Optimization Techniques

Teacher

Dr. Mohammed Siddique

Category

Core Courses

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Course Name : Optimization Techniques

Code(Credit) : CUTM1532 (3-1-0)

Course Objectives

  • To introduce a brief understanding about Non Linear Programming Problems.
  • To cater the characteristics of Non Linear Programming Problems and its Applications.
  • To demonstration of the utilization of Non Linear Programming Problems in industry and business.
  • To apply the evolutionary optimization techniques in machine learning prediction model
  • To solve the case study related to strategic management

Learning Outcomes

Upon successful completion of this course, students will be able to:

  • Formulate the necessary and sufficient optimality conditions for Non linear programming and demonstrate the geometrical interpretation of these conditions.
  • Use Evolutionary optimization techniques to optimize the forecasting models in machine learning.
  • Use the optimization techniques learned in this course to formulate new applications as optimal decision problems and seek appropriate solutions algorithms.

Course Syllabus

Module-I (5 Hours)

Non Linear Constrained Optimization Problem: Constrained optimization using Lagrange Method, Lagrange Multiplier Equality Constraints, Constrained optimization using Kuhn Tucker Method, Kuhn Tucker inequality Constraints.

 

Practice-1: (2 Hours)

Solving minimization constrained optimization problem using python

 

Practice-2: (2 Hours)

Solving maximization constrained optimization problem using python

 

Module-II (5 Hours)

Direct Search Method for Unconstrained Optimization Problem: Univariate Search Method, Golden Section Search Method and Application of Golden Section Search Method.

 

Practice-3: (2 Hours)

Solving nonlinear system of equations using Python

 

Module-III (4 Hours)

Gradient Method for Unconstrained Optimization Problem: Gradient Descent Method, Algorithm for Gradient Descent Method, Steepest Descent Gradient Method.

 

Practice-4: (2 Hours)

Implementing Gradient Descent algorithm in Python

 

Practice-5: (2 Hours)

Linear Regression using Gradient Descent in Python

 

Module-IV (4 Hours)

Sequencing Models: Problems with n' Jobs through Two Machines, Problems with 'n' Jobs through Three Machines, Problems with Two Jobs through 'm' Machines.

 

Module-V (4 Hours)

Particle Swarm Optimization: Particle Swarm Optimization Theory, Particle Swarm Optimization Algorithm, Application of Particle Swarm Optimization,

 

Practice-6 & 7: (2+2 Hours)

Implementing the Particle Swarm Optimization (PSO) Algorithm in Python

 

Module-VI (4 Hours)

Game with Pure Strategy: Game and  Strategy, Maximin-Minimax principle, Two person zero-sum game with Saddle Point, Solving matching coin problem using game theory.

 

Module-VII (4 Hours)

Game with Mixed Strategy: Mixed Strategy Game, Game without Saddle Point, Graphical Method to Solve Mixed Strategy Game, Dominance Principle to Solve Mixed Strategy Game.

 

Text Books:

 

Kanti Swarup, P.K. Gupta and Man Mohan-Operations Research, S. Chand and Co. Pvt.Ltd.

 

Engineering Optimization Theory and Practice by Singiresu S. Rao, JOHN WILEY & SONS, INC., Fourth Edition

 

Reference Book:

Mathematical Programming by N. S. Kambo, East West Press.

Session Plan

Session 1

Constrained optimization using Lagrange Method

https://www.youtube.com/watch?v=7f7q2jdFbcU

Session 3

Constrained optimization using Kuhn Tucker Method

https://www.youtube.com/watch?v=Qqu_xBTxn_Y&t=116s&spfreload=10

Session 4 & 5

Kuhn Tucker inequality Constraints and its problems dicussion

https://www.youtube.com/watch?v=p7-v5D3Zcm8

Session 6 & 7

Practice 1

Solving minimization constrained optimization problem using python

https://www.youtube.com/watch?v=cXHvC_FGx24

Session 8 & 9

Practice 2

Solving maximization constrained optimization problem using python

https://www.youtube.com/watch?v=cXHvC_FGx24

Session 13 & 14

Session 15 & 16

Practice 3

Solving Nonlinear System of Equations using Python

https://www.youtube.com/watch?v=S4Qg2CsiIj8

Session 17

Session 18

Algorithm for Gradient Descent Method

https://www.youtube.com/watch?v=8AT3AV-QcxM

Session 21 & 22

Practice 4

Implementing Gradient Descent algorithm in Python

https://www.youtube.com/watch?v=gurGhGPg-6s

Session 23 & 24

Practice 5

Linear Regression using Gradient Descent in Python

https://www.youtube.com/watch?v=4PHI11lX11I

Session 25

Introduction to sequencing problem

https://www.youtube.com/watch?v=ZuKsXvbOIjw

Session 26

Problems with n' Jobs through Two Machines

https://www.youtube.com/watch?v=-sZlxpC7N6w

Session 27

Problems with 'n' Jobs through Three Machines

https://www.youtube.com/watch?v=VB3UTftGeP4

Session 28

Problems with Two Jobs through 'm' Machines

https://www.youtube.com/watch?v=4OdutS9mSZA

Session 29

Particle Swarm Optimization Theory

https://www.youtube.com/watch?v=hRwOog_bg_g

Session 30

Particle Swarm Optimization Algorithm

https://www.youtube.com/watch?v=ckbdXbbNNNA

Session 31 & 32

Application of Particle swarm optimization

https://www.youtube.com/watch?v=FKBgCpJlX48

Session 33 to 36

Practice 6 & 7

Implementing the Particle Swarm Optimization (PSO) Algorithm in Python

https://www.youtube.com/watch?v=SXp0HrrgCrs

Session 37

Introduction to Game and Strategy

https://www.youtube.com/watch?v=3Si7YTCIPM0

Session 38

Maximin-Minimax principle for saddle point

https://www.youtube.com/watch?v=2frw1TarJuQ

Session 39

Two person zero-sum game with Saddle Point

https://www.youtube.com/watch?v=R7Sbc8s3FxA

Session 40

Solving matching coin problem using game theory

https://www.youtube.com/watch?v=QliuxYSQsDo

Session 41

Session 42

Session 43

Graphical Method to Solve Mixed Strategy Game

https://www.youtube.com/watch?v=Bnhd_IiKJ6w

Session 44

Dominance Principle to Solve Mixed Strategy Game

https://www.youtube.com/watch?v=s7rvfZ5l0cY

Our Main Teachers

Dr. Mohammed Siddique

Asst. Prof. Department of Mathematics
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Dr. Mohammed Siddique, received Ph. D in Mathematics in the area of Optimization Techniques and Machine Learning from KIIT, Deemed to be University, Bhubaneswar and completed his M.Sc in Mathematics and M.Tech in Computer Science from Utkal University, Bhubaneswar.  He is having more than 16 years of teaching experience. He is having more than 50 […]