麻省理工学院“开放式课程网页” | 航空宇航工程 | 16.888 2004春季课程：跨领域系统设计最优化

节	课程单元	讲师	重要日期
单元1：问题阐述和计划 Module 1: Problem Formulation and Setup
1	多领域系统设计最优化导论 Introduction to Multidisciplinary System Design Optimization 课程管理、学习目标、MSDO对工程系统的重要性、“牛奶农场”问题示例 Course Administration, Learning Objectives, Importance of MSDO for Engineering Systems, "Dairy Farm" Sample Problems	de Weck, and Willcox
2	开放实验 Open Lab
3	问题阐述 Problem Formulation 定义、数学符号、设计变量导论、参数、约束、目标 Definitions, Mathematical Notation, Introduction of Design Variables, Parameters, Constraints, Objectives 形式化的最佳设计问题定义 Formal Optimal Design Problem Definition 仿真模型和优化器的区别 Distinction between Simulation Model and Optimizer 随堂练习：课堂角色扮演（学生小组）来找出一系列复杂系统或产品的问题描述 Active Learning Exercise: In Class Role Play (Student Groups) to Find Problem Formulation for a Range of Complex Systems/Products	Willcox	布置作业1 Assignment 1 handed out
4	建模和仿真（分发iSIGHT CD光盘） Modeling and Simulation (iSIGHT CD-ROM handed out) 设计变量－>目标映射，仿真模块识别，基于物理建模(控制方程)vs. 经验建模，N²方图和设计结构矩阵（DSM），模型的精确度和评测基准，建模环境，减少运行时间的策略 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 随堂练习：找出通信卫星的N²方图 Active Learning: Find N² Diagram for Communication Satellite	de Weck
5	实验1：最优化导论 Lab 1: Introduction to Optimization	Kim
6	分解和组合 Decomposition and Coupling 任务序列，并行化，类C语言－优化器组合，处理整合和设计优化（PIDO）环境，形式化的MDO方法：协作优化（CO），并发子空间优化（CSSO），两级集成系统合成（BLISS） 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	设计空间检索 Design Space Exploration 实验设计：全阶乘，蒙特卡罗（Monte Carlo），参数学习（单变量搜索），一次一个，正交矩阵（Taguchi），拉丁超立方体 Design of Experiments (DoE): Full Factorial, Monte Carlo, Parameter Study (Univariate Search), one-at-a-time, Orthogonal Arrays (Taguchi), Latin Hypercubes 随堂练习：纸飞机 Active Learning Exercise: Paper Airplane	Willcox
8	实验1：最优化导论（续） Lab 1: Introduction to Optimization (cont.)	Kim
单元2:最优化与搜索方法　Module 2: Optimization and Search Methods
9	数值最优化 Numerical Optimization I 最优解的存在性和唯一性，Karush-Kuhn-Tucke条件，凸集和非凸集空间，无约束问题，线性规划随堂作业 Existence and Uniqueness of an Optimum Solution, Karush-Kuhn-Tucker Conditions, Convex and Non-convex Spaces, Unconstrained Problems, Linear Programming Active Learning Exercise	Willcox	交作业1 Assignment 1 due 布置作业2 Assignment 2 handed out
10	数值最优化II Numerical Optimization II 约束问题，降低梯度和梯度投影方法，惩罚和障碍方法，扩张拉格朗日法，投影拉格朗日法，收敛终止条件，混合整数规划，例子 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 随堂练习 Active Learning Exercise	Willcox
11	开放实验 Open Lab
12	灵敏度分析 Sensitivity Analysis Jacobian, Hessian矩阵属性，灵敏度分析w.r.t设计变量，固定参数和约束，归一化，有限差分逼近算法，自动差分算法，ANOVA，伴随矩阵法，例子 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 随堂练习 Active Learning Exercise	Willcox
13	客席演讲1 Guest Lecture 1 MDO概述，最优化中的问题 Overview of MDO, Issues in Optimization	Dr. Jaroslaw Sobieski - NASA LaRC
14	模拟退火 Simulated Annealing (SA) 统计力学类比，模拟退火算法，Metropolis步骤，系统温度冷却调整控制，相对于遗传算法的优势和不足，多目标模拟退火，Tabu搜索，例子 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	遗传算法I Genetic Algorithms I 组合最优化问题，启发（随机）式搜索方法概述，进化计算，基本的遗传算法，染色体解码和编码，选择，交叉，变异算子，群体策略 Combinatorial Optimization Problems, Overview of Heuristic (Stochastic) Search Methods, Evolutionary Computing, Basic Genetic Algorithm, Chromosome Encoding/Decoding, Selection, Crossover, Mutation Operators, Population Strategies 随堂练习：二进制遗传算法游戏 Active learning exercise: The binary GA game	de Weck	Assignment 2 due Assignment 3 handed out
16	Genetic Algorithms II 遗传算法专业变量：并行遗传算法，扩散遗传算法，微系统遗传算法和细胞自动机 Specialty Variants of GA's: Parallel GA's, Diffusion GA, Micro-GA and Cellular automata 约束决定在多目标最优化中遗传算法的应用，杂交限制，Pareto适应群，物种形成 Constraint Resolution, Application of GA's in Multiobjective Optimization, Mating Restrictions, Pareto Fitness Ranking, Speciation	de Weck
17	实验2：最优化算法 Lab 2: Optimization Algoritms	Kim
