- Course Description
- Purpose and Target Audience
- Need Assessment
- Course and Learning Objectives
- Pedagogy
- Course Staff
- Detailed Syllabus
- Physical and Computational Infrastructure
- Grading
1. Course Description (What does this course cover?)
16.888/ESD.77J Multidisciplinary System Design Optimization (MSDO) (Spring) H-Level (graduate)
Units
3-3-6
Prerequisites
18.085 or permission of instructor
Grading
Letter A-F, no final exam
Engineering systems modeling for design and optimization. Selection of design variables, objective functions and constraints. Overview of principles, methods and tools in multidisciplinary design optimization (MDO) for systems. Subsystem identification, development and interface design. Review of linear and non-linear constrained optimization formulations. Scalar versus vector optimization problems from systems engineering and architecting of complex systems. Heuristic search methods: Tabu search, simulated annealing, genetic algorithms. Sensitivity, tradeoff analysis, goal programming and isoperformance. Multiobjective optimization and Pareto optimality. System design for value. Specific applications from aerospace, mechanical, civil engineering and system architecture.
2. Purpose and Target Audience (Who should take this course and why?)
This course is offered for graduate students who are interested in the multidisciplinary design aspects of complex systems. These aspects appear frequently during the conceptual and preliminary design phases of complex new systems and products, where technical disciplines (structures, propulsion, aerodynamics, controls, optics etc…) and possibly non-technical disciplines (lifecycle costing, manufacturing, marketing, etc…) have to be tightly coupled in order to arrive at a competitive solution.
During the product development process (PDP) both quantitative and qualitative effort streams are present, where qualitative work gives rise to quantitative questions and vice-versa. This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). We will attempt to show the strengths of MSDO, but also its limitations in the greater qualitative context of design. A simple way to say this is: "Qualitative, conceptual design and system architecting define the design vector, quantitative, computational design attempts to populate this vector with values that will lead to a good product or system".
The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context. The focus will be equally strong on all three aspects of the problem:
- The multidisciplinary character of engineering systems
- Design of these complex systems, and
- Tools for optimization
A more detailed discussion of these three aspects along with working definitions can be found in Appendix A. The course content is applicable to the design of a broad range of systems including space systems, aircraft, automobiles, marine and transportation systems as well as the energy, civil architecture and telecommunications sectors, among others. This subject is designed to be fundamentally different from a traditional university optimization course.
Given the multidisciplinary nature of the course, we expect significant interest from ESD students, graduate students from the various School of Engineering departments and potentially students from the Sloan School of Management. The course is targeted for second year graduate and Ph.D. level students. The expected nominal enrollment for the MSDO course is:
Nominal enrollment: 24 graduate students (Listeners only allowed when there is low enrollment)
Repartition
| Course 16 (AA) |
50% |
| ESD |
20% |
| Course 2 (ME) and Course 1 (CEE) |
10% |
| Course 15 (Sloan) |
10% |
| Others |
10% |
| Total |
100% |
The actual enrollment numbers in the first two years the course was offered were:
Spring 2002: 25
Spring 2003: 44
3. Need Assessment (Why is this course being offered?)
This course, we believe, adds value to the current MIT offerings in system optimization. MIT has a strong and comprehensive program in optimization methods, mainly via course 15 (Sloan) and the Operations Research Center (ORC). This, however, is the only course that focuses on applying optimization techniques in a multidisciplinary design context. Important factors which are not covered by traditional optimization courses include system characterization for multidisciplinary analysis and optimization, trade-off analysis, heuristic techniques and multiobjective optimization for the design of complex, multidisciplinary systems such as aircraft, spacecraft, automobiles, transportation systems and communication networks.
The current catalog of optimization courses at MIT focuses heavily on two areas: The first is linear programming (simplex, interior point methods, large scale optimization) which are widely applicable and can solve many problems in management, revenue optimization, production planning and scheduling. The second area is more related to systems, and can be described by a set of continuous PDE’s. Here convex, constrained optimization methods such as steepest gradient search, projected gradient and Newton’s method are important and are covered well in the existing offerings. This course fills the gap in the areas of multidisciplinary design, heuristic methods and multiobjective optimization.
Even though heuristic methods are mentioned in most optimization course syllabi, there is usually only one lecture devoted to them. This does not reflect the true importance of these methods in MSDO. Multiobjective optimization is another emerging field, since many systems are usually trying to satisfy multiple, often conflicting performance, cost and risk objectives. The existence of this course will support teaching and research in system architecture and systems engineering, since many problems have non-linear objectives or constraints and are amenable to heuristic optimization and tradeoff analysis.
