: Vanderplaats Research & Development Inc., 2001. ISBN: 0944956017.
Steuer, R. E. Multiple Criteria Optimization: Theory, Computation and Application. New York: Wiley, 1986. ISBN: 047188846X.
Goldberg, David E. Genetic Algorithms – in Search, Optimization & Machine Learning. Reading, MA: Addison-Wesley, 1989. ISBN: 0201157675.
Alexandrov, N. M., and M. Y. Hussaini, eds. Multidisciplinary Design Optimization: State of the Art. Proceedings in Applied Mathematics Series, No. 80. Soc for Industrial & Applied Math, 1997. ISBN: 0898713595.
Fogel, Owens, and Walsh. Artificial Intelligence Through Simulated Evolution. New York: John Wiley & Sons, 1966.
Statnikov, Roman B., and Joseph B. Matusov. Multicriteria Optimization and Engineering. New York: Chapman and Hall, 1995. ISBN: 0412992310.
Readings will be assigned at the end of a lecture. Selected research articles will be handed out and/or posted electronically throughout the semester.
| SES # | TOPICS | READINGS | |
|---|---|---|---|
| Module 1: Problem for Formulation and Setup | |||
| 1 | Introduction to Multidisciplinary System Design Optimization Course Administration, Learning Objectives, Importance of MSDO for Engineering Systems, "Dairy Farm" Sample Problems | Course syllabus Papalambros. Principles of Optimal Design. Chapter 1. "White Paper on Current State of the Art." AIAA MDO White Paper, 1991. | |
| 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 | Kroo, I. "MDO Applications in Preliminary Design: Status and Directions." AIAA Paper 97-1408, 1997. Kroo, I. and V. Manning. "Collaborative Optimization: Status and Directions." AIAA Paper 2000-4721, 2000. Sobieski, I., and I. Kroo. "Aircraft Design Using Collaborative Optimization." AIAA Paper 96-0715, 1996. Balling, R., and C. Wilkinson. "Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems." AIAA Paper 96-4033, 1996. Giesing, J., and J. Barthelemy. "A Summary of Industry MDO Applications and Needs." AIAA White Paper, 1998. "Current state-of-the-art in Multidisciplinary Design Optimization." AIAA MDO Technical Committee, 1991. | |
| 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 | Kockler, F. R., et al. Systems Engineering Management Guide. Defense Systems Management College, Gov't Printing Office, 1990. Rogers, James L. DeMAID/GA User's Guide - Design Manager's Aid for Intelligent Decomposition with a Genetic Algorithm. April 1996. NASA TM - 110241. Steward, D. V. System Analysis and Management: Structure, Strategy and Design. New York: Petrocelli, 1981. Steward, D. V. "Partitioning and Tearing Systems of Equations." SIAM Journal of Numerical Analysis. Ser. B. 2, no. 2 (1965): 345-65. Ulrich, K. T., and S. D. Eppinger. Product Design and Development. McGraw-Hill. Walton, M., and D. Hastings. "Striving Toward Lean Clean Sheet Design of Space Systems." Procedings of the AIAA Space Conference and Exposition. CA: Long Beach, September 1981. The MIT Design Structure Matrix | |
| 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) | Sobieski, Jaroslaw, Altus, Phillips, and Sandusky. "Bi-level Integrated System Synthesis for Concurrent and Distributed Processing." AIAA Journal 41, no. 10 (October 2003): 1996-2003. Sobieski, I. P., and I. M. Kroo. "Collaborative Optimization Using Response Surface Estimation." AIAA Journal 38, no. 10 (October 2000). Braun, R. D., and I. M. Kroo. "Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment." ICASE/NASA Langley Workshop on MDO, March 13-16, 1995. Cramer, Erin J., et al. "Problem Formulation for Multidisciplinary Optimization." SIAM Journal of Optimization 4, no. 4 (November 1994): 754-776. Alexandrov, Natalia M., ed. "Multidisciplinary Design Optimization – State of the Art." SIAM (1994). Kroo, I. "MDO Applications in Preliminary Design: Status and Directions." AIAA Paper 97-1408, 1997. Kroo, I., and V. Manning. "Collaborative Optimization: Status and Directions." AIAA Paper 2000-4721, 2000. Sobieski, I., and I. Kroo. "Aircraft design using Collaborative Optimization." AIAA Paper 96-0715, 1996. Balling, R., and C. Wilkinson. "Execution of Multidisciplinary Design Optimization Approaches on common test problems." AIAA Paper 96-4033, 1996. Giesing, J., and J. Barthelemy. "A summary of industry MDO Applications and Needs." AIAA White Paper, 1998. "Current state-of-the-art in Multidisciplinary Design Optimization." AIAA MDO Technical Committee, 1991. "Optimal Design in Multidisciplinary Systems." AIAA Professional Development Short Course Notes, September 2002. | |
