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
Course Outcomes
| COs | Course outcomes | Mapping Cos with POs (High-3, Medium-2, Low-1) |
| CO1 | Formulate the necessary and sufficient optimality conditions for Non-linear programming and demonstrate the geometrical interpretation of these conditions. | PO1(3), PO9(3) |
| CO3 | Use Evolutionary optimization techniques to optimize the forecasting models in machine learning. | PO4(3), PO2(2), |
| CO5 | Use the optimization techniques learned in this course to formulate new applications as optimal decision problems and seek appropriate solutions algorithms. | PO5(2), PO9(2) |
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
Session 2
Lagrange Multiplier Equality Constraints
https://www.youtube.com/watch?v=g5YlNGzhwnQ
https://www.youtube.com/watch?v=N_CyeSqqYs4
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 3
Constrained optimization using Kuhn Tucker Method
https://www.youtube.com/watch?v=Qqu_xBTxn_Y&t=116s&spfreload=10
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 4 & 5
Kuhn Tucker inequality Constraints and its problems dicussion
https://www.youtube.com/watch?v=p7-v5D3Zcm8
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
https://nptel.ac.in/content/storage2/courses/105108127/pdf/Module_2/M2L5slides.pdf
Session 6 & 7
Practice 1
Solving minimization constrained optimization problem using python
Session 8 & 9
Practice 2
Solving maximization constrained optimization problem using python
Session 10 & 11
Session 13 & 14
Application of Golden Section Search Method
https://www.youtube.com/watch?v=eyuvAL624Qw
https://www.youtube.com/watch?v=8WDAh0T0hzI
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 15 & 16
Practice 3
Solving Nonlinear System of Equations using Python
Session 17
Session 19 & 20
Session 21 & 22
Practice 4
Implementing Gradient Descent algorithm in Python
Session 23 & 24
Practice 5
Linear Regression using Gradient Descent in Python
Session 26
Problems with n' Jobs through Two Machines
https://www.youtube.com/watch?v=-sZlxpC7N6w
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 27
Problems with 'n' Jobs through Three Machines
https://www.youtube.com/watch?v=VB3UTftGeP4
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 28
Problems with Two Jobs through 'm' Machines
https://www.youtube.com/watch?v=4OdutS9mSZA
https://www.slideshare.net/MohammedSiddique15/clipboards/my-clips
Session 29
Particle Swarm Optimization Theory
https://www.youtube.com/watch?v=hRwOog_bg_g
https://www.slideshare.net/khashe62/practical-swarm-optimization-pso
Session 31 & 32
Application of Particle swarm optimization
https://www.youtube.com/watch?v=FKBgCpJlX48
https://www.slideshare.net/stelabouras/particle-swarm-optimization
Session 33 to 36
Practice 6 & 7
Implementing the Particle Swarm Optimization (PSO) Algorithm in Python
Session 40
Solving matching coin problem using game theory
Session 43
Graphical Method to Solve Mixed Strategy Game
Session 44
Dominance Principle to Solve Mixed Strategy Game
Our Main Teachers
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 […]