In the name of ALLAH The Most Beneficent The Most Merciful

1. In the name of ALLAHThe Most BeneficentThe Most Merciful

2. Multidisciplinary Engineering Design Optimization (MCE 540 Graduate Course – Mechanical Engineering Department) • Instructor: • Assist. Prof. Dr.-Ing. Mostafa Ranjbar • Ph.D. (Dr-Ing.), Multidisciplinary Engineering Design Optimization of Structures,TechnischeUniversität Dresden, Germany, 2011 • M.Sc., Vibration Monitoring and Fault Diagnosis of Structures, TarbiatModares University, Tehran, Iran, 2000 • B.Sc., Mechanical Engineering, Shiraz university, Iran, 1998

3. MULTIDISCIPLINARY SYSTEM DESIGNOptimization LECTURE # 3

4. INTRODUCTION • PHASE-I • Introduction to Multidisciplinary System Design Optimization • Terminology and Problem Statement • Introduction to Optimization • Classification of Optimization Problems • Numerical Optimization • MSDO Architectures • Practical Applications

5. OPTIMZATION LECTURE # 3

6. INTRODUCTION • PHASE-I • Introduction to Multidisciplinary System Design Optimization • Terminology and Problem Statement • Introduction to Optimization • Classification of Optimization Problems • Numerical Optimization • MSDO Architectures • Practical Applications

7. INTRODUCTION toOPTIMIZATION

8. WHAT CAN BE ACHIEVED? • Optimization techniques can be used for: • Getting a design/system to work • Reaching the optimal performance • Making a design/system reliable and robust • Also provide insight in • Design problem • Underlying physics • Model dynamics

9. OPTIMIZATION PROBLEM • General form of optimization problem:

10. Responses Derivatives ofresponses (design sensitivities) SOLVING OPTIMIZATION PROBLEMS • Optimization problems are typically solved using an iterative algorithm: Model Constants Designvariables Optimizer

11. Take 1 s per computation, 10 variables, 10 samples: total time 317 years! CURSE OF DIMENSIONALITY Looks complicated … why not just sample the design space, and take the best one? • Consider problem with n design variables • Sample each variable with m samples • Number of computations required: mn

12. Parallel computing • Still, for large problems, optimization requires lots of computing power • Parallel computing

13. Conventional design process: Optimization-based design process: Identify: • Design variables • Objective function • Constraints Collect data to describe the system Collect data to describe the system Estimate initial design Estimate initial design Analyze the system Analyze the system Check performance criteria Check the constraints Does the design satisfy convergence criteria? Is design satisfactory? Done Done Change the design using an optimization method Change design based on experience / heuristics / wild guesses OPTIMIZATION IN THE DESIGN PROCESS

14. OPTIMIZATION POPULARITY Increasingly popular: • Increasing availability of numerical modeling techniques • Increasing availability of cheap computer power • Increased competition, global markets • Better and more powerful optimization techniques • Increasingly expensive production processes (trial-and-error approach too expensive) • More engineers having optimization knowledge

15. OPTIMIZATION PITFALLS! • Proper problem formulation critical! • Choosing the right algorithmfor a given problem • Many algorithms contain lots of control parameters • Optimization tends to exploit weaknesses in models • Optimization can result in very sensitive designs • Some problems are simply too hard / large / expensive

16. OVERVIEW • Traditional description of the design phases comprised of; • Problem Definition: Recognition of the original need is followed by a technical statement of the problem, • Synthesis: The creation of one or more physical configurations, • Analysis: The study of the configuration‘s performance using engineering science, • Optimization: The selection of "best" alternative. • The process concludes with testing of the prototype against the original need.

17. OVERVIEW • Optimization deals with betterment and improvement. • “The concept of optimization is intrinsically tied to humanity’s desire to excel. Though we may not consciously recognize it, and though the optimization process takes different forms in a different field of endeavor, this drive to do better than before, whether we are athletes, artists, business-person, or engineers” • Optimization is defined as “the process of achieving the most favorable system condition on the basis of a metric or set of metrics [Merriam-Webster, 1998]. • Optimization means the maximizing or minimizing of a given function possibly subject to some type of constraints and controlled by decision variables.

18. OVERVIEW • Broadly, • The efforts and processes of making a decision, a design or a system as perfect, effective or functional as possible. • Narrowly, • The specific methodology, techniques and procedures used to decide on the one specific solution in a defined set of possible alternatives that will best satisfy a selected criterion. “The main aim of OPTIMIZATION is to construct a model that can be easily understood and that provides good solutions in a reasonable amount of computing time”

19. OVERVIEW • Optimization, in engineering interpretation, is referred as the process of finding appropriate solutions with the intention of finding the best solutions to the system design problem. • Optimization is a computational design method which helps us select an optimal design among a number of (or an infinite set of ) possible options, such that a certain requirement or a set of requirements is best satisfied.

20. OVERVIEW • Optimization is applied in virtually all areas of human endeavor, including; • Engineering system design • Optical system design • Power systems • Water and land use • Transportation systems • Resource allocation • Personnel planning • Portfolio selection • Mining operations • Structural design • Control systems

21. OVERVIEW • The first (key) step in modern optimization is to obtain a mathematical description of the process or system to be optimized. • System models used in optimization is classified in various ways, • Linear versus nonlinear • Static versus dynamic • Deterministic versus stochastic • Time-invariant versus time-varying.

22. OVERVIEW • In forming a model for use with optimization, all of the important aspects of the problem should be included, so that they will be taken into account in the solution. • In some cases, the constraints and objective values or goals can be exchanged. • The model of a system must account for constraints that are imposed on the system. Some of the constraints restrict the values that can be assumed by variables of a system. • The types of constraints involved in any given problem are determined by the physical nature of the problem and by the level of complexity used in forming the mathematical model.

