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]
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
Introduction to Design and
Optimal Design Formulation
Prof. Rajkumar S. Pant Aerospace Engineering Department
AE-310 Engineering Design Optimization Capsule-0
INTRODUCTION TO DESIGN Capsule -01
AE-310 Engineering Design Optimization Capsule-0
Overall process of designing systems
Distinguish between Design & Analysis
Conventional v/s Optimum Design process
Aims
AE-310 Engineering Design Optimization Capsule-0
The Design Process
Needs & Objectives
System Specs
Preliminary Design
Detailed Design
Prototype Fabrication
System Testing Final
Design
AE-310 Engineering Design Optimization Capsule-0
Design v/s Analysis
Analysis
Design
Parameters Response
Parameters Desired Response
Analysis
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
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
AE-310 Engineering Design Optimization Capsule-0
MY EARLY EXPERIENCES 1993-2000
AE-310 Engineering Design Optimization Capsule-0
First research paper
AE-310 Engineering Design Optimization Capsule-0
Problem Formulation
AE-310 Engineering Design Optimization Capsule-0
Classification of parameters
AE-310 Engineering Design Optimization Capsule-0
Design & Optimization Procedure
AE-310 Engineering Design Optimization Capsule-0
Aircraft Design
AE-310 Engineering Design Optimization Capsule-0
Problem Formulation
AE-310 Engineering Design Optimization Capsule-0
AE-310 Engineering Design Optimization Capsule-0
Constraint Analysis using Optimization
AE-310 Engineering Design Optimization Capsule-0
Constraint Analysis using Optimization
AE-310 Engineering Design Optimization Capsule-0
Constraint Analysis: Graphical Method
AE-310 Engineering Design Optimization Capsule-0
AE-310 Engineering Design Optimization Capsule-0
EXAMPLE OF PROBLEM FORMULATION
Next Class on Friday 11 Jan