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SYLLABUS

UNIT-I

INTRODUCTION AND CLASSICAL OPTIMIZATION TECHNIQUE Statement of an Optimization problem-Design Vector – Design Constraints – Constraints Surface – Objective Function – Objective Function Surfaces – Classification of Optimization Problems. Classical Optimization Techniques – Single Variable Optimization – Multi Variable Optimization Without Constraints- Necessary and Sufficient Conditions for Minimum/Maximum – Multi Variable Optimization With Equality Constraints Solution by Method of Lagrange Multipliers – Multi Variable Optimization With Inequality Constraints – Kuhn – Tucker Conditions.

UNIT-II

LINEAR PROGRAMMING Standard Form of Linear Programming Problem- Geometry of Linear Programming Problems – Definitions and Theorems – Solution of a system of Linear Simultaneous Equations- Pivotal Reduction of a General System of Equations – Motivation to the Simplex Method – Simplex Algorithm – Revised Simplex Method – Two Phase Simplex Method - Initial Basic Feasible Solution by North – West Corner Rule, Approximation Method.

UNIT-III

UNCONSTRAINED NONLINEAR PROGRAMMING One-Dimensional Minimization Methods: Classifications, Fibonacci Method and Quadratic Interpolation Method – Unconstrained Optimization Techniques – Univariate Method, Powell's Method, Steepest Descent Method, Newtons Method.

UNIT-IV

CONSTRAINED NONLINEAR PROGRAMMING Characteristics of a Constrained Problem, Classification, Basic Approach of Penalty Function Method; Basic Approaches of Interior and Exterior Penalty Function Methods, Introduction to convex Programming Problem.

UNIT-V

SOFT COMPUTING METHODS Evolutionary programming methods – Introduction to Genetic Algorithms (GA) – Control parameters – Numbers of generation, population size, selection, reproduction, crossover and mutation – Operator selection criteria – Simple mapping of objective function to fitness function – constraints – Genetic algorithm steps – Stopping criteria – Simple examples. Swarm intelligence programming methods – Basic Partial Swarm Optimization – Method – Characteristic features of PSO procedure of the global version – Parameters of PSO (Simple PSO algorithm – Operators selection criteria – Fitness function constraints)