Unit 1

Single Variable Optimization: Introduction to Optimization, Optimality Criteria – Bracketing Methods: Exhaustive Search Method, Bounding Phase Method, Region Elimination Methods, Golden Section Search Method, Gradient Based Methods: Newton-Raphson Method, Bisection Method, Secant Method, Cubic Search Method.

Unit 2

Multivariable Optimization: Optimality Criteria – Gradient Based Methods: Steepest Descent Method, Conjugate Direction Method, Conjugate Gradient Method and Newton’s Method – Constrained Optimization: Karush-Kuhn-Tucker Optimality Criteria, Direct Methods, Indirect Methods, Penalty Function Methods.

Unit 3

Global Optimization: Simulated Annealing, Genetic Algorithm, Particle Swarm Optimization, Multi-Objective Optimization – Pareto Optimality – Global Function /Weighted Sum.

Course Objectives

• The objective of this course is to provide the students with the basic concepts of optimization, the modeling skills necessary to formulate and solve the optimization problems.

Course Outcomes

• CO1: Understand the terms optimization, design variables, objective functions, constraints and the types of optimization.
• CO2: Understand the single variable, multi-variable optimization with and without constraints.
• CO3: Apply the suitable optimization algorithm for the given problem.
• CO4: Analyse the accuracy of the optimization algorithms.
• CO5: Understanding and apply the non-conventional optimization methods for multi-objective functions. and to know about types of non-conventional optimization methods.

CO – PO Mapping

Textbook(s)

• Kalyanmoy Deb, “Optimization for Engineering Design Algorithms and Examples”, 2^nd edition, Prentice Hall of India, New Delhi, 2012.

Reference(s)

• Kalyanmoy Deb, “Multi-Objective Optimization using Evolutionary Algorithms”, Wiley, 2010.
• J. Arora, “Introduction to Optimum Design,” 3^rd Edition, Elsevier, 2012.

Evaluation Pattern