R.K. Bhattacharjya/CE/IITG
1
Introduction To Genetic Algorithms
Dr. Rajib Kumar Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: rkbc@iitg.ernet.in
7 November 2013
References
R.K. Bhattacharjya/CE/IITG
2
D. E. Goldberg, Genetic Algorithm

Engineering Optimization
Rajib Kumar Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: rkbc@iitg.ernet.in
19 August 2013
R.K. Bhattacharjya/CE/IITG
1
Course content
Basics of engineering analysis and design, need for optimal
design, formul

Transformation method
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
15
Minimize
10
Infeasible
region
f(x)
5
0
10 2
10
Feasible
region
Subject to
3
Or, 3 0
-5
-10
-15
0
1
2
3
4
5
The problem can be written as
x
F ,
The bracket o

Linear Problem (LP)
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Linear programming
It is an optimization method applicable for the solution of optimization problem
where objective function and the constraints are linear
It was first a

Introduction to Particle
Swarm Optimization
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahati
Particle Swarm Algorithm
Inspired by social behavior of bird flocking and fish schooling
Suppose a group of birds

Convex Function
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
CONVEX FUNCTION
CONVEX FUNCTION
CONVEX
CONVEX
CONVEX FUNCTION
A function is said to be convex if for any pair of points = , , , ,
and = , , , , and all where 0 1
+ 1 +

Region Elimination Method
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahati
a
x1
x2
b
a
x1
x2
b
a
X1
X2
b
Interval halving method
a
X1
Xm
X2
b
Interval halving method
a
x1
Xm
X2
b
Interval halving method
a
x

Optimization Formulation
An Example
Objectives
Topology: Optimal
connectivity of the
structure
Minimum cost of material:
optimal cross section of all
the members
We will consider the
second objective only
The design variables are the cross
sectional area

Introduction to Differential Evolution
Rajib Kumar Bhattacharjya
Department of Civil Engineering
Indian Institute of Technology Guwahtai
Differential Evolution
It is a stochastic, population-based optimization algorithm for solving nonlinear
optimization

Multivariable problem with
equality and inequality
constraints
Rajib Bhattacharjya
Department of Civil Engineering
IIT Guwahati
Email: rkbc@iitg.ernet.in
General formulation
Min/Max
Where = , , , ,
Subject to
= 0
= 1,2,3, ,
This is the minimum point