Intro. to Optimal Design and Problem Formulation

AE-310 Engineering Design Optimization Capsule-0

Course Layout Engineering Design Optimization

AE-310

Prof. Rajkumar S. Pant & Prof. R. P. Shimpi [email protected] [email protected]


Started as Optimization for Engg. Design Core course M. Tech. (Systems Design & Engg.) Elective for B. Tech. (Aerospace) & M. Tech

Became very popular, almost entire batch took it Converted to UG Core in 2008 Taught by two instructors

RSP (Theory, Calculus based Methods, Special Topics) RPS (Evolutionary Algorithms)

Background


Introduction: Design process, problem formulation in design, design variables, objective function, equality and inequality constraints, classification of optimization problems, local and global optima, nonlinear and linear problems.

Theoretical Concepts: Unconstrained optima, Constrained optima, Lagrange multipliers, Post optimality analysis.

Linear Programming: Problem definition, basic concepts and LP terminology, Simplex method, 2-phase Simplex

Calculus based Optimization Methods: Non-linear programming, steepest descent, conjugate-gradient method, Newton’s methods, BFGS, SLP algorithm, CSD method Meta Modeling techniques, Multi-criteria Optimization, Introduction to Multi-disciplinary Design Optimization

Evolutionary methods: Genetic Algorithms, Simulated Annealing, Ant Colony, Particle Swarm Optimization.

Syllabus


Arora, J. S., Introduction to Optimum Design, McGraw-Hill, 1989.

Rao, S. S., Engineering Optimization: Theory and Practice, 3rd

edition, New Age International, 1998.

Deb, K., Optimization for Engineering Design-Algorithms and

Examples, Prentice Hall India, 1995.

Goldberg, D., Genetic Algorithms in Search, Optimization, and

Machine Learning, ISBN-13: 978-0201157673, Addison Wesley

Publishing Company, 2001

Books / Reference Texts


Six Capsules 1. Introduction to Engg. Design & Optimization (4)

2. Theoretical Concepts (4)

3. Linear Programming (2)

4. Gradient Based Methods (4)

5. Evolutionary Optimization (8)

6. Special Topics (2)

Figures in brackets indicate 90-min lectures for each topic


Introduction to Design and

Optimal Design Formulation

Prof. Rajkumar S. Pant Aerospace Engineering Department


INTRODUCTION TO DESIGN Capsule -01


Overall process of designing systems

Distinguish between Design & Analysis

Conventional v/s Optimum Design process

Aims


The Design Process

Needs & Objectives

System Specs

Preliminary Design

Detailed Design

Prototype Fabrication

System Testing Final

Design


Design v/s Analysis

Analysis

Design

Parameters Response

Parameters Desired Response

Analysis


Conventional design process Less formal approach Based on past experience, heuristics & thumb-rules Can be time consuming, inefficient, uneconomical

Optimum design process Rigorous formulation of the problem Identification of design variables, Obj. function & constraints Better insight to the problem

Interactive Design Optimization Optimum design process aided by designer’s interaction

Conventional v/s Optimal Design


Conventional Design Process Describe the system using past data

Choose a starting design based on experience

Carry out system analysis

Check performance criteria

OK ? Stop

Change design based on past

data / heuristics Yes

No


Optimal Design Process Identify Design Variable(s), Constraint(s) & Objective Function(s)

Estimate Initial design

Carry out system analysis

Check constraints

Converged ?

Stop

Change design using

Optimization

Yes

No

System identification using data collection


Why Computer Aided Optimum Design ?

More accurate analysis of engineering systems

Iterative nature of design

Better display of complex design data

Decision making capabilities to allow human interaction

Problem Formulation

Transcribing a verbal description to a mathematical statement

Takes nearly 50% of the effort required for problem solving

Optimal Design Process


Find x = [x1, x2, x3 , ………………xn] that minimizes f (x), subject to gj(x) ≤ 0 j = 1, 2, 3, ……m hk(x) = 0 k = 1, 2, 3, ……p x = xi, i = 1, n ‘n’ Design Variables ui ≥ xi ≥ li, i = 1, n Bounds on ‘n’ Design Variables f (x) Objective Function gj(x) ‘m’ Inequality Constraint hk(x) ‘p’ Equality Constraint Note: f (x) could also be f (x) Multi-criteria Optimization

Optimization Problem Statement


Identification of Design Variables (DVs) Set of variables that describe the system Values of DVs represent a solution DVs should preferably be independent of each other

Identification of Objective Function(s) (OF) Criteria for comparison of various design solutions Should be a function of DVs Optimum solution ==> minimum or maximum value of OF

Identification of Design Constraints (DCs) Limitation on values of certain parameters for design feasibility Must be expressed in terms of DVs Could be Inequality or Equality

Steps in Problem Formulation


1. Problem statement

2. Data and information collection

3. Identification/definition of design variables

4. Identification of constraints

5. Identification of a criterion to be optimized

5-step problem formulation process


MY EARLY EXPERIENCES 1993-2000


First research paper


Problem Formulation


Classification of parameters


Design & Optimization Procedure


Aircraft Design


Problem Formulation



Constraint Analysis using Optimization


Constraint Analysis using Optimization


Constraint Analysis: Graphical Method



EXAMPLE OF PROBLEM FORMULATION

Next Class on Friday 11 Jan

Documents

Intro. to Optimal Design and Problem Formulation