| 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 | Phadke. Quality Engineering Using Robust Design. Prentice Hall, 1995. Box, G., W. Hunter, and J. Hunter. Statistics for Experimenters. John Wiley and Sons, 1978. | |
| 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 | ||
| 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 | Gill, P. E., W. Murray and M. H. Wright. Practical Optimization. Academic Press, 1986. Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design. Vanderplaats R&D, 1999. Optimal Design in Multidisciplinary Systems. AIAA Professional Development Short Course Notes, September 2002. | |
| 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 | Papalambros – Section 8.2 Computing Derivatives | |
| 13 | Guest Lecture 1 Overview of MDO, Issues in Optimization | ||
| 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 | Cerny, V. "Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm." J. Opt. Theory Appl. 45, no. 1 (1985): 41-51. de Weck, O. L. "System Optimization with Simulated Annealing (SA)." Memorandum. Cohanim B., J. Hewitt, and O. L. de Weck. "The Design of Radio Telescope Array Configurations using Multiobjective Optimization: Imaging Performance versus Cable Length." The Astrophysical Journal (2004). (in press) Jilla, C. D., and D. W. Miller. "Assessing the Performance of a Heuristic Simulated Annealing Algorithm for the Design of Distributed Satellite Systems." Acta Astronautica 48, no. 5-12 (2001): 529-43. Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi. "Optimization by Simulated Annealing." Science 220, no. 4598 (13 May 1983): 671-80. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. "Equation of State Calculations by Fast Computing Machines." J. Chem. Phys. 21, no. 6 (1953): 1087-1092. Brooks, R. R., S. S. Iyenger, and S. Rai. "Comparison of Genetic Algorithms and Simulated Annealing for Cost Minimization in a Multisensor System." Optical Engineering 37, no. 2 (Feb. 1998): 505-16. Jilla, C. D., D. W. Miller, and R. J. Sedwick. "Application of Multidisciplinary Design Optimization Techniques to Distributed Satellite Systems." Journal of Spacecraft and Rockets 37, no. 4 (2000): 481-90. Schulz, A. S. "Metaheuristics." 15.057 Systems Optimization Course Notes, MIT, 1999. Tech. Reports on Simulated Annealing & Related Topics Simulated Annealing Information | |
| 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 | Holland J. "Adaptation in Natural and Artificial Systems." University of Michigan Press, 1975. Goldberg, D. E. "Genetic Algorithms in Search, Optimization and Machine Learning." Addison Wesley, 1989. Schulz, A. S. 15.057 Systems Optimization, Course Notes. Note a number of charts in this lecture are derived from notes. Baeck, T. Evolutionary Algorithms in Theory and Practice. N. Y.: Oxford, 1996. Zalzala, A., and P. J. Fleming, eds. "Genetic Algorithms in Engineering Systems." Control Engineering Series 55. The Institution of Electrical Engineers (IEE), 1997. | |
| 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 | ||
| 17 | Lab 2: Optimization Algoritms | ||
| 18 | Particle Swarm Optimization | Kennedy, J., and R. Eberhart. "Particle Swarm Optimization." Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 1995, pp. 1942-45. Venter, G., and J. Sobieski. "Particle Swarm Optimization." AIAA 2002-1235, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, CO., April 2002. Kennedy, J., and R. Eberhart. Swarm Intelligence. 1st ed. San Diego, CA: Academic Press, 2001. | |
| 19 | Post-optimality Analysis Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory | Gill, P. E., W. Murray, and M. H. Wright. Practical Optimization. London: Academic Press, 1981. Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design. Vanderplaats R&D, 1999. Willcox, K. and S. Wakayama. "Simultaneous Optimization of a Multiple-Aircraft Family." AIAA Paper 2002-1423, 2002. | |