23. OVERVIEW • When constraints have been established, it is necessary to determine if there are any solutions to the problem that simultaneously satisfy all of the constraints. Any such solution is called a feasible solution. • A key step in the formulation of any optimization problem is the assignment of performance measures that are to be optimized. “The success of any optimization result is critically dependent on the selection of meaningful performance measures”

24. OPTIMIZATION

25. OPTIMIZATION------WHY????? • Today’s mantra of “Faster, Better and Cheaper” has caused problem solvers to rethink how to reach at possible solution of a given problem. • Maybe the only way forward in the current daily technological advances. • The continuing push for reducingdesign costs and cycle time using computer-based models makes the use of optimization tools inevitable. • Suitable for generating more than a single solution, and this added information gives more flexibility to the user to choose a few solutions for further investigation. “Need of modern era is not only to design a system which fits a customer’s needs, but it is also required to deliver an optimized system”

26. OPTIMIZATION------WHY????? YES FINE HOW TO MODIFY THE DESIGN???? NO WITH EXPERIENCE….TRIAL and ERROR WITH OPTIMIZATION METHODS

27. OPTIMIZATION------WHY????? Is there one aircraft which is the fastest, most efficient, quietest, most inexpensive, most light weight ??????

28. OPTIMIZATION------WHY?????

29. OVERVIEW • Informally, but rigorously, we can say that design optimization involves: • 1. The selection of a set of variables to describe the design alternatives. • 2. The selection of an objective (criterion), expressed in terms of the design variables, which we seek to minimize or maximize. • 3. The determination of a set of constraints, expressed in terms of the design variables, which must be satisfied by any acceptable design. • 4. The determination of a set of values for the design variables, which minimize (or maximize) the objective, while satisfying all the constraints. • This definition of optimization suggests a philosophical and tactical approach during the design process.

30. OVERVIEW • It is not a phase in the process but rather a pervasive viewpoint. • Philosophically, optimization formalizes what humans (and designers) have always done. • Operationally, it can be used in design, in any situation where analysis is used, and is therefore subjected to the same limitations.

31. OPTIMIZATIONMODEL

32. Definition of OPTIMIZATION Problem---OPTIMIZATION MODEL The first step in modern optimization is to obtain a mathematical description of the process or the system to be optimized. Design Space: The space of working (Hill in this case) Objective: Find the Highest Point. Design Variables: Longitude and latitude. Constraints: Stay inside the fences.

33. OPTIMIZATION MODEL

34. OPTIMIZATION MODEL

35. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space

36. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space • Each point in the n-dimensional design space is called a design point and represents either a possible or an impossible solution to the design problem • In many practical problems, the design variables cannot be chosen arbitrarily; rather, they have to satisfy certain specified functional and other requirements. • The restrictions that must be satisfied to produce an acceptable design are collectively called design constraints. • Constraints that represent limitations on the behavior or performance of the system are termed behavioror functional constraints. • Constraints that represent physical limitations on design variables, such as availability, fabricability, and transportability, are known as geometricor side constraints.

37. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space

38. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space • Figure shows a hypothetical two-dimensional design space where the infeasible region is indicated by hatched lines. • A design point that lies on one or more than one constraint surface is called a bound point , and the associated constraint is called an active constraint . • Design points that do not lie on any constraint surface are known as free points.

39. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space • Depending on whether a particular design point belongs to the acceptable or unacceptable region, it can be identified as one of the following four types 1. Free and acceptable point 2. Free and unacceptable point 3. Bound and acceptable point 4. Bound and unacceptable point

40. OPTIMIZATION MODELConstraint surfaces in a hypothetical two-dimensional design space • Depending on whether a particular design point belongs to the acceptable or unacceptable region, it can be identified as one of the following four types 1. Free and acceptable point 2. Free and unacceptable point 3. Bound and acceptable point 4. Bound and unacceptable point

41. OPTIMIZATIONMODEL_________________DESIGN SPACE

42. OPTIMIZATION MODEL DESIGN SPACE

43. OPTIMIZATION MODEL DESIGN SPACE Design Space Design Space

44. OPTIMIZATIONMODEL_________________DESIGN OBJECTIVE

45. OPTIMIZATION MODEL DESIGN OBJECTIVE • Design objectives usually represent the desires of the decision makers (designers). • A design objective can be considered as a criterion about whether or not a given design is better than others. • A design objective is determined by the objective function f(d)= f(d1,d2,…,dn).

46. OPTIMIZATIONMODEL_________________DESIGN VARIABLES

47. OPTIMIZATION MODEL DESIGN VARIABLES • A design variable is a decision variable or a control variable that can be changed by designers during a design process. • A design variable have an impact on the performances of a design. • Different combinations of design variables represent different designs. • Design variables should be as independent of each other as possible. Optimization is the process of choosing the design variables that yield an optimum design

48. OPTIMIZATION MODEL DESIGN VARIABLES • Design variables are also known as design parameters and will be represented by the vector x. They are the variables in the problem that we allow to vary in the design process. • During design space exploration or optimization we change the entries of x in some rational fashion to achieve a desired effect.

49. OPTIMIZATIONMODEL___________________DESIGN CONSTRAINTS

50. OPTIMIZATION MODEL DESIGN CONSTRAINTS • Few practical engineering optimizations problems are unconstrained. • We can not optimize our objectives infinitely because we have limited resources. • Constraints on the design variables are called bounds and are easy to enforce. • Constraints are restrictions or requirements imposed to a design. • A constraint function is expressed in a mathematical form in terms of design variables. • gi(d)<0, i=1,2,…,n • hj(d)=0, j=1,2,…,n • mk(d)>0, k=1,2,…,n