4. Course and Learning Objectives (What will be achieved and learned?)
The course
-
fills an existing gap in MIT’s offerings in the area of analysis and optimization of multidisciplinary systems during the conceive and design phases
-
develops and codifies a prescriptive approach to multidisciplinary modeling and quantitative assessment of new or existing system/product architectures
-
engages junior faculty and graduate students in the emerging research field of MDO,
while providing an opportunity to anchor the CDIO (conceive-design-implement-operate)
principles in the graduate curriculum
The students will
-
learn how MSDO can support the product development process of complex, multidisciplinary engineered systems
-
learn how to rationalize and quantify a system architecture or product design problem by selecting appropriate objective functions, design parameters and constraints
-
subdivide a complex system into smaller disciplinary models, manage their interfaces and reintegrate them into an overall system model
-
be able to use gradient-based numerical optimization algorithms, e.g. sequential quadratic programming (SQP) and various modern heuristic optimization techniques such as simulated annealing (SA) or genetic algorithms (GA) and select the ones most suitable to the problem at hand
-
perform a critical evaluation and interpretation of analysis and optimization results, including sensitivity analysis and exploration of performance, cost and risk tradeoffs
-
be familiar with the basic concepts of multiobjective optimization, including the conditions for optimality and Pareto front computation techniques
-
understand the concept of design for value and be familiar with ways to quantitatively assess the expected lifecycle cost of a new system or product
-
sharpen their presentation skills, acquire critical reasoning with respect to the validity and fidelity of their MSDO models and experience the advantages and challenges of teamwork
5. Pedagogy (How will these learning objectives be met?)
Our goal is that students will acquire knowledge and skills in the principles, methods (= techniques) and tools of multidisciplinary, computational design. To this end the course pedagogy will be using a number of activities to achieve the learning objectives. Figure 1 shows the different pedagogical instruments used in the MSDO course as the sides of an imaginary folded box. In order to understand the box, one needs to look at it from all sides.
(Image courtesy of MIT OCW.)
Lectures
The lectures are 90 minutes long and take place twice a week (usually Monday and Wednesday 9:30-11:00a.m.). We lecture mainly using Microsoft® PowerPoint slides, but enhance the material with some active learning exercises and handouts. The lectures are broken down into four modules:
-
Module 1: Problem Formulation and Setup (L1-L5)
-
Module 2: Optimization and Search Methods (L6-L14)
-
Module 3: Multiobjective and Stochastic Challenges (L15-L20)
-
Module 4: Implementation Issues and Real World Applications (L21-L24)
Guest Lectures
These will provide an outside perspective and show industrial applications.
Readings
The readings will use the recommended textbooks and give an overview of the published literature in the field. Normally readings are assigned at the end of each lecture in preparation of the next lecture.
Laboratory Sessions
They will introduce and exercise state-of-the art MDO tools in the computer lab (Design Studio).
Assignments
-
Part a: Will challenge the students and ensure that all participants apply and deepen the theoretical knowledge from the lectures, regardless of their disciplinary background.
-
Part b: Provides an opportunity to gradually develop the terms project throughout the semester. This ensures coupling of the course with the student's research interests.
Term Project
This is central to the success of the course. Students form small teams with between one to three members. They can choose between a number of sample projects provided by the faculty or pick a project based on their own research. The semester culminates with a final project presentation and writing of a final report in the form of a conference article.
Each group will select a multidisciplinary system to study early in the semester. Examples include (but are not restricted to) an aircraft, a space system, a ship, an automobile, a communications network or a transportation system. Projects can also be carried out at the component or subsystem level. A number of projects (airplane, communications satellites, space shuttle main tank, high speed business jet wing) are available as "canned" initial projects for those who do not have a suitable research project of their own. The faculty will screen the project proposals during the first two weeks and offer advice in problem selection and scoping if necessary. The projects will parallel the lecture content. The overall aim is to teach general tools and methods in the lectures, while allowing students to apply these tools to a specific application that is aligned with their background and interests.
6. Course Staff (Who will teach and administer this course?)
Instructors
Prof. Olivier de Weck (Isoperformance, Multiobjective Opt., Heuristics, Space Systems)
Prof. Karen Willcox (Aircraft MDO, Gradient Methods, Approximation, Design for Value)
Contributors
A number of people are also contributing materials from their own research, including Dr. Cyrus Jilla (Simulated Annealing), Dr. Rania Hassan (Particle Swarm Optimization).