| 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 | ||
| 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) | ||
| 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 | Edgeworth, F. Y. Mathematical Psychics. P. Keagan, London, England, 1881. Pareto, V. Manuale di Economia Politica. Societa Editrice Libraria, Milano, Italy, 1906. Translated into English by A. S. Schwier as Manual of Political Economy. New York: Macmillan, 1971. Ehrgott, M. Multicriteria Optimization. Springer-Verlag, New York, NY, 2000. Stadler, W. "A Survey of Multicriteria Optimization, or the Vector Maximum Problem." Journal of Optimization Theory and Applications 29 (1979): 1-52. Stadler, W. "Applications of Multicriteria Optimization in Engineering and the Sciences (A Survey)." Multiple Criteria Decision Making – past Decade and Future Trends. Edited by M. Zeleny. Greenwich, Connecticut: JAI Press, 1984. Stadler, W. Multicriteria Optimization in Engineering and in the Sciences. New York, NY: Plenum Press, 1988. Steuer, Ralph. "Multiple Criteria Optimization - Theory, Computation and Application." 1985. | |
| 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 | Bendsoe, M. O., and N. Kikuchi. "Generating Optimal Topologies in Structural Design using a Homogenization Method." Comp. Meth. Appl. Mech. Engng. 71 (1988): 197-224. Yang, R. J., and C. H. Chuang. "Optimal Topology Design using Linear Programming." Comp. Struct. 52, no. 2 (1994): 265-275. Xie, Y. M., and G. P. Steven. "A Simple Evolutionary procedure for Structural Optimization." Comput. And Struct. 49 (1993): 885-896. Hassani B., and E. Hinton. "A Review of Homogenization and Topology Optimization I - Homogenization Theory for Media with Periodic Structure." Comput. Mech. 69, no. 6 (1998): 707-717. Olhoff, N., et al. "On Cad-Integrated Structural Topology and Design Optimization." Computer Meth. In Appl. Mech. Engng. 89 (1991): 259-79. Bremicker, M., M. Chirehdast, N. Kikuch, and P. Y. Papalambros. "Integrated Topology and Shape Optimization in Structural Design." Mech. Struct. and Mach. 19, no. 4 (1991): 551-587. Hinton, E., et al. "Integrating Structural Topology, Shape and Sizing Optimization Methods." Computational Mechanics, New Trends and Applications. Barcelona, Spain, 1998. Ramm, E., K. Maute and S. Schwarz. "Adaptive Topology and Shape Optimization." Computational Mechanics, New Trends and Applications. Barcelona, Spain, 1998. Kim, Yong II, and Byung Man Kwak. "Design Space Optimization using a Numerical Design Continuation Method." International Journal for Numerical Methods in Engineering 53 (2002): 1979-2002. | |
| 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 | Barthelemy, J-F. M., and R. T. Haftka. "Approximation Concepts for Optimum Structural Design – a Review." Structural Optimization 5 (1993): 129-144. Giunta, A. A. and L. T. Watson. "A Comparison of Approximation Modeling Techniques: Polynomial versus Interpolating Models." AIAA Paper 98-4758, 1998. LeGresley, P. A. and J. J. Alonso. "Airfoil Design Optimization using Reduced Order Models Based on Proper Orthogonal Decomposition." AIAA Paper 2000-2545. Alexandrov, N., J. E. Dennis, R. M. Lewis and V. Torczon. "A Trust Region Framework for Managing the use of Approximation Models in Optimization." NASA CR-201745, ICASE Report No. 97-50, October 1997. Gill, P. E., W. Murray and M. H. Wright. Practical Optimization. Academic Press, 1986. Vanderplaats, G. N. Numerical Optimization Techniques for Engineering Design. Vanderplaats R&D, 1999. | |
| 28 | Guest Lecture 2 MDO at General Motors (IFAD/CDQM) | ||
| 29 | Lab 3: Multiobjective Optimization | ||
| 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 | ||
| 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 | Stanford University Course Parallel Methods in Numerical Analysis Prof. Juan Alonso | |
| 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 | ||
| 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 | ||