Engineering Optimization - iitg.ac.in · R.K. Bhattacharjya/CE/IITG Course content Basics of...

R.K. Bhattacharjya/CE/IITG

Engineering Optimization

Rajib Kumar BhattacharjyaDepartment of Civil Engineering

IIT Guwahati

Email: [email protected]

19 August 2013 1


Course contentBasics of engineering analysis and design, need for optimaldesign, formulation of optimal design problems, basicdifficulties associated with solution of optimal problems,classical optimization methods, necessary and sufficientoptimality criteria for unconstrained and constrained problems,Kuhn-Tucker conditions, global optimality and convex analysis,linear optimal problems, Simplex method, Introduction toKarmarkars algorithm; numerical methods for nonlinearunconstrained and constrained problems, sensitivity analysis,linear post optimal analysis, sensitivity analysis of discrete anddistributed systems; introduction to variational methods ofsensitivity analysis, shape sensitivity, introduction to integerprogramming, dynamic programming, stochastic programmingand geometric programming, introduction to genetic algorithmand simulated annealing.

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Books K. Deb., Optimization for Engineering Design:

Algorithms and Examples, PHI Pvt Ltd., 1998.

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

S.S. Rao, Engineering optimization: Theory and Practice, New age international (P) Ltd. 2001

D. E. Goldberg, Genetic Algorithms in search and optimization, Pearson publication, 1990.

K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, Chichester, UK : Wiley

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Are you using optimization?

The word optimization may be very familiar or maybe quite new to you. But whether you know aboutoptimization or not, you are using optimization inmany occasions in your day to day life.

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Assessment Assignment : 10

Quiz : 15

Mid semester exam : 25

End semester exam : 40

Project : 10

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What is Optimization? Optimization is the act of obtaining the best result

under a given circumstances.

Optimization is the mathematical discipline which isconcerned with finding the maxima and minima offunctions, possibly subject to constraints.

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Introduction to optimization

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Global optimaLocal optima

Local optima

Local optima

Local optima

f

X

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Introduction to optimization

Single variable optimizationObjective function is defined as

Minimization/Maximization f(x)

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Single variable optimizationStationary points

For a continuous and differentiable function f(x) astationary point x* is a point at which the slope of thefunction is zero, i.e. f (x) = 0 at x = x*,

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Minima Maxima Inflection point


Global minimum and maximum A function is said to have aglobal or absoluteminimum at x = x* if f (x* ) f(x) for all x in thedomain over which f(x) isdefined.

A function is said to have aglobal or absolutemaximum at x = x* if f (x*) f(x) for all x in thedomain over which f(x) isdefined.

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Golden ratio

0.618=1/1.618

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Multivariable optimization problem

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R.K. Bhattacharjya/CE/IITG8/19/2013 14


THANKS

19 August 2013 23

Engineering Optimization - iitg.ac.in · R.K. Bhattacharjya/CE/IITG Course content Basics of...

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