Introduction:
Introduction to optimization, engineering applications of optimization, Formulation of structural optimization problems as programming problems. Optimization Techniques: Classical optimization techniques, single variable optimization, multivariable optimization with no constraints, unconstrained minimization techniques and algorithms constrained optimization solutions by penalty function techniques, Lagrange multipliers techniques and feasibility techniques.
Linear Programming:
Linear programming, standard form of linear programming, geometry of linear programming problems, solution of a system of linear simultaneous equations, pivotal production of general systems of equations, simplex algorithms, revised simpler methods, duality in linear programming
Non-linear programming:
Non-linear programming, one dimensional minimization methods, elimination methods, Fibonacci method, golden section method, interpolation methods, quadratic and cubic methods, Unconstrained optimization methods, direct search methods, random search methods, descent methods
Constrained optimization techniques such as direct methods, the complex methods, cutting plane method, exterior penalty function methods for structural engineering problems. Formulation and solution of structural optimization problems by different technique
Geometric programming:
Geometric programming, conversion ofNLP as a sequence of LP/ geometric programming. Dynamic programming: Dynamic programming conversion ofNLP as a sequence of LP/ Dynamic programming
Course outcomes:
On completion of this course, students are able to:
• Co1:Achieve Knowledge of design and development of problem solving skills.
• Co2: Understand the principles of optimization.
• Co3: Design and develop analytical skills.
• Co4: Summarize the Linear, Non-linear and Geometric Programming
• Co5: Understands the concept of Dynamic programming
Question paper pattern:
• The question paper will have ten questions.
• There will be 2 full questions (with a maximum of four sub questions) from eachmodule.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer 5 full questions, selecting one full question from eachmodule.
Reference Books:
1. Spunt,“Optimum Structural Design”- Prentice Hall
2. S.S. Rao, “Optimization – Theory and Practice”- Wiley Eastern Ltd.
3. Uri Krisch, “Optimum Structural Design”- McGraw Hill
4. Richard Bronson, “Operation Research”- Schaum’s Outline Series
5. Bhavikatti S.S.- “Structural optimization using sequential linear programming”- Vikas publishing house