7. Detailed Syllabus (What are the detailed topics to be taught?)
Module 1: Problem Formulation and Setup
-
Identification of objectives, design variables, constraints, subsystems
-
System-level coupling and interactions
-
Examples of MSDO in practice
-
Model partitioning and decomposition, interface control
-
Subsystem model selection: fidelity versus expense
-
Model and simulation development and validation
Module 2: Optimization and Search Methods
-
Review of linear and nonlinear programming
-
Heuristic techniques: genetic algorithms simulated annealing, Tabu search, particle swarm optimization
-
Design Space Exploration: Design of Experiments (DOE): Full factorial search, parameter study, Taguchi/orthogonal arrays, Latin Hypercubes
-
Mixed integer programming (application to hub spoke/network problems)
-
Jacobian matrix, Hessian, finite differences
-
Adjoint methods and Lagrange multipliers
Module 3: Multiobjective and Stochastic Challenges
-
Goal programming and isoperformance
-
Intuitive, experience-based design vs. systematic optimization
-
Weighted sum optimization, weak and strong dominance
-
Pareto front computation
-
Utility theory (von Neumann and Morgenstern)
-
Game theory and design optimization
-
Monte-Carlo Sampling, reliability analysis, Taguchi methods
Module 4: Implementation Issues and Real World Applications
-
What is optimality?
-
Design for value: including lifecycle costing
-
Model reduction
-
Approximation techniques: response surfaces, kriging, neural networks
-
Visualization techniques in design optimization
-
Parallel Computing
8. Physical and Computational Infrastructure (What is the learning environment?)
Lectures will be held for Concept and Management Forum and Computer Laboratory Sessions will be held in Design Studio.
A course in multidisciplinary design optimization naturally has to have access to an environment that is conducive to concurrent engineering (CE) and computational work. We are fortunate to have such a facility, namely the "Design Studio" owned and operated by the Department of Aeronautics and Astronautics at MIT. This room was created as a consequence of the new strategic plan which calls for "lifecycle experiences" to be integrated into the curriculum. This course focuses on the conceive and design phases of CDIO, while attempting to take into account the downstream implementation and operation phases as much as possible. The Design Studio was carefully designed as a concurrent engineering facility; it is not just another computer cluster.
Since the Design Studio is heavily used, we ask that you follow these rules:
-
You only have reserved access to the room during 16.888/ESD.77J lab hours, except...
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off-class access is possible only if no other class is on-going, consult the schedule and be sensitive to others during peak times
-
Full access requires your MIT electronic card for door access and a username and password
for computer access to the AA-DESIGN network
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During off-class hours the workstations are used on a first-come-first-serve basis
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Do not lock up a PC if you leave your seat for more than 5 minutes
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Don’t leave any food, paper or personal items laying around
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Clean up when you are done; this is a professional environment
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Make sure that all the equipment is working, the printer is stocked, unjammed etc…
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Report any system failures, network problems etc… immediately to the system administrator
For their projects and homework assignments, the students will be free to choose the platform and software of their choice. They can code their simulation modules in Matlab®, Microsoft® Excel (Visual Basic), Java®, FORTRAN or C/C++ among others. In terms of using optimization software, we recommend the following three options:
iSIGHT
This is currently the most popular multidisciplinary design optimization software available on the market. This tool is state-of-the-art and is used in many large corporations that focus on the design and development of large, complex engineering systems. The program can be "wrapped around" any user specific simulation code (e.g. in Microsoft® Excel, Matlab®, C, FORTRAN …) and has excellent design space exploration, optimization and robust design capabilities. An introduction to this tool will be provided in class.
The developer of iSIGHT is Engineous Software, Inc., located in North Carolina. The origin of this tool is the "Software Robot" developed by Dr. Siu Tong during his doctoral research at MIT, Department of Aeronautics and Astronautics, from 1979-1983. We thank Dr. Tong, who is the Co-founder and Chairman of the Board of Engineous Software Inc. for his support.
As a participant in 16.888/ESD.77 you are eligible to purchase a student license for iSIGHT. The program iSIGHT academic is available for $50 per one year license per machine. This product is essentially identical to the one our students Beta tested at this time last year, but with an increased number of design variables (25 instead of 10) and at reduced cost ($50 instead of $100 per copy). The program iSIGHT academic is based on a "Professional" license of version 7.1 and includes 14 optimization techniques, 4 methods of approximation, 6 ways of doing a Design of Experiments problem and 5 Quality Engineering methods. It differs from the commercial version in the following ways:
-
Can only be used for educational purposes
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Problems are limited to 25 design variables
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There can be no subtasks - single level problems only
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Single machine operation - no parallel or distributed functionality
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Runs on Windows NT, 2000 and XP Pro only
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Sells for $50 for a one-year license
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Software provided to professors on CDs for distribution
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Website payment and registration
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No technical support
We will hand out iSIGHT CD's to the students in the first week. It is not mandatory to obtain iSIGHT, but we strongly recommend it. Many computer labs and some homework assignments will be much easier to conduct with this software.
We ask you not to contact Engineous directly, but to funnel all problems and request via the faculty and the TA. Other optimization programs you may want to use in parallel to iSIGHT are the Solver in Microsoft® Excel, as well as the Optimization Toolbox in Matlab®.
The use of commercial disciplinary codes such as MSC/Nastran™ for structural modeling, ProEngineer®, SolidWorks® for Computer Aided Design or CPLEX for the solution of linear programs is also a possibility for your projects. We are attempting to install the FEMLAB® toolbox for MATLAB®-based finite element analysis in the Design Studio as well. There will be less emphasis on this point, however, since proficiency in these tools takes a long time to acquire and many of these codes have steep learning curves. Hence, the emphasis of the course is rather on learning the process of setting up, solving and interpreting multidisciplinary problems, rather than on creating physical models of very high fidelity as would be expected in an industry environment.
Finally, it is a long-term vision of the instructors to not only be users of the Design Studio, but also to contribute to furthering its physical and computational infrastructure. We hope to achieve this by implementing various multidisciplinary design processes and approaches, gaining experience with multidisciplinary software tools, and improving the course and facility from year-to-year based on your suggestions, criticism and project experiences.
9. Grading (How will the learning success be measured?)
There will be two types of assignments in the course:
"Assignments A1 - A5" (5 Total):
-
Part (a): Small, simple problems to be solved individually. Many of these can be solved analytically by hand or with a calculator. The goal is to ensure learning of the key ideas across the class, regardless of the chosen project
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Part (b): Application of theory to your term project from either an existing "canned" class project
or a project related to your research. Solutions must be provided individually. The assignments are due biweekly. Typically an assignment is handed out on a Monday, a related tutorial is given on the following Friday and the assignment itself is due on a Monday two weeks later.
The term project is our main means of assessing whether you can learn the material at a deeper level and apply it to a graduate level research project. There are two major deliverables here towards the end of the term:
-
Project Presentation (ca. 30 minutes including Q&A)
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Final Report in the format of a scientific conference article
The grading will be on the letter scale A - F and be weighted as follows:
Grading Policy
| Assignments A1-A5 |
50% (10% each assignment) |
| Project Presentation |
20% |
| Final Project Report ("paper") |
20% |
| Active Participation/Attendance |
10% |
No mid-term or final exams.
Appendix A
Definition and Discussion of key terms:
Multidisciplinary
A key component of this course is learning how to integrate different models from various disciplinary fields together into a single macro-model. All too often specialists in different fields (structures, fluids, propulsion, controls etc.) exert a great deal of effort modeling and designing within their area of expertise with little understanding of how their design decisions affect other subsystems within the entire macro-system. Also frequently lacking is an understanding of how such design decisions impact system lifecycle cost and program risk. Understanding of and fluency in integrated, multidisciplinary modeling is essential to the success of contemporary and future complex systems.
System
A system is a physical or virtual object that is composed of more than one element and that exhibits some behavior or performs some function as a consequence of interactions between these constituent elements.
Design
This course focuses on engineering design problems (e.g. aerospace vehicles, transportation systems, communication networks) and not primarily management problems (resource allocation, supply chain optimization, revenue management, etc.). As such, students should have a background and interest in engineering and system or product design and have had previous exposure to optimization. The course will be a good complement to existing courses in product development and system architecture, which do not typically present many quantitative methods and tools.
Optimization
Optimization is a mathematical method and gives rise to a number of algorithmic tools. As such it represents a bridge, which enables the use of integrated multidisciplinary models to do more effective design engineering work. It should be stressed that the use of optimization is not intended to remove the human from the design loop. Rather, optimization enables engineers and system architects to explore vast design spaces, often resulting in non-intuitive insights. This may result in system designs that exhibit higher performance or are more cost-effective compared to previously considered traditional designs.