18	粒子流优选法 Particle Swarm Optimization	Dr. Rania Hassan
19	后最优性分析 Post-optimality Analysis 基于梯度和启发式算法的收敛，拉格朗日乘数，对偶理论 Convergence for Gradient-Based and Heuristic Algorithms, Lagrange Multipliers, Duality Theory	Willcox, and de Weck
20	实验2：最优化算法 Lab 2: Optimization Algoritms	Kim
单元3：多目标和随机的挑战 Module 3: Multiobjective and Stochastic Challenges
21	目标规划 Goal Programming 目标vs. 约束 Objectives Versus Constraints 作为等式约束的性能目标，同效性，轮廓跟踪算法，Jacobian单值分解，目标规划，令人满意的设计理念，目标层叠 Performance Targets as Equality Constraints, Isoperformance, Contour following Algorithms, Singular Value Decomposition of Jacobian, Goal Programming, Satisficing Design Philosophy, Target Cascading	de Weck	交作业3 Assignment 3 due 布置作业4 Assignment 4 handed out
22	多目标最优化 IMultiobjective Optimization I 标量vs.矢量最优化，矢量最大值问题，Edgeworth-Pareto最优性，一般性的Karush-Kuhn-Tucker条件，强势和弱势管理，占优矩阵，多目标线性规划（MOLP），优选权和集合方法（第一代方法） 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	开放实验 Open Lab
24	多目标优化II Multiobjective Optimization II Pareto 边界（2维）和多面体表面（多维）的形成，正态边界交点NBI，多目标进化（第二代）算法，基于适应群体理论的Pareto方法回顾 Generation of Pareto Frontier (2D) and Surface (Multidimensional), Normal-boundary-intersection (NBI), Multiobjective Evolutionary (2nd Generation) Algorithms, Review of Pareto Based Fitness Ranking Schemes 相关研究和工业应用实例，权衡分辨力/设计可选性，效用和游戏理论的关系 Research and Industrial Examples, Tradeoff Resolution/Design Selection, Relationship with Utility and Game Theory	de Weck
25	设计空间最优化 Design Space Optimization 多级优化问题，设计空间最优化－设计变量的个数作为一个设计变量，概念设计最优化，概念选择时的S-pareto方法结构拓扑最优化和MEMS的应用 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	实验3：多目标最优化 Lab 3: Multiobjective Optimization	Kim
27	逼近方法 Approximation Methods 设计变量链接，基于规约的方法，反应曲面逼近，Kriging，与多变量函数近似的神经网络，变量精确度模型 Design Variable Linking, Reduced-basis Methods, Response Surface Approximations, Kriging, Neural Networks as Multivariable Function Approximators, Variable-fidelity Models	Willcox	交作业4 Assignment 4 due 布置作业5 Assignment 5 handed out
28	客席演讲2 Guest Lecture 2 通用汽车中的MDO MDO at General Motors (IFAD/CDQM)	Dr. Peter Fenyes, GM Research Center
29	实验3：多目标最优化（续） Lab 3: Multiobjective Optimization (cont.)	Kim
单元4：实行问题和实际应用 Module 4: Implementation Issues and Real World Applications
30	稳健设计 Robust Design 概率统计回顾，概率密度函数，可靠性分析，Taguchi稳健设计方法，稳健设计最优化中的计算问题 Review of Probability and Statistics, Probability Density Functions, Reliability Analysis, Taguchi Robust Design Method, Computational Issues in Robust Design Optimization	Prof. Dan Frey
31	开放实验 Open Lab
32	可视化技术 Visualization Techniques 执行最优化过程中的收敛，目标向量和活动约束集的监视，多变量绘图技术：雷达绘图、地毯绘图和浮雕绘图 Convergence, Objective Vector and Active Constraint Set Monitoring during Optimization Execution, Multivariable Plotting Techniques: Radar Plots, Carpet Plots and Glyphs 与动态设计展示的优化链接 Linking of Optimization to Dynamic (Geometric) Design Representation	Willcox	交作业5 Assignment 5 due 布置期末报告作业 Final Report Assignment handed out
33	计算策略 Computational Strategies 并行计算，网格计算，编译vs.解释语言 Parallel Computing, Grid Computing, Compiled versus Interpretive Languages	de Weck
34	开放实验 Open Lab
35	项目陈述I Project Presentations I	学生 Students
36	项目陈述II Project Presentations II	学生 Students
37	项目陈述III Project Presentations III	学生 Students
38	价值设计 Design for Value 净现值，什么是价值、怎样衡量价值，怎样按照价值进行设计，一个价值框架 Net Present Value, What is Value and How do we Quantify it? How do we Design for Value? A Value Framework 成本模型，收益模型，来自飞机、航天飞机和汽车工程的例子 Cost Models, Revenue Models, Examples from Aircraft, Spacecraft and Automotive Engineering	Willcox	交期末报告（期刊论文格式） Final report (journal article paper format) due
39	课程总结 Course Summary 提供课程总结和重点，将学过的内容划分成原理、方法和工具等几类，提供课程结束后进一步学习的资源链接，留出时间给学生反馈及对课程的批评 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