JNTUK B.Tech Optimization Techniques (Open Elective) R13 Syllabus for Engineering it gives you detail information about Optimization Techniques (Open Elective) syllabus.
Preamble
Optimization techniques have gained importance to solve many engineering design problems by developing linear and nonlinear mathematical models. The aim of this course is to educate the student to develop a mathematical model by defining an objective function and constraints in terms of design variables and then apply a particular mathematical programming technique. This course covers classical optimization techniques, linear programming, nonlinear programming and dynamic programming techniques.
Learning Objectives
- To define an objective function and constraint functions in terms of design variables, and then state the optimization problem.
- To state single variable and multi variable optimization problems, without and with constraints.
- To explain linear programming technique to an optimization problem, define slack and surplus variables, by using Simplex method.
- To state transportation and assignment problem as a linear programming problem to determine optimality conditions by using Simplex method.
- To study and explain nonlinear programming techniques, unconstrained or constrained, and define exterior and interior penalty functions for optimization problems.
- To explain Dynamic programming technique as a powerful tool for making a sequence of interrelated decisions.
UNIT – I
Introduction and Classical Optimization Techniques: Statement of an Optimization problem – design vector – design constraints – constraint surface – objective function – objective function surfaces – classification of Optimization problems.
UNIT – II
Classical Optimization Techniques : Single variable Optimization – multi variable Optimization without constraints – necessary and sufficient conditions for minimum/maximum – multivariable Optimization with equality constraints. Solution by method of Lagrange multipliers – multivariable Optimization with inequality constraints – Kuhn – Tucker conditions.
UNIT – III
Linear Programming : Standard form of a 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 – Duality in Linear Programming – Dual Simplex method.
UNIT – IV
Transportation Problem : Finding initial basic feasible solution by north – west corner rule, least cost method and Vogel’s approximation method – testing for optimality of balanced transportation problems – Special cases in transportation problem.
UNIT – V
Nonlinear Programming : Unconstrained cases – One – dimensional minimization methods: Classification, Fibonacci method and Quadratic interpolation method – Univariate method, Powell’s method and steepest descent method. Constrained cases – 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 – VI
Dynamic Programming : Dynamic programming multistage decision processes – types – concept of sub optimization and the principle of optimality –computational procedure in dynamic programming – examples illustrating the calculus method of solution – examples illustrating the tabular method of solution.
Learning Outcomes
The student should be able to:
- State and formulate the optimization problem, without and with constraints, by using design variables from an engineering design problem.
- Apply classical optimization techniques to minimize or maximize a multi-variable objective function, without or with constraints, and arrive at an optimal solution.
- Formulate a mathematical model and apply linear programming technique by using Simplex method. Also extend the concept of dual Simplex method for optimal solutions.
- Solve transportation and assignment problem by using Linear programming Simplex method. Apply gradient and non-gradient methods to nonlinear optimization
- problems and use interior or exterior penalty functions for the constraints to derive the optimal solutions.
- Formulate and apply Dynamic programming technique to inventory control, production planning, engineering design problems etc. to reach a final optimal solution from the current optimal solution.
Text Books
- “Engineering optimization: Theory and practice”-by S. S.Rao, New Age International (P) Limited, 3rd edition, 1998.
- “Introductory Operations Research” by H.S. Kasene & K.D. Kumar, Springer (India), Pvt. LTd.
Reference Books
- “Optimization Methods in Operations Research and systems Analysis” – by K.V. Mital and C. Mohan, New Age International (P)
- Limited, Publishers, 3rd edition, 1996.
- Operations Research – by Dr. S.D.Sharma, Kedarnath, Ramnath & Co
- “Operations Research: An Introduction” – by H.A.Taha, PHI Pvt. Ltd., 6th edition
- Linear Programming–by G.Hadley.
Note : This Elective can be offered to Students of All Branches except EEE